Regression analysis:
In “Statistical Methods” has defined Regression as, “The measure of the average relationship between two or more variables in terms of the original units of the data”.
Morris Hamburg has defined Regression Analysis as, “The method by which estimates are made of the values of a variable from knowledge of the values of one or more other variables and to the measurement of the errors involved in this estimation process”.
Correlation analysis attempts to study the relationship between the two variables x and y. Regression analysis attempts to predict the average x for a given y. in Regression it is attempted to quantify the dependence of one variable on the other. Example; There are two variables x and y. y depends on x. the dependence is expressed in the form of the following equation:
Y=a+bx
Regression analysis used to estimate the values of the dependent variables from the values of the independent variables.
Regression analysis uses to get a measure of the error involved while using the regression line as a basis for estimation.
Regression coefficient is used to calculate correlation coefficient. The square of correlation coefficient measures the degree of association of correlation that prevails between the given two variables.
Correlation coefficient measures the degree of co variability between the given variables x and y. the regression analysis uses to study the ‘nature of relationship’ between the given variables; the value of one variable is predicted based on another.
Correlation analysis does not study cause and effect relationship of the given variables. It is not stated that one variable is the cause and other the effect. In regression analysis one variable is taken as dependent and another independent. Here there is possibility to study the cause and effect relationship.
In statistics, regression analysis examines the relation of a dependent variable (response variable) to specified independent variables (explanatory variables). The mathematical model of their relationship is the regression equation. The dependent variable is modeled as a random variable because of uncertainty as to its value, given only the value of each independent variable. A regression equation contains estimates of one or more hypothesized regression parameters ("constants"). These estimates are constructed using data for the variables, such as from a sample. The estimates measure the relationship between the dependent variable and each of the independent variables. They also allow estimating the value of the dependent variable for a given value of each respective independent variable.
Uses of regression include curve fitting, prediction (including forecasting of time-series data), modeling of causal relationships, and testing scientific hypotheses about relationships between variables.
Wednesday, January 16, 2008
Briefly explain the concepts of Correlation in your own words
Types of Correlation are given below:
a. Positive of Negative
b. Simple, Partial and Multiple
c. Linear and Non-Linear
a. Positive Correlation: Both the variables (X and Y) will vary in the same direction. If variable X increases, variable Y also will increase; if variable X decreases, variable Y also will decrease.
Negative Correlation: The given variables will vary in opposite direction. If on variable increases, other variable will decrease.
b. Simple, Partial and Multiple Correlations: In simple correlation, relationship between two variables are studies. In partial and multiple correlations three or more variables are studies. Three or more variables are simultaneously studied in multiple correlation. In partial correlation more than two variables are studied, but the effect on one variable is kept constant and relationship between other two variables is studied.
c. Linear and Non-Linear Correlation: It depends upon the constance of the ration of change between the variables. In linear correlation the percentage change in one variable will be equal to the percentage change in another variable. It is not so in non-linear correlation.
Method of Studying Correlation::
The various methods of studying correlation are given below.
a. Scatter Diagram Method.
b. Graphic Method
c. Karl Pearson’s Coefficient of Correlation
d. Concurrent Deviation Method
e. Method of Least Squares
In probability theory and statistics, correlation, also called correlation coefficient, indicates the strength and direction of a linear relationship between two random variables. In general statistical usage, correlation or co-relation refers to the departure of two variables from independence. In this broad sense there are several coefficients, measuring the degree of correlation, adapted to the nature of data.
A number of different coefficients are used for different situations. The best known is the Pearson product-moment correlation coefficient, which is obtained by dividing the covariance of the two variables by the product of their standard deviations.
a. Positive of Negative
b. Simple, Partial and Multiple
c. Linear and Non-Linear
a. Positive Correlation: Both the variables (X and Y) will vary in the same direction. If variable X increases, variable Y also will increase; if variable X decreases, variable Y also will decrease.
Negative Correlation: The given variables will vary in opposite direction. If on variable increases, other variable will decrease.
b. Simple, Partial and Multiple Correlations: In simple correlation, relationship between two variables are studies. In partial and multiple correlations three or more variables are studies. Three or more variables are simultaneously studied in multiple correlation. In partial correlation more than two variables are studied, but the effect on one variable is kept constant and relationship between other two variables is studied.
c. Linear and Non-Linear Correlation: It depends upon the constance of the ration of change between the variables. In linear correlation the percentage change in one variable will be equal to the percentage change in another variable. It is not so in non-linear correlation.
Method of Studying Correlation::
The various methods of studying correlation are given below.
a. Scatter Diagram Method.
b. Graphic Method
c. Karl Pearson’s Coefficient of Correlation
d. Concurrent Deviation Method
e. Method of Least Squares
In probability theory and statistics, correlation, also called correlation coefficient, indicates the strength and direction of a linear relationship between two random variables. In general statistical usage, correlation or co-relation refers to the departure of two variables from independence. In this broad sense there are several coefficients, measuring the degree of correlation, adapted to the nature of data.
A number of different coefficients are used for different situations. The best known is the Pearson product-moment correlation coefficient, which is obtained by dividing the covariance of the two variables by the product of their standard deviations.
Write down the properties of Chi-square distribution
Ans. Properties of χ2 distribution:
1. Mean of χ2 distribution = Degrees of freedom = V
2. SD of χ2 distribution = √2V
3. Median of χ2 distribution divides the area of the curve into two equal parts, each part being 0.5
4. Mode of χ2 distribution is equal to degrees of freedom less 2 i.e., V-2
5. χ2 values are always positively skewed.
6. χ2 values increase with the increase in the DF, there is a new χ2 distribution with every increase in the no. of degrees of freedom.
7. The lowest value of χ2 is zero and the highest is infinity i.e. 0 < χ2 <
8. When two chi-squares γ 2\1 and χ2/2 are independent following χ2 distribution with n1 and n2 degrees of freedom, their sum χ2/2 +χ2/2 will follow χ2 distribution with n1 + n2 degrees of freedom.
9. When V>30, √2χ2 - √2V -1 approximately follows the standard normal distribution.
Chi-Square Distribution:
This article is about the mathematics of the chi-square distribution. For its uses in statistics, see Chi-Square Test.
Explain Type I and Type II errors in testing of Hypothesis
Types of hypothesis:
A proposition may take the form of asserting a causal relationship (such as "A causes B"). A proposition often (but not necessarily) involves an assertion of causation. For example, if a particular independent variable changes, then a certain dependent variable also changes. This formulation, also known as an "If and Then" statement, applies whether or not a proposition asserts a direct cause-and-effect relationship.
A hypothesis about possible correlation does not stipulate the cause and effect per se, only stating that "A is related to B". Investigators may have more difficulty in verifying causal relationships than other correlations, because quite commonly intervening variables also become involved, possibly giving rise to the appearance of a possibly direct cause-and-effect relationship, but which (upon further investigation) turn out to have some other, more direct causal factor not mentioned in the proposition. Also, a mere observation of a change in one variable, when correlated with a change in another variable, can actually mistake the effect for the cause, and vice-versa (i.e., potentially get the hypothesized cause and effect backwards).
Empirical hypotheses that experimenters have repeatedly verified may become sufficiently dependable that, at some point in time, they become considered as "proven". Some people may succumb to the temptation to term such hypotheses "laws", but they would do so mistakenly, since by definition a hypothesis explains and a law describes (for example, a law can state: "Matter can neither be created or destroyed, only changed in form"). More accurately, one could refer to repeatedly verified hypotheses simply as "adequately verified", or as "dependable".
Statistics features a rather more general concept of a hypothesis: this involves making assertions about the probability distributions or likelihoods of events.
Statisticians use two kinds of hypothesis: first, the null hypothesis or H0; secondly, the alternative hypothesis or H1. To give the simplest non-trivial example, one might formulate two hypotheses about tossing a coin:
• H0: coin-tossing operates "fairly" (equally likely to fall "Heads" or "Tails")
• H1: coin-tossing operates in a biased manner to give a 90% probability of falling "Heads"
No finite sequence of results could utterly falsify either hypothesis. However, various statistical approaches (such as Bayesian statistics and classical statistics (i.e. t-tests)) can quantify the strong intuition that H1 appears much less likely than H0 if, in 1,000 tosses, 495 came out "Heads" — and much more likely if 895 came out "Heads". In more complex sciences, researchers generally evaluate experiments statistically rather than as simple verifications or falsifications.
A hypothesis (from Greek ὑπόθεσις) consists either of a suggested explanation for a phenomenon or of a reasoned proposal suggesting a possible correlation between multiple phenomena. The term derives from the Greek, hypotithenai meaning "to put under" or "to suppose." The scientific method requires that one can test a scientific hypothesis. Scientists generally base such hypotheses on previous observations or on extensions of scientific theories.
Type I and Type II errors:
Rejecting a null hypothesis when it is true is called a Type I error, and its probability ( Which, as we have seen, is also the significance level of the test) is symbolized α (alpha). Alternatively, accepting a null hypothesis when it is false is called a Type II error, and its probability is symbolized β (beta). There is a trade-off between these two errors: the probability of making one type of error can be reduced only if we are willing to increase the probability of making the other type or error. With an acceptance region this small, we will rarely accept a null hypothesis when it is not true, but as a cost of being this sure, we will often reject a null hypothesis when it is true.
Put another way, in order to get a low β, we will have to put up with a high α. To deal with this trade-off in personal and professional situations, decision makers decide the appropriate level of significance by examining the costs or penalties attached to both types of errors.
When Type I error is preferred:
Suppose that making a Type I error (rejecting a null hypothesis when it is true) involves the time and trouble of reworking a batch of chemicals that should have been accepted. At the same time, making a Type II error (accepting a null hypothesis when it is false) means talking a chance that an entire group of users of this chemical compound will be poisoned. Obviously, the management of this company will prefer a Type I error to a Type II error and, as a result, will set very high levels of significance in its testing to get low β s.
When Type II error is preferred:
Suppose, on the other hand, that making a Type I error involves disassembling an entire engine at the factory, but making a Type II error involves relatively inexpensive warranty repairs by the dealers. Then the manufacturer is more likely to prefer a Type II error and will set lower significance levels in its testing.
A proposition may take the form of asserting a causal relationship (such as "A causes B"). A proposition often (but not necessarily) involves an assertion of causation. For example, if a particular independent variable changes, then a certain dependent variable also changes. This formulation, also known as an "If and Then" statement, applies whether or not a proposition asserts a direct cause-and-effect relationship.
A hypothesis about possible correlation does not stipulate the cause and effect per se, only stating that "A is related to B". Investigators may have more difficulty in verifying causal relationships than other correlations, because quite commonly intervening variables also become involved, possibly giving rise to the appearance of a possibly direct cause-and-effect relationship, but which (upon further investigation) turn out to have some other, more direct causal factor not mentioned in the proposition. Also, a mere observation of a change in one variable, when correlated with a change in another variable, can actually mistake the effect for the cause, and vice-versa (i.e., potentially get the hypothesized cause and effect backwards).
Empirical hypotheses that experimenters have repeatedly verified may become sufficiently dependable that, at some point in time, they become considered as "proven". Some people may succumb to the temptation to term such hypotheses "laws", but they would do so mistakenly, since by definition a hypothesis explains and a law describes (for example, a law can state: "Matter can neither be created or destroyed, only changed in form"). More accurately, one could refer to repeatedly verified hypotheses simply as "adequately verified", or as "dependable".
Statistics features a rather more general concept of a hypothesis: this involves making assertions about the probability distributions or likelihoods of events.
Statisticians use two kinds of hypothesis: first, the null hypothesis or H0; secondly, the alternative hypothesis or H1. To give the simplest non-trivial example, one might formulate two hypotheses about tossing a coin:
• H0: coin-tossing operates "fairly" (equally likely to fall "Heads" or "Tails")
• H1: coin-tossing operates in a biased manner to give a 90% probability of falling "Heads"
No finite sequence of results could utterly falsify either hypothesis. However, various statistical approaches (such as Bayesian statistics and classical statistics (i.e. t-tests)) can quantify the strong intuition that H1 appears much less likely than H0 if, in 1,000 tosses, 495 came out "Heads" — and much more likely if 895 came out "Heads". In more complex sciences, researchers generally evaluate experiments statistically rather than as simple verifications or falsifications.
A hypothesis (from Greek ὑπόθεσις) consists either of a suggested explanation for a phenomenon or of a reasoned proposal suggesting a possible correlation between multiple phenomena. The term derives from the Greek, hypotithenai meaning "to put under" or "to suppose." The scientific method requires that one can test a scientific hypothesis. Scientists generally base such hypotheses on previous observations or on extensions of scientific theories.
Type I and Type II errors:
Rejecting a null hypothesis when it is true is called a Type I error, and its probability ( Which, as we have seen, is also the significance level of the test) is symbolized α (alpha). Alternatively, accepting a null hypothesis when it is false is called a Type II error, and its probability is symbolized β (beta). There is a trade-off between these two errors: the probability of making one type of error can be reduced only if we are willing to increase the probability of making the other type or error. With an acceptance region this small, we will rarely accept a null hypothesis when it is not true, but as a cost of being this sure, we will often reject a null hypothesis when it is true.
Put another way, in order to get a low β, we will have to put up with a high α. To deal with this trade-off in personal and professional situations, decision makers decide the appropriate level of significance by examining the costs or penalties attached to both types of errors.
When Type I error is preferred:
Suppose that making a Type I error (rejecting a null hypothesis when it is true) involves the time and trouble of reworking a batch of chemicals that should have been accepted. At the same time, making a Type II error (accepting a null hypothesis when it is false) means talking a chance that an entire group of users of this chemical compound will be poisoned. Obviously, the management of this company will prefer a Type I error to a Type II error and, as a result, will set very high levels of significance in its testing to get low β s.
When Type II error is preferred:
Suppose, on the other hand, that making a Type I error involves disassembling an entire engine at the factory, but making a Type II error involves relatively inexpensive warranty repairs by the dealers. Then the manufacturer is more likely to prefer a Type II error and will set lower significance levels in its testing.
Write short notes on Interval estimates
Interval estimation:
The purpose of gathering samples is to learn more about a population. We can compute this information from the sample data as either point estimates, An Interval estimate describes a range of values within which a population parameter is likely to lie.
Interval estimation:
In statistics, interval estimation is the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter. The most prevalent forms of interval estimation are confidence intervals (a frequentist method) and credible intervals (a Bayesian method).
* Behrens-Fisher problem
* fiducial inference
Other common interval estimation are
* Tolerance interval
* Prediction interval - used mainly in Regression Analysis.
The purpose of gathering samples is to learn more about a population. We can compute this information from the sample data as either point estimates, An Interval estimate describes a range of values within which a population parameter is likely to lie.
Interval estimation:
In statistics, interval estimation is the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter. The most prevalent forms of interval estimation are confidence intervals (a frequentist method) and credible intervals (a Bayesian method).
* Behrens-Fisher problem
* fiducial inference
Other common interval estimation are
* Tolerance interval
* Prediction interval - used mainly in Regression Analysis.
What is the criteria of a good estimator, explain the points in your own word
There are two number of estimates about a population:
1. A point estimate and
2. An interval estimate:
Estimator:
In statistics, an estimator is a function of the observable sample data that is used to estimate an unknown population parameter; an estimate is the result from the actual application of the function to a particular set of data. Many different estimators are possible for any given parameter. Some criterion is used to choose between the estimators, although it is often the case that a criterion cannot be used to clearly pick one estimator over another. To estimate a parameter of interest (e.g., a population mean, a binomial proportion, a difference between two population means, or a ratio of two population standard deviation), the usual procedure is as follows:
1. Select a random sample from the population of interest.
2. Calculate the point estimate of the parameter.
3. Calculate a measure of its variability, often a confidence interval.
4. Associate with this estimate a measure of variability.
There are two types of estimators: Point Estimators and Interval Estimators.
1. A point Estimate: is a single number that is used to estimate an unknown population parameter. A point estimate is often insufficient, because it is either right or wrong. If you are told only that her point estimate of enrollment is wrong, you do not know how wrong it is, and you cannot be certain of the estimate’s reliability. If you learn that is off by only 10 students, you would accept 350 students as a good estimate of future enrollment.
Point estimation:
In statistics, point estimation involves the use of sample data to calculate a single value (known as a statistic) which is to serve as a "best guess" for an unknown (fixed or random) population parameter.
More formally, it is the application of a point estimator to the data.
Point estimation should be contrasted with Bayesian methods of estimation, where the goal is usually to compute (perhaps to an approximation) the posterior distributions of parameters and other quantities of interest. The contrast here is between estimating a single point (point estimation), versus estimating a weighted set of points (a probability density function).
2. An interval estimator: is a range of values used to estimate a population parameter. It indicates the error in two ways: by the parameter lying within that range.
Interval estimation:
In statistics, interval estimation is the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter. The most prevalent forms of interval estimation are confidence intervals (a frequentist method) and credible intervals (a Bayesian method).
* Behrens-Fisher problem
* fiducial inference
Other common interval estimation are
* Tolerance interval
* Prediction interval - used mainly in Regression Analysis
Criteria of a good estimator:
1. Unbiasedness: This is a desirable property for a good estimator to have. The term unbiasedness refers to the fact that a sample mean is an unbiased estimator of a population mean because the mean of the sampling distribution of sample means taken from the same population is equal to the population mean itself. We can say that a statistic is an unbiased estimator if, on average, it tends to assume values that ate the same extent as it tends to assume values that are below the population parameter being estimated.
2. Efficiency: Another desirable property of a good estimator is that it be efficient. Efficiency refers to the size of the standard error of the statistic. If we compare two statistics from a sample of the same size and try to decide which one is the more efficient estimator, we would pick the statistic that has the smaller standard error, or standard deviation of the sampling distribution. Suppose we choose a sample of a given size and must decide whether to use the sample mean or the sample median to estimate the population mean. If we calculate the standard error of the sample mean and find it to be 1.05 and then calculate the standard error of the sample median and find it to be 1.6, we would say that the sample mean is a more efficient estimator of the population mean be cause its standard error is smaller. It makes sense that an estimator with a smaller standard error (with less variation) will have more chance of producing an estimate nearer to the population parameter under consideration.
3. Consistency: A statistic is a consistent estimator of a population parameter if as the sample size increases, it becomes almost certain that the value of the statistic comes very close to the value of the population parameter. If an estimator is consistent, it becomes more reliable with large samples. Thus, if you are wondering whether to increase the sample size to get more information about a population parameter, find out first whether your statistic is a consistent estimator. If it is not, you will waste time and money by taking larger samples.
Consistency:
A Consistent Estimator is an estimator that converges in probability to the quantity being estimated as the sample size grows without bound.
An estimator tn (where n is the sample size) is a consistent estimator for parameter θ if and only if, for all ε > 0, no matter how small, we have
\lim_{n\to\infty}\Pr\left\{ \left| t_n-\theta\right|<\epsilon \right\}=1.
It is called strongly consistent, if it converges almost surely to the true value.
4. Sufficiency: An estimator is sufficient if it makes so much use of the information in the sample that no other estimator could extract from the sample additional information about the population parameter being estimated.
Efficiency:
Main article: Efficiency (statistics)
The quality of an estimator is generally judged by its mean squared error.
However, occasionally one chooses the unbiased estimator with the lowest variance. Efficient estimators are those that have the lowest possible variance among all unbiased estimators. In some cases, a biased estimator may have a uniformly smaller mean squared error than does any unbiased estimator, so one should not make too much of this concept. For that and other reasons, it is sometimes preferable not to limit oneself to unbiased estimators; see estimator bias. Concerning such "best unbiased estimators", see also Cramér-Rao bound, Gauss-Markov theorem, Lehmann-Scheffé theorem, Rao-Blackwell theorem.
1. A point estimate and
2. An interval estimate:
Estimator:
In statistics, an estimator is a function of the observable sample data that is used to estimate an unknown population parameter; an estimate is the result from the actual application of the function to a particular set of data. Many different estimators are possible for any given parameter. Some criterion is used to choose between the estimators, although it is often the case that a criterion cannot be used to clearly pick one estimator over another. To estimate a parameter of interest (e.g., a population mean, a binomial proportion, a difference between two population means, or a ratio of two population standard deviation), the usual procedure is as follows:
1. Select a random sample from the population of interest.
2. Calculate the point estimate of the parameter.
3. Calculate a measure of its variability, often a confidence interval.
4. Associate with this estimate a measure of variability.
There are two types of estimators: Point Estimators and Interval Estimators.
1. A point Estimate: is a single number that is used to estimate an unknown population parameter. A point estimate is often insufficient, because it is either right or wrong. If you are told only that her point estimate of enrollment is wrong, you do not know how wrong it is, and you cannot be certain of the estimate’s reliability. If you learn that is off by only 10 students, you would accept 350 students as a good estimate of future enrollment.
Point estimation:
In statistics, point estimation involves the use of sample data to calculate a single value (known as a statistic) which is to serve as a "best guess" for an unknown (fixed or random) population parameter.
More formally, it is the application of a point estimator to the data.
Point estimation should be contrasted with Bayesian methods of estimation, where the goal is usually to compute (perhaps to an approximation) the posterior distributions of parameters and other quantities of interest. The contrast here is between estimating a single point (point estimation), versus estimating a weighted set of points (a probability density function).
2. An interval estimator: is a range of values used to estimate a population parameter. It indicates the error in two ways: by the parameter lying within that range.
Interval estimation:
In statistics, interval estimation is the use of sample data to calculate an interval of possible (or probable) values of an unknown population parameter. The most prevalent forms of interval estimation are confidence intervals (a frequentist method) and credible intervals (a Bayesian method).
* Behrens-Fisher problem
* fiducial inference
Other common interval estimation are
* Tolerance interval
* Prediction interval - used mainly in Regression Analysis
Criteria of a good estimator:
1. Unbiasedness: This is a desirable property for a good estimator to have. The term unbiasedness refers to the fact that a sample mean is an unbiased estimator of a population mean because the mean of the sampling distribution of sample means taken from the same population is equal to the population mean itself. We can say that a statistic is an unbiased estimator if, on average, it tends to assume values that ate the same extent as it tends to assume values that are below the population parameter being estimated.
2. Efficiency: Another desirable property of a good estimator is that it be efficient. Efficiency refers to the size of the standard error of the statistic. If we compare two statistics from a sample of the same size and try to decide which one is the more efficient estimator, we would pick the statistic that has the smaller standard error, or standard deviation of the sampling distribution. Suppose we choose a sample of a given size and must decide whether to use the sample mean or the sample median to estimate the population mean. If we calculate the standard error of the sample mean and find it to be 1.05 and then calculate the standard error of the sample median and find it to be 1.6, we would say that the sample mean is a more efficient estimator of the population mean be cause its standard error is smaller. It makes sense that an estimator with a smaller standard error (with less variation) will have more chance of producing an estimate nearer to the population parameter under consideration.
3. Consistency: A statistic is a consistent estimator of a population parameter if as the sample size increases, it becomes almost certain that the value of the statistic comes very close to the value of the population parameter. If an estimator is consistent, it becomes more reliable with large samples. Thus, if you are wondering whether to increase the sample size to get more information about a population parameter, find out first whether your statistic is a consistent estimator. If it is not, you will waste time and money by taking larger samples.
Consistency:
A Consistent Estimator is an estimator that converges in probability to the quantity being estimated as the sample size grows without bound.
An estimator tn (where n is the sample size) is a consistent estimator for parameter θ if and only if, for all ε > 0, no matter how small, we have
\lim_{n\to\infty}\Pr\left\{ \left| t_n-\theta\right|<\epsilon \right\}=1.
It is called strongly consistent, if it converges almost surely to the true value.
4. Sufficiency: An estimator is sufficient if it makes so much use of the information in the sample that no other estimator could extract from the sample additional information about the population parameter being estimated.
Efficiency:
Main article: Efficiency (statistics)
The quality of an estimator is generally judged by its mean squared error.
However, occasionally one chooses the unbiased estimator with the lowest variance. Efficient estimators are those that have the lowest possible variance among all unbiased estimators. In some cases, a biased estimator may have a uniformly smaller mean squared error than does any unbiased estimator, so one should not make too much of this concept. For that and other reasons, it is sometimes preferable not to limit oneself to unbiased estimators; see estimator bias. Concerning such "best unbiased estimators", see also Cramér-Rao bound, Gauss-Markov theorem, Lehmann-Scheffé theorem, Rao-Blackwell theorem.
State Central Limit Theorem. Explain in your own words
A Central Limit Theorem is any of a set of weak-convergence results in probability theory. They all express the fact that any sum of many independent and identically-distributed random variables will tend to be distributed according to a particular "attractor distribution". The most important and famous result is called The Central Limit Theorem which states that if the sum of the variables has a finite variance, then it will be approximately normally distributed (i.e., following a Gaussian distribution).
Since many real processes yield distributions with finite variance, this explains the ubiquity of the normal probability distribution.
Several generalizations for finite variance exist which do not require identical distribution but incorporate some condition which guarantees that none of the variables exert a much larger influence than the others. Two such conditions are the Lindeberg condition and the Lyapunov condition. Other generalizations even allow some "weak" dependence of the random variables. Also, a generalization due to Gnedenko and Kolmogorov states that the sum of a number of independent random variables with power-law tail distributions decreasing as 1/|x|α+1 with 0 < α < href="http://en.wikipedia.org/wiki/L%C3%A9vy_skew_alpha-stable_distribution" title="Lévy skew alpha-stable distribution">Lévy distribution as the number of variables grows. This article will only be concerned with the central limit theorem as it applies to distributions with finite variance.
History:
“The central limit theorem has an interesting history. The first version of this theorem was postulated by the French-born English mathematician Abraham de Moivre, who, in a remarkable article published in 1733, used the normal distribution to approximate the distribution of the number of heads resulting from many tosses of a fair coin. This finding was far ahead of its time, and was nearly forgotten until the famous French mathematician Pierre-Simon Laplace rescued it from obscurity in his monumental work Théorie Analytique des Probabilités, which was published in 1812. Laplace expanded De Moivre's finding by approximating the binomial distribution with the normal distribution. But as with De Moivre, Laplace's finding received little attention in his own time. It was not until the nineteenth century was at an end that the importance of the central limit theorem was discerned, when, in 1901, Russian mathematician Aleksandr Lyapunov defined it in general terms and proved precisely how it worked mathematically. Nowadays, the central limit theorem is considered to be the unofficial sovereign of probability theory. ”
See Bernstein (1945) for a historical discussion focusing on the work of Pafnuty Chebyshev and his students Andrey Markov and Aleksandr Lyapunov that led to the first proofs of the C.L.T. in a general setting.
Proof of the central limit theorem:
For a theorem of such fundamental importance to statistics and applied probability, the central limit theorem has a remarkably simple proof using characteristic functions. It is similar to the proof of a (weak) law of large numbers. For any random variable, Y, with zero mean and unit variance (var(Y) = 1), the characteristic function of Y is, by Taylor's theorem,
\varphi_Y(t) = 1 - {t^2 \over 2} + o(t^2), \quad t \rightarrow 0
Where o (t2 ) is "little o notation" for some function of t that goes to zero more rapidly than t2. Letting Yi be (Xi − μ)/σ, the standardised value of Xi, it is easy to see that the standardised mean of the observations X1, X2, ..., Xn is just
Z_n = \frac{n\overline{X}_n-n\mu}{\sigma\sqrt{n}} = \sum_{i=1}^n {Y_i \over \sqrt{n}}.
By simple properties of characteristic functions, the characteristic function of Zn is
\left[\varphi_Y\left({t \over \sqrt{n}}\right)\right]^n = \left[ 1 - {t^2 \over 2n} + o\left({t^2 \over n}\right) \right]^n \, \rightarrow \, e^{-t^2/2}, \quad n \rightarrow \infty.
But, this limit is just the characteristic function of a standard normal distribution, N(0,1), and the central limit theorem follows from the Lévy continuity theorem, which confirms that the convergence of characteristic functions implies convergence in distribution.
Since many real processes yield distributions with finite variance, this explains the ubiquity of the normal probability distribution.
Several generalizations for finite variance exist which do not require identical distribution but incorporate some condition which guarantees that none of the variables exert a much larger influence than the others. Two such conditions are the Lindeberg condition and the Lyapunov condition. Other generalizations even allow some "weak" dependence of the random variables. Also, a generalization due to Gnedenko and Kolmogorov states that the sum of a number of independent random variables with power-law tail distributions decreasing as 1/|x|α+1 with 0 < α < href="http://en.wikipedia.org/wiki/L%C3%A9vy_skew_alpha-stable_distribution" title="Lévy skew alpha-stable distribution">Lévy distribution as the number of variables grows. This article will only be concerned with the central limit theorem as it applies to distributions with finite variance.
History:
“The central limit theorem has an interesting history. The first version of this theorem was postulated by the French-born English mathematician Abraham de Moivre, who, in a remarkable article published in 1733, used the normal distribution to approximate the distribution of the number of heads resulting from many tosses of a fair coin. This finding was far ahead of its time, and was nearly forgotten until the famous French mathematician Pierre-Simon Laplace rescued it from obscurity in his monumental work Théorie Analytique des Probabilités, which was published in 1812. Laplace expanded De Moivre's finding by approximating the binomial distribution with the normal distribution. But as with De Moivre, Laplace's finding received little attention in his own time. It was not until the nineteenth century was at an end that the importance of the central limit theorem was discerned, when, in 1901, Russian mathematician Aleksandr Lyapunov defined it in general terms and proved precisely how it worked mathematically. Nowadays, the central limit theorem is considered to be the unofficial sovereign of probability theory. ”
See Bernstein (1945) for a historical discussion focusing on the work of Pafnuty Chebyshev and his students Andrey Markov and Aleksandr Lyapunov that led to the first proofs of the C.L.T. in a general setting.
Proof of the central limit theorem:
For a theorem of such fundamental importance to statistics and applied probability, the central limit theorem has a remarkably simple proof using characteristic functions. It is similar to the proof of a (weak) law of large numbers. For any random variable, Y, with zero mean and unit variance (var(Y) = 1), the characteristic function of Y is, by Taylor's theorem,
\varphi_Y(t) = 1 - {t^2 \over 2} + o(t^2), \quad t \rightarrow 0
Where o (t2 ) is "little o notation" for some function of t that goes to zero more rapidly than t2. Letting Yi be (Xi − μ)/σ, the standardised value of Xi, it is easy to see that the standardised mean of the observations X1, X2, ..., Xn is just
Z_n = \frac{n\overline{X}_n-n\mu}{\sigma\sqrt{n}} = \sum_{i=1}^n {Y_i \over \sqrt{n}}.
By simple properties of characteristic functions, the characteristic function of Zn is
\left[\varphi_Y\left({t \over \sqrt{n}}\right)\right]^n = \left[ 1 - {t^2 \over 2n} + o\left({t^2 \over n}\right) \right]^n \, \rightarrow \, e^{-t^2/2}, \quad n \rightarrow \infty.
But, this limit is just the characteristic function of a standard normal distribution, N(0,1), and the central limit theorem follows from the Lévy continuity theorem, which confirms that the convergence of characteristic functions implies convergence in distribution.
Write short notes on Simple Random Sampling
In statistics, a Simple Random Sample is a group of subjects (a sample) chosen from a larger group (a population). Each subject from the population is chosen randomly and entirely by chance, such that each subject has the same probability of being chosen at any stage during the sampling process. This process and technique is known as Simple Random Sampling, and should not be confused with Random Sampling.
In small populations such sampling is typically done "without replacement", i.e., one deliberately avoids choosing any member of the population more than once. An unbiased random selection of subjects is important so that in the long run, the sample represents the population. However, this does not guarantee that a particular sample is a perfect representation of the population. Simple random sampling merely allows one to draw externally valid conclusions about the entire population based on the sample. Although simple random sampling can be conducted with replacement instead, this is less common and would normally be described more fully as simple random sampling with replacement.
Conceptually, simple random sampling is the simplest of the probability sampling techniques. It requires a complete sampling frame, which may not be available or feasible to construct for large populations. Even if a complete frame is available, more efficient approaches may be possible if other useful information is available about the units in the population.
Advantages are that it is free of classification error, and it requires minimum advance knowledge of the population. It best suits situations where not much information is available about the population and data collection can be efficiently conducted on randomly distributed items. If these conditions are not true, stratified sampling or cluster sampling may be a better choice.
Simple Random Sampling:
Simple Random Sampling selects samples by methods that allow each possible sample to have an equal probability of being picked and each item in the entire population to have an equal chance of being included in the sample.
Suppose we have a population of four students in a seminar and we want samples of two students at a time for interviewing purposes. The table below illustrates all of the possible combinations of samples of two students in a population size of four, the probability of each sample being picked, and the probability that each student will be in a sample.
Discuss briefly the Continuous Probability Distribution
The Normal Distribution/ Continuous Probability, also called the Gaussian distribution, is an important family of continuous probability distributions, applicable in many fields. Each member of the family may be defined by two parameters, location and scale: the mean ("average", μ) and variance ("variability", σ2), respectively. The Standard Normal Distribution is the normal distribution with a mean of zero and a variance of one (the green curves in the plots to the right). Carl Friedrich Gauss became associated with this set of distributions when he analyzed astronomical data using them [1], and defined the equation of its probability density function. It is often called the bell curve because the graph of its probability density resembles a bell.
The importance of the normal distribution as a model of quantitative phenomena in the natural and behavioral sciences is due to the central limit theorem. Many psychological measurements and physical phenomena (like noise) can be approximated well by the normal distribution. While the mechanisms underlying these phenomena are often unknown, the use of the normal model can be theoretically justified by assuming that many small, independent effects are additively contributing to each observation.
The normal distribution also arises in many areas of statistics. For example, the sampling distribution of the sample mean is approximately normal, even if the distribution of the population from which the sample is taken is not normal. In addition, the normal distribution maximizes information entropy among all distributions with known mean and variance, which makes it the natural choice of underlying distribution for data summarized in terms of sample mean and variance. The normal distribution is the most widely used family of distributions in statistics and many statistical tests are based on the assumption of normality. In probability theory, normal distributions arise as the limiting distributions of several continuous and discrete families of distributions.
So far in this subsection, we have been concerned with discrete probability distributions (Binomial and Poisson). In this section, we shall turn to cases in which the variable can take on any value within a given range and in which the probability distribution is continuous.
A very important continuous probability distribution is the normal distribution. Several mathematicians were instrumental in its development, including the eighteenth-century mathematician-astronomer Karl Gauss. In honour of his work, the normal probability distribution is often called the Gaussian distribution.
There are two basic reasons why the normal distribution occupies such a prominent place in statistics. First, it has some properties that make it applicable to a great many situations in which it is necessary to make inferences by taking samples. In subsequent units, we will find that the normal distribution is a useful sampling distribution. Second, the normal distribution comes close to fitting the actual observed frequency distributions of many phenomena, including human characteristics (weights, heights, and IQs), outputs from physical processes (dimensions and yields), and other measures of interest to managers in both the public and private sectors.
Write short notes on Bernoulli distribution. Also write the use of Bernoulli process
In probability theory and statistics, the Bernoulli distribution, named after Swiss scientist Jakob Bernoulli, is a discrete probability distribution, which takes value 1 with success probability p and value 0 with failure probability q = 1 − p. So if X is a random variable with this distribution, we have:
Definition:
A Bernoulli process is a discrete-time stochastic process consisting of a finite or infinite sequence of independent random variables X1, X2, X3,..., such that
- For each i, the value of Xi is either 0 or 1;
- For all values of i, the probability that Xi = 1 is the same number p.
In other words, a Bernoulli process is a sequence of independent identically distributed Bernoulli trials. The two possible values of each Xi are often called "success" and "failure", so that, when expressed as a number, 0 or 1, the value is said to be the number of successes on the ith "trial". The individual success/failure variables Xi are also called Bernoulli trials.
Random variables associated with the Bernoulli process include:
- The number of successes in the first n trials; this has a binomial distribution;
- The number of trials needed to get r successes; this has a negative binomial distribution.
- The number of trials needed to get one success; this has a geometric distribution, which is a special case of the negative binomial distribution.
The problem of determining the process, given only a limited sample of Bernoulli trials, is known as the problem of checking if a coin is fair.
Bernoulli distribution:
One widely used probability distribution of a discrete random variable is the binomial distribution. It describes a variety of processes of interest to managers. The binomial distribution describes discrete, not continuous, data, resulting from an experiment known as a Bernoulli process, after the seventeenth-century Swiss mathematician Jacob Bernoulli. The tossing of a fair coin a fixed number of times is a Bernoulli process, and the outcomes of such tosses can be represented by the binomial probability distribution. The success or failure of interviewees on an aptitude test may also be described by a Bernoulli process. On the other hand, the frequency distribution of the lives of fluorescent lights in a factory would be measured on a continuous scale of hours and would not quality as a binomial distribution.
Use of the Bernoulli process:
We can use the outcomes of a fixed number of tosses of a fair coin as an example of a Bernoulli process. We can describe this process as follows:
1. Each trial (each toss, in this case) has only two possible outcomes: heads or tails, yes or no, success or failure.
2. The probability of the outcome of any trial (toss) remains fixed over time with a fair coin, the probability of heads remains 0.5 for each toss regardless of the number of times the coin is tossed.
3. The trials are statistically independent; that is, the outcome of one toss does not affect the outcome of any other toss.
Briefly explain relative frequency of occurrence in your own words
Relative Frequency of Occurrence:-
In statistics the frequency of an event i is the number ni of times the event occurred in the experiment or the study. These frequencies are often graphically represented in histograms.
We speak of absolute frequencies, when the counts ni themselves are given and of (relative) frequencies, when those are normalized by the total number of events:
f_i = \frac{n_i}{N} = \frac{n_i}{\sum_i n_i}
Taking the fi for all i and tabulating or plotting them leads to a frequency distribution.
The Relative Frequency Density of occurrence of an event is the relative frequency of i divided by the size of the bin used to classify i.
For example: If the lower extreme of the class you are measuring the density of is 15 and the upper extreme of the class you are measuring is 30, given a relative frequency of 0.0625, you would calculate the frequency density for this class to be:
Rel.freq / (Upper Extreme of Class - Lower Extreme of Class) = Density
0.0625 / (30 - 15) = 0.0625 / 15 = 0.0041666.. That is: 0.00417 to 5 S.F.
In biology, relative frequency is the occurrence of a single gene in a specific species that makes up a gene pool.
The Limiting Relative Frequency of an event over a long series of trials is the conceptual foundation of the frequency interpretation of probability. In this framework, it is assumed that as the length of the series increases without bound, the fraction of the experiments in which we observe the event will stabilize. This interpretation is often contrasted with Bayesian probability.
Frequency is the measurement of the number of occurrences of a repeated event per unit of time. It is also defined as the rate of change of phase of a sinusoidal waveform.
Relative Frequency of Occurrence:-
Question like : “What is the probability that I will live to be 85 ? or “ what are the chances that I will below one of my stereo speakers if I turn my 200 –watt amplifier up to wide open?” or “what is the probability that the location of a new paper plant on the river near our town will cause a substantial fish kill?. We quickly see that we may not be able to state in advance, without experimentation, what these probabilities are. Other approaches may be more useful.
In the 1800s, British statisticians, interested in a theoretical foundation for calculating risk of losses in life insurance and commercial insurance, began defining probabilities from statistical data collected on births and deaths. Today, this approach is called The relative frequency of Occurrence. It defines probability as either:
1. The observed relative frequency of an event in a very large number of trials, or
2. The proportion of times that an event occurs in the long run when conditions are stable.
This method used the relative frequencies of past occurrences as probabilities. We determine how often something has happened in the past and use that figure to predict the probability that it will happen again in the future.
For example. Suppose an insurance company knows from past actuarial data that of all males 40 years old, about 60 out or every 100,000 will die within a 1 – year period. Using this method, the company estimates the probability of death of that age group as:
___60____ or 0.0006
1000
A second characteristic of probabilities established by the relative frequency of occurrence method can be shown by tossing one of our fair coins 300 times. Here we can see that although the proportion of heads was far from 0.5 in the first 100 tosses, it seemed to stabilize and approach 0.5 as the number of tosses increased.
In statistical language, we would say that the relative frequency becomes stable as the number of tosses becomes large (if we are tossing the coin under uniform conditions). Thus, when we use the relative frequency approach to establish probabilities, our probability figure will gain accuracy as we increase the number of observations. Of course, this improved accuracy is not free; although more tosses of our coin will produce a more accurate probability of head occurring, we must bear the time and the cost of additional observations.
One difficulty with the relative frequency approach is that people often use it without evaluating a sufficient number of outcomes. If you heard someone say, “My aunt and uncle got the flu this year, and they are both over 65, so everyone in that age bracket will probably get the flu, “you would know that your friend did not base his assumptions on enough evidence. His observations were insufficient data for establishing a relative frequency of occurrence probability.
In statistics the frequency of an event i is the number ni of times the event occurred in the experiment or the study. These frequencies are often graphically represented in histograms.
We speak of absolute frequencies, when the counts ni themselves are given and of (relative) frequencies, when those are normalized by the total number of events:
f_i = \frac{n_i}{N} = \frac{n_i}{\sum_i n_i}
Taking the fi for all i and tabulating or plotting them leads to a frequency distribution.
The Relative Frequency Density of occurrence of an event is the relative frequency of i divided by the size of the bin used to classify i.
For example: If the lower extreme of the class you are measuring the density of is 15 and the upper extreme of the class you are measuring is 30, given a relative frequency of 0.0625, you would calculate the frequency density for this class to be:
Rel.freq / (Upper Extreme of Class - Lower Extreme of Class) = Density
0.0625 / (30 - 15) = 0.0625 / 15 = 0.0041666.. That is: 0.00417 to 5 S.F.
In biology, relative frequency is the occurrence of a single gene in a specific species that makes up a gene pool.
The Limiting Relative Frequency of an event over a long series of trials is the conceptual foundation of the frequency interpretation of probability. In this framework, it is assumed that as the length of the series increases without bound, the fraction of the experiments in which we observe the event will stabilize. This interpretation is often contrasted with Bayesian probability.
Frequency is the measurement of the number of occurrences of a repeated event per unit of time. It is also defined as the rate of change of phase of a sinusoidal waveform.
Relative Frequency of Occurrence:-
Question like : “What is the probability that I will live to be 85 ? or “ what are the chances that I will below one of my stereo speakers if I turn my 200 –watt amplifier up to wide open?” or “what is the probability that the location of a new paper plant on the river near our town will cause a substantial fish kill?. We quickly see that we may not be able to state in advance, without experimentation, what these probabilities are. Other approaches may be more useful.
In the 1800s, British statisticians, interested in a theoretical foundation for calculating risk of losses in life insurance and commercial insurance, began defining probabilities from statistical data collected on births and deaths. Today, this approach is called The relative frequency of Occurrence. It defines probability as either:
1. The observed relative frequency of an event in a very large number of trials, or
2. The proportion of times that an event occurs in the long run when conditions are stable.
This method used the relative frequencies of past occurrences as probabilities. We determine how often something has happened in the past and use that figure to predict the probability that it will happen again in the future.
For example. Suppose an insurance company knows from past actuarial data that of all males 40 years old, about 60 out or every 100,000 will die within a 1 – year period. Using this method, the company estimates the probability of death of that age group as:
___60____ or 0.0006
1000
A second characteristic of probabilities established by the relative frequency of occurrence method can be shown by tossing one of our fair coins 300 times. Here we can see that although the proportion of heads was far from 0.5 in the first 100 tosses, it seemed to stabilize and approach 0.5 as the number of tosses increased.
In statistical language, we would say that the relative frequency becomes stable as the number of tosses becomes large (if we are tossing the coin under uniform conditions). Thus, when we use the relative frequency approach to establish probabilities, our probability figure will gain accuracy as we increase the number of observations. Of course, this improved accuracy is not free; although more tosses of our coin will produce a more accurate probability of head occurring, we must bear the time and the cost of additional observations.
One difficulty with the relative frequency approach is that people often use it without evaluating a sufficient number of outcomes. If you heard someone say, “My aunt and uncle got the flu this year, and they are both over 65, so everyone in that age bracket will probably get the flu, “you would know that your friend did not base his assumptions on enough evidence. His observations were insufficient data for establishing a relative frequency of occurrence probability.
Explain the limitations of statistics in your own words
Limitations of Statistics:
1. Statistics does not deal with qualitative data. It deals only with quantitative data: Statistical methods can be applied only to numerically expressed data. Qualitative characteristics can be studied only if an alternative method of numerical measurement is introduced.
2. Statistics does not deal with individual fact: Statistical methods can be applied only to aggregate of facts. Single fact cannot be statistically studied.
3. Statistical inferences (conclusions) are not exact: Statistical inferences are true only on an average. They are probabilistic statements.
4. Statistics can be misused: Increasing misuse of Statistics has led to increasing distrust in statistics.
5. Common men cannot handle statistics properly: Only statisticians can handle statistics properly. An illogical analysis of statistical data leads to statistical fallacies.
Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities. Statistics are also used for making informed decisions.
Statistical methods can be used to summarize or describe a collection of data; this is called descriptive statistics. In addition, patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations, and then used to draw inferences about the process or population being studied; this is called inferential statistics. Both descriptive and inferential statistics comprise applied statistics. There is also a discipline called mathematical statistics, which is concerned with the theoretical basis of the subject.
1. Statistics does not deal with qualitative data. It deals only with quantitative data: Statistical methods can be applied only to numerically expressed data. Qualitative characteristics can be studied only if an alternative method of numerical measurement is introduced.
2. Statistics does not deal with individual fact: Statistical methods can be applied only to aggregate of facts. Single fact cannot be statistically studied.
3. Statistical inferences (conclusions) are not exact: Statistical inferences are true only on an average. They are probabilistic statements.
4. Statistics can be misused: Increasing misuse of Statistics has led to increasing distrust in statistics.
5. Common men cannot handle statistics properly: Only statisticians can handle statistics properly. An illogical analysis of statistical data leads to statistical fallacies.
Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities. Statistics are also used for making informed decisions.
Statistical methods can be used to summarize or describe a collection of data; this is called descriptive statistics. In addition, patterns in the data may be modeled in a way that accounts for randomness and uncertainty in the observations, and then used to draw inferences about the process or population being studied; this is called inferential statistics. Both descriptive and inferential statistics comprise applied statistics. There is also a discipline called mathematical statistics, which is concerned with the theoretical basis of the subject.
Liability of Past Members
A past member (i.e., List B contributory) shall not be liable to contribute
1. If he had ceased to be a member of the company one year or more before the
commencement of the winding-up.
2. In respect of any debt or liability of the company contracted after he ceased to
be a member.
3. If it appears to the Court that the present members will be able to satisfy the
contributions required to be made by them.
If a company goes into liquidation more than a year after the forfeiture of certain shares for non-payment of calls, the owners of such shares would be liable not as contributories, but as debtors of the company {Ladies’ Dress Association Ltd. V s. Pulbrook (1900) 2 QB 376]. The only effect of forfeiture is that the shares pass out of their hands, but the liability incurred previously to pay the call money remains [Shiromani Sugar Mills Ltd. Vs. Debi Prasad (1950) 20 Compo Cas. 296 (All)].
If transferees fail to pay the calls made in respect of the shares transferred to them, the shares will be forfeited for the benefit of the company; and the transferors will be liable to be placed on the list of contributories as past members of the company, if the shares were transferred within a year before the commencement of winding-up
[Accidental Marine Insurance Corpn., In re (1869) 4
the same shares made immediately before one year of winding-up would result in all the past owners of the said shares being treated as past members. However, their liability as contributories would arise only if it is apparent that the present members are unable to satisfy the debts of the company [Land Credit Company of
It may be noted that the plea of voidability or illegality of contract to take shares cannot be taken after winding-up to avoid liability as a contributory. The contract so vitiated should be sought to be set aside before the company goes into liquidation. The original contract may supply the reason for his name having been placed on the register in respect ( f the shares, but after the winding-up his liability in respect of the shares arises ex lege and ex contractu [Hansraj Gupta Vs. N.P. Asthana (1932) 2 Compo Cas. 543 (PC) and Mahomed Akbar Abdulla Fazalbhoy Vs. Official Liquidator (1950) 20 Compo Cas 26 (Bom.). On a winding up order being made the liability of a contributory becomes an absolute statutory liability. The unpaid calls can be recovered even though barred by limitation when the winding-up order is made [People’s Insurance Co. Ltd., In re (1962) 32 Compo Cas. 632 (Punj.) and T. M. Mathew Vs. Industrial Bank Ltd. (1972) 42 Compo Cas. 55 (Ker.)].
Tuesday, January 8, 2008
SECRETARIAL PRACTICE
SECRETARIAL PRACTICE
1. Draft:
(a) the notice of the first Board meeting,
(b) the agenda of the first Board meeting,
(c) the agenda of the subsequent Board meeting, and
(d) a notice cancelling a Board meeting and issuing notice for a fresh Board
meeting.
(a) Notice of the First Board Meeting
ABC Ltd.
To
(Director)
Dear Sir /Madam,
This is to inform you that the first meeting of the Board of Directors will be held
at the Registered Office of the company on 5th September at 3 p.m. to transact the
business as per the enclosed agenda.
1. Election of the chairman of the meeting.
2. To produce the Certificate of Incorporation, the Memorandum and the Ar
ticles of Association.
3. Election of the Chairman of the Company.
4. Appointment of Managing Director, Secretary, Solicitors, Auditors and
Bankers.
5. Adoption of the company’s seal.
6. Fixing quorum for the Board’s meeting.
7. Consideration and approval of the opening of a Bank account and its opera
tion.
8. Approval of the statement of preliminary expenses by the promoters.
9. Authorising the Secretary to purchase books and registers as are necessary.
10. Consideration and approval of the draft of prospectus.
11. Consideration and adoption of the preliminary contracts and underwriting
contracts.
12. Consideration of the application to the stock exchange for the listing of shares. 13. Any other business with the permission of the Chair.
14. Fixing the date of the next Board meeting.
(c) Agenda of the Subsequent Board Meeting
Agenda
1.To read and approve the minutes of the last Board meeting.
2.To consider application for transfer of shares.
3.To consider letter of resignation of the Manager of Kanpur Branch.
4.To consider trading returns for the quarter ended 19....
5.To fix the date for the closure of Register of members.
6.To consider the annual accounts of the company for the year ended........
7.To consider the Auditors’ report and the draft of the Directors’ report.
8.To consider appropriation of profit and recommendation of dividends.
9.To take note of Directors liable to retire by rotation.
10.To authorise the Secretary to print the annual accounts and other documents
and to issue notice of the annual general meeting.
11.To consider any other business with the permission of the Chair.
Draft the minutes of the first Board meeting of a public limited company. YLns.
Minutes of the First Board Meeting
Minutes of meeting of the Board of Directors held at on day of Ltd.
Present in Attendance
1. Draft:
(a) the notice of the first Board meeting,
(b) the agenda of the first Board meeting,
(c) the agenda of the subsequent Board meeting, and
(d) a notice cancelling a Board meeting and issuing notice for a fresh Board
meeting.
(a) Notice of the First Board Meeting
ABC Ltd.
To
(Director)
Dear Sir /Madam,
This is to inform you that the first meeting of the Board of Directors will be held
at the Registered Office of the company on 5th September at 3 p.m. to transact the
business as per the enclosed agenda.
1. Election of the chairman of the meeting.
2. To produce the Certificate of Incorporation, the Memorandum and the Ar
ticles of Association.
3. Election of the Chairman of the Company.
4. Appointment of Managing Director, Secretary, Solicitors, Auditors and
Bankers.
5. Adoption of the company’s seal.
6. Fixing quorum for the Board’s meeting.
7. Consideration and approval of the opening of a Bank account and its opera
tion.
8. Approval of the statement of preliminary expenses by the promoters.
9. Authorising the Secretary to purchase books and registers as are necessary.
10. Consideration and approval of the draft of prospectus.
11. Consideration and adoption of the preliminary contracts and underwriting
contracts.
12. Consideration of the application to the stock exchange for the listing of shares. 13. Any other business with the permission of the Chair.
14. Fixing the date of the next Board meeting.
(c) Agenda of the Subsequent Board Meeting
Agenda
1.To read and approve the minutes of the last Board meeting.
2.To consider application for transfer of shares.
3.To consider letter of resignation of the Manager of Kanpur Branch.
4.To consider trading returns for the quarter ended 19....
5.To fix the date for the closure of Register of members.
6.To consider the annual accounts of the company for the year ended........
7.To consider the Auditors’ report and the draft of the Directors’ report.
8.To consider appropriation of profit and recommendation of dividends.
9.To take note of Directors liable to retire by rotation.
10.To authorise the Secretary to print the annual accounts and other documents
and to issue notice of the annual general meeting.
11.To consider any other business with the permission of the Chair.
Draft the minutes of the first Board meeting of a public limited company. YLns.
Minutes of the First Board Meeting
Minutes of meeting of the Board of Directors held at on day of Ltd.
Present in Attendance
Provision contrary to the specific provisions
It may be noted that Articles cannot contain a provision contrary to the specific provisions of the Act. Any such stipulation .shall be void. Again, Section 36 of the Companies Act constitutes a binding relationship between the company and the members; not between the company and the Directors. Thus, under the present law, service of notice to James at his foreign address is not mandatory. However, in view of the present liberalised scenerio, law needs to be amended.
The Board of Directors of MIs. Infotech Consultants Limited, registered in Calcutta, proposes to hold the next Board meeting in the month of May, 2000. They seek your advice in respect of the following matters:
(i)Can the Board meeting be held in Chennai, when all the Directors of the
company reside at Calcutta?
(ii)Whether the Board meeting can be called on a public holiday and that too after
business hours as the majority of the Directors of the company have gone to
Chennai on vacation.
Is it necessary that the notice of the Board meeting should specify the nature
of business to be transacted?
Advise with reference to the relevant provisions of the Companies Act.
(i)Place of Board Meeting. Section 301(5) provides, inter alia, that the register of contracts shall be kept at the Registered Office of the Company. The said register has to be made available at the Board meeting also. Accordingly, if a Board meeting is held at a place other than the Registered Office, it will involve removal of the register of contracts outside the Registered Office and thus resulting in violation of the provisions of Section 301(5). The Department of Company Affairs has, however, clarified that it would be sufficient compliance with the provisions of Section 301(5) if the company gives adequate notice to its shareholders, either once for all or from time to time indicating the prescribed periods during business hours and the days on which they may inspect the register kept under Section 301(2) at the Registered Office. In view of the aforesaid clarification, it is clear that it is legally possibly to hold Board meeting at any place if the requisite notice to shareholders has been given. Thus, in the given
problem, the Board meeting may be held in Chennai.
(ii) Board Meetings on Public Holidays. Under Section 288(1) adjourned Board meeting cannot be held on a public holiday. The Company Law Board has, therefore, advised that Section 288 does not prohibit a company from holding its original Board meetings on public holiday except where Articles of Association provide otherwise. Accordingly, the Board meeting may be held on a public holiday. Again, the Act is
silent about the time of holding the Board meeting. Therefore, there should be no objection to the meeting being held outside the business hours.
(iii) Agenda of the Board Meeting. The Companies Act does not require an agenda for the meeting of the Directors to accompany the notice thereof. Section 286 only requires that notice of every meeting of the Board of Directors of a company shall be given to every director. Thus, any business can he transacted at a Board meeting. However, in case of some matters, prior notice is a practical necessity. These include appointment as Managing Director of a person who is already Managing Director /Manager of another company (Section 316); inter-company loans and investments (Section 372 A); appointment of a person as Manager who is already Managing Director /Manager of another company (Section 386).
P. 10. Cosmos Ltd. has 11 directors out of which 4 were abroad. One of such directors had left his foreign address for all communications. In regard to an urgent matter, which could not wait till the next meeting, it circulated a resolution for approval of the directors, 4 out of 7 directors in India approved the resolution. Cosmos Ltd.
claimed that the resolution was passed. Examine. For provisions of the Act, see Answer to Accordingly, resolution is invalid. The resolution by circulation must have been approved by all the directors in India, seven directors who were in India or by majority of total number of directors who were entitled to vote, Le., six directors.
The Board of Directors of MIs. Infotech Consultants Limited, registered in Calcutta, proposes to hold the next Board meeting in the month of May, 2000. They seek your advice in respect of the following matters:
(i)Can the Board meeting be held in Chennai, when all the Directors of the
company reside at Calcutta?
(ii)Whether the Board meeting can be called on a public holiday and that too after
business hours as the majority of the Directors of the company have gone to
Chennai on vacation.
Is it necessary that the notice of the Board meeting should specify the nature
of business to be transacted?
Advise with reference to the relevant provisions of the Companies Act.
(i)Place of Board Meeting. Section 301(5) provides, inter alia, that the register of contracts shall be kept at the Registered Office of the Company. The said register has to be made available at the Board meeting also. Accordingly, if a Board meeting is held at a place other than the Registered Office, it will involve removal of the register of contracts outside the Registered Office and thus resulting in violation of the provisions of Section 301(5). The Department of Company Affairs has, however, clarified that it would be sufficient compliance with the provisions of Section 301(5) if the company gives adequate notice to its shareholders, either once for all or from time to time indicating the prescribed periods during business hours and the days on which they may inspect the register kept under Section 301(2) at the Registered Office. In view of the aforesaid clarification, it is clear that it is legally possibly to hold Board meeting at any place if the requisite notice to shareholders has been given. Thus, in the given
problem, the Board meeting may be held in Chennai.
(ii) Board Meetings on Public Holidays. Under Section 288(1) adjourned Board meeting cannot be held on a public holiday. The Company Law Board has, therefore, advised that Section 288 does not prohibit a company from holding its original Board meetings on public holiday except where Articles of Association provide otherwise. Accordingly, the Board meeting may be held on a public holiday. Again, the Act is
silent about the time of holding the Board meeting. Therefore, there should be no objection to the meeting being held outside the business hours.
(iii) Agenda of the Board Meeting. The Companies Act does not require an agenda for the meeting of the Directors to accompany the notice thereof. Section 286 only requires that notice of every meeting of the Board of Directors of a company shall be given to every director. Thus, any business can he transacted at a Board meeting. However, in case of some matters, prior notice is a practical necessity. These include appointment as Managing Director of a person who is already Managing Director /Manager of another company (Section 316); inter-company loans and investments (Section 372 A); appointment of a person as Manager who is already Managing Director /Manager of another company (Section 386).
P. 10. Cosmos Ltd. has 11 directors out of which 4 were abroad. One of such directors had left his foreign address for all communications. In regard to an urgent matter, which could not wait till the next meeting, it circulated a resolution for approval of the directors, 4 out of 7 directors in India approved the resolution. Cosmos Ltd.
claimed that the resolution was passed. Examine. For provisions of the Act, see Answer to Accordingly, resolution is invalid. The resolution by circulation must have been approved by all the directors in India, seven directors who were in India or by majority of total number of directors who were entitled to vote, Le., six directors.
Relevant provisions of the Companies Act
Section 286 of the Companies Act, 1956 provides that notice of every meeting of the Board of Directors of a company shall be given in writing to every Director for the time being in India, and at his usual address in India to every other Director (Sub-section (1)). Where however, notice is not given as required but all Directors attend the meeting and do not object to the absence of notice, or where the absentee Directors do not complain of want of notice, the proceedings at the meeting will not be invalid, especially, if they are ratified at a subsequent meeting at which the absentee Directors are present. It is open to a regularly constituted meeting of the Board of Directors to ratify that action which, though unauthorised, is done on behalf of the company. Ratification generally relates back to the date of the act ratified. [Bharat Fire tlnd General Insurance Co. Ltd. Vs. Parmeshwari Prasad Gupta, AIR 1968, Delhi; see also Parmeshwari Prasad Gupta Vs. Union of India (1974)
On the basis of the above, answer to the first question is that the meeting and proceedings both are quite valid. Answer to the second question is that the Board of Directors are quite competent to ratify the decisions at a later regularly constituted meeting of the Board. The ratification in this case will relate back to the date of the act ratified.
Advise the company with reference to the relevant provisions of the Companies Act about sending notice of board meetings to the following Directors:
(i)Mr. Rohit, a Director, states that he will not be able to attend the next board meeting.
(ii) Mr. Bipin Ram goes abroad for four months from 4.1.1999 and an alternate
Director has been appointed in his place.
(iii)Mr. James is a Director residing abroad representing the foreign collaborator
and the Articles of Association of the company provide for sending notice to
such Directors.
According to Section 286 of the Companies Act, 1956 notice of every board meeting shall be given in writing to every Director for the time being in India and at his usual address in India to every other Director.
(i)Notice should be given even if Mr. Rohit expressed his inability to attend the next Board meeting. Otherwise Section 286(1) will be violated. [In re: Portuguese Consolidated Copper Mines Ltd. (1889) 42, Ch. D. 160 (CA)].
(ii) Although there is no legal precedent in this regard, it would be a prudent practice (under Section 286) that notice should be served to both, the alternate. Director as well as the original Director Mr. Bipin Ram, who is outside India, at his usual address in India.
(iii)In the case of a company having foreign collaboration, Articles generally provide that notice ofBoard Meeting should be sent by Air Mail. But a question crops up whether such provision is valid, as Section 286 (1) requires service of such notice to a Director to be sent at his usual address in India.
On the basis of the above, answer to the first question is that the meeting and proceedings both are quite valid. Answer to the second question is that the Board of Directors are quite competent to ratify the decisions at a later regularly constituted meeting of the Board. The ratification in this case will relate back to the date of the act ratified.
Advise the company with reference to the relevant provisions of the Companies Act about sending notice of board meetings to the following Directors:
(i)Mr. Rohit, a Director, states that he will not be able to attend the next board meeting.
(ii) Mr. Bipin Ram goes abroad for four months from 4.1.1999 and an alternate
Director has been appointed in his place.
(iii)Mr. James is a Director residing abroad representing the foreign collaborator
and the Articles of Association of the company provide for sending notice to
such Directors.
According to Section 286 of the Companies Act, 1956 notice of every board meeting shall be given in writing to every Director for the time being in India and at his usual address in India to every other Director.
(i)Notice should be given even if Mr. Rohit expressed his inability to attend the next Board meeting. Otherwise Section 286(1) will be violated. [In re: Portuguese Consolidated Copper Mines Ltd. (1889) 42, Ch. D. 160 (CA)].
(ii) Although there is no legal precedent in this regard, it would be a prudent practice (under Section 286) that notice should be served to both, the alternate. Director as well as the original Director Mr. Bipin Ram, who is outside India, at his usual address in India.
(iii)In the case of a company having foreign collaboration, Articles generally provide that notice ofBoard Meeting should be sent by Air Mail. But a question crops up whether such provision is valid, as Section 286 (1) requires service of such notice to a Director to be sent at his usual address in India.
Total strength of Directors
The proviso to Section 287(2) cannot also be availed of as the interested Directors, who are three, are not equal to or more than two-thirds of the total strength of Directors. The figure representing two-thirds will be 4 by rounding off fraction, if any. Hence, it can be assumed that the allotinent made at the Board meeting will not be valid.
As per Section 288 of the Companies Act, 1956 if a meeting of the Board could not be held for want of quorum, then unless the Articles provide otherwise, the meeting shall automatically stand adjourned to, the same day in the next week, at the same time and place or if that day is a public holiday till the next succeeding day which is not a public holiday.
Sub-section (2) of Section 288 further provides that the provisions of Section 285 shall not be deemed to have been contravened merely by reason of the fact that meeting of the Board which has been called in compliance with the terms of that section, could not be held for want of quorum.
©. According to Section 286 of the Companies Act, 1956, notice of every meeting of the Board shall be given in writing to every Director in India and to every other Director at his usual address in India. As this is a compulsory requirement, failure to do so will make the meeting and the resolution passed at the meeting null and void. [Kllldip Singh Dhillon Vs.
Paragon Utility Financiers (P) Ltd.’”(1988)
The Companies Act contains no provision either specifically permitting
or prohibiting inspection by the shareholders of the minutes of the meet
XYZCompany Limited calls a meeting of the Board of Directors without giving notice to Directors as required under the Companies Act, 1956. The meeting is attended by all the Directors. None of the Directors of the company objected to the absence of notice. The proceedings of the meeting are ratified later by the Board of
I Directors at a regularly constituted meeting.
Decide giving reasons for your answer whether:
(i) the meeting and the proceedings are valid?
(ii)the Board of Directors are competent to ratify at a later meeting the above
proceedings
As per Section 288 of the Companies Act, 1956 if a meeting of the Board could not be held for want of quorum, then unless the Articles provide otherwise, the meeting shall automatically stand adjourned to, the same day in the next week, at the same time and place or if that day is a public holiday till the next succeeding day which is not a public holiday.
Sub-section (2) of Section 288 further provides that the provisions of Section 285 shall not be deemed to have been contravened merely by reason of the fact that meeting of the Board which has been called in compliance with the terms of that section, could not be held for want of quorum.
©. According to Section 286 of the Companies Act, 1956, notice of every meeting of the Board shall be given in writing to every Director in India and to every other Director at his usual address in India. As this is a compulsory requirement, failure to do so will make the meeting and the resolution passed at the meeting null and void. [Kllldip Singh Dhillon Vs.
Paragon Utility Financiers (P) Ltd.’”(1988)
The Companies Act contains no provision either specifically permitting
or prohibiting inspection by the shareholders of the minutes of the meet
XYZCompany Limited calls a meeting of the Board of Directors without giving notice to Directors as required under the Companies Act, 1956. The meeting is attended by all the Directors. None of the Directors of the company objected to the absence of notice. The proceedings of the meeting are ratified later by the Board of
I Directors at a regularly constituted meeting.
Decide giving reasons for your answer whether:
(i) the meeting and the proceedings are valid?
(ii)the Board of Directors are competent to ratify at a later meeting the above
proceedings
Accordance with the provisions of the Companies Act
In a Board meeting, a few Directors raise disagreements on the minutes of the earlier Board meeting alleging that the decisions were recorded wrongly.
Advise the Chairman
The minutes of a Board meeting once recorded cannot be changed. However the current meeting, the disagreeing Directors, with the permission of the Chairman,
may move a motion for passing a resolution modifying the earlier resolutions recorded in the minutes which, they feel, have been wrongly recorded.
During the year 1993, A Ltd. held four meetings of the Board on 2nd Jan. 1993, 10th May 1993, 16th Oct. 1993 and 31 st Dec. 1993. Examine whether this was in accordance with the provisions of the Companies Act, 1956?
As per Section 285 of the Companies Act, in case of every company, a meeting of its Board of Directors shall be held at least once in every three calendar months and at least four such meetings shall be held in every year. In the present case no meeting was held during the quarter July-September, 1993. Hence Section 285 has been violated.
(a) The Articles of Association of a company fixed 3 as the quorum for a meeting of the Board. At a meeting of the Board, all the 5 Directors were present. They allotted the shares of the company to 3 of the Directors.
Is it valid.? .
(b) A meeting of the Board of Directors of a company was convened to be
held on 30th December, 1994, but the meeting could not be held for want
of quorum. The last meeting of the Board of Directors was held on 14th August, 1994. Advise.
(c)By an oversight, a notice of meeting of the Board was not sent to one of
the Directors who was in India. Is the meeting valid?
(d) A member wants to inspect the minutes book of the meetings of the
Board. Advise.
(a)The provisions in regard to quorum for a Board meeting are contained in Section 287 of the Companies Act, 1956. It is provided therein that the quorum for a Board meeting shall be one-third of the total number of Directors of a company (any fraction contained in that one-third shall be rounded off as one) or two Directors whichever is higher. It is further provided that where at any time the number of interested Directors exceeds or is equal to two-thirds of the total strengths, the number of disinterested Directors present at the meeting being not less than two shall form the quorum. The company is, however, free to fix a higher quorum for the Board meeting.
Viewed in the context of the above provisions, the company has fixed the quorum for a Board meeting at 3. In this case, out of five Directors present at the meeting, the number of interested Directors is three. As such, the remaining two Directors who are n01 interested donot cons.titute a quorum and hence the meeting cannot be validly convened. Therefore, the allotment of shares at the aforesaid meeting is not valid, (Re: Sir Hormllsji & Wadia AIR 1921 Bombay 372).
Advise the Chairman
The minutes of a Board meeting once recorded cannot be changed. However the current meeting, the disagreeing Directors, with the permission of the Chairman,
may move a motion for passing a resolution modifying the earlier resolutions recorded in the minutes which, they feel, have been wrongly recorded.
During the year 1993, A Ltd. held four meetings of the Board on 2nd Jan. 1993, 10th May 1993, 16th Oct. 1993 and 31 st Dec. 1993. Examine whether this was in accordance with the provisions of the Companies Act, 1956?
As per Section 285 of the Companies Act, in case of every company, a meeting of its Board of Directors shall be held at least once in every three calendar months and at least four such meetings shall be held in every year. In the present case no meeting was held during the quarter July-September, 1993. Hence Section 285 has been violated.
(a) The Articles of Association of a company fixed 3 as the quorum for a meeting of the Board. At a meeting of the Board, all the 5 Directors were present. They allotted the shares of the company to 3 of the Directors.
Is it valid.? .
(b) A meeting of the Board of Directors of a company was convened to be
held on 30th December, 1994, but the meeting could not be held for want
of quorum. The last meeting of the Board of Directors was held on 14th August, 1994. Advise.
(c)By an oversight, a notice of meeting of the Board was not sent to one of
the Directors who was in India. Is the meeting valid?
(d) A member wants to inspect the minutes book of the meetings of the
Board. Advise.
(a)The provisions in regard to quorum for a Board meeting are contained in Section 287 of the Companies Act, 1956. It is provided therein that the quorum for a Board meeting shall be one-third of the total number of Directors of a company (any fraction contained in that one-third shall be rounded off as one) or two Directors whichever is higher. It is further provided that where at any time the number of interested Directors exceeds or is equal to two-thirds of the total strengths, the number of disinterested Directors present at the meeting being not less than two shall form the quorum. The company is, however, free to fix a higher quorum for the Board meeting.
Viewed in the context of the above provisions, the company has fixed the quorum for a Board meeting at 3. In this case, out of five Directors present at the meeting, the number of interested Directors is three. As such, the remaining two Directors who are n01 interested donot cons.titute a quorum and hence the meeting cannot be validly convened. Therefore, the allotment of shares at the aforesaid meeting is not valid, (Re: Sir Hormllsji & Wadia AIR 1921 Bombay 372).
The Board of Directors of a public company
The Board of Directors of a public company met on three times in the previos year, the fourth meeting though called could not be held for want of quorum on two occasions successivy. Discuss whether any provisions of the Companies Act has been contravened.
Or
Examine, with reference to the relevant provisions of the Companies Act, 1956.
the validity/legality of the following:
A meeting of the Board of Directors of OPO Co. Ltd. due to be held on 30.9.2001 did not take place for want of quorum. As a result, the Company did not hold any Board meeting for the quarter ended 30.9.2001 and there is a complaint that the company
has violated the provisions of the Act in this regard. [C.A. (Final) Nov., 2001J
As per Section 285 of the Companies Act, 1956, a company must holg
of its Board of Directors at least once in every three calendar monthsanatl\ere should be ac least four meetings of the Board every year. But, Section 288(2) provides that
where a meeting was called but could not be held for want of quorum, there is no contravention of any provisions of the Companies Act, 1956.
The Auditor of a company wanted to see the minutes book of Directors’ meetings. The Chairman of the company refused on the ground that matters of confidential nature were contained therein. Advise the Auditor.
Under Section 227(1) of the Act, the Auditor of a company has the right of access at all times to all books and information which he considers necessary for the proper performance of his duties, even though the information is of a confidential nature. He has, accordingly, a statutory right to inspect the Director’ minutes book. In case, he is denied access to it, he should state that in his report alongwith the reasons therefor. The Board of Directors are bound to give the fullest information and explanations in their report on the accounts of the company, on every reservation, qualification or adverse remark contained in the Auditor’s report.
Or
Examine, with reference to the relevant provisions of the Companies Act, 1956.
the validity/legality of the following:
A meeting of the Board of Directors of OPO Co. Ltd. due to be held on 30.9.2001 did not take place for want of quorum. As a result, the Company did not hold any Board meeting for the quarter ended 30.9.2001 and there is a complaint that the company
has violated the provisions of the Act in this regard. [C.A. (Final) Nov., 2001J
As per Section 285 of the Companies Act, 1956, a company must holg
of its Board of Directors at least once in every three calendar monthsanatl\ere should be ac least four meetings of the Board every year. But, Section 288(2) provides that
where a meeting was called but could not be held for want of quorum, there is no contravention of any provisions of the Companies Act, 1956.
The Auditor of a company wanted to see the minutes book of Directors’ meetings. The Chairman of the company refused on the ground that matters of confidential nature were contained therein. Advise the Auditor.
Under Section 227(1) of the Act, the Auditor of a company has the right of access at all times to all books and information which he considers necessary for the proper performance of his duties, even though the information is of a confidential nature. He has, accordingly, a statutory right to inspect the Director’ minutes book. In case, he is denied access to it, he should state that in his report alongwith the reasons therefor. The Board of Directors are bound to give the fullest information and explanations in their report on the accounts of the company, on every reservation, qualification or adverse remark contained in the Auditor’s report.
resolution by circulation
Thus, no ‘resolution by circulation’ can be passed if the number of Directors then present in India is less than the number which is necessary to form the quorum had there been a meeting of the Board. Similarly, no ‘resolution by circulation’ can be passed by a Committee of Directors if at the relevant time the number of Directors present in India out of the total number of Directors forming the committee is less than the quorum fixed for the committee.
Since passing a resolution by circulation does not involve any meeting, neither any notice nor any agenda showing the items of the business is necessary. However, Section 289 requires that while sending the draft of the resolution necessary papers are also sent therewith. “Necessary Papers” would refer to those papers or documents which would explain the purpose of the resolution as also the urgency for passing the same by circulation.
PRACTICAL PROBLEMS
1. The Articles of Association of a company provide that the meeting of the Board of Directors ofthe company will be held on the last Friday of every month. The Secretary of the company as a result does not serve the notice to the individual Directors of the company. Consequently, a meeting of the Board of Directors was held on 23rd February, 1996. The meeting was attended by all the Directors with the exception of two Directors out of a total of 10 Directors and certain resolutions were passed. The two absentee Directors object to the meeting and the proceedings of the meeting for want of notice. Referring to the provisions of the Companies Act, 1956, decide:
(i) Whether the objection raised by the two absentee Directors is valid?
(ii) Would your answer be the same in case the Secretary of the company, instead
of sending notice on a usual format to the individual Directors, sent a copy of
the Articles of Association to each one of the Directors?
Period and form of notice. Section 286 does not specify any form of notice or period of notice. Usually, a week’s notice is considered sufficient. However, if the Articles provide that Board meetings will be held on fixed days of every month or where the directors are duly informed that in future all meetings of the Board will be held on a fixed day of every month (say, first Saturday of every month), it will be sufficient compliance with the statute-A Chettiar Firm V s. Kaleshwar Mills [1957] But, even where meetings are held on a fixed day of every month, a notice is usually sent to the Directors as a reminder.
Since passing a resolution by circulation does not involve any meeting, neither any notice nor any agenda showing the items of the business is necessary. However, Section 289 requires that while sending the draft of the resolution necessary papers are also sent therewith. “Necessary Papers” would refer to those papers or documents which would explain the purpose of the resolution as also the urgency for passing the same by circulation.
PRACTICAL PROBLEMS
1. The Articles of Association of a company provide that the meeting of the Board of Directors ofthe company will be held on the last Friday of every month. The Secretary of the company as a result does not serve the notice to the individual Directors of the company. Consequently, a meeting of the Board of Directors was held on 23rd February, 1996. The meeting was attended by all the Directors with the exception of two Directors out of a total of 10 Directors and certain resolutions were passed. The two absentee Directors object to the meeting and the proceedings of the meeting for want of notice. Referring to the provisions of the Companies Act, 1956, decide:
(i) Whether the objection raised by the two absentee Directors is valid?
(ii) Would your answer be the same in case the Secretary of the company, instead
of sending notice on a usual format to the individual Directors, sent a copy of
the Articles of Association to each one of the Directors?
Period and form of notice. Section 286 does not specify any form of notice or period of notice. Usually, a week’s notice is considered sufficient. However, if the Articles provide that Board meetings will be held on fixed days of every month or where the directors are duly informed that in future all meetings of the Board will be held on a fixed day of every month (say, first Saturday of every month), it will be sufficient compliance with the statute-A Chettiar Firm V s. Kaleshwar Mills [1957] But, even where meetings are held on a fixed day of every month, a notice is usually sent to the Directors as a reminder.
Specifically permits delegation
Regulation 77 of Table A specifically permits delegation, stating that the Board may, subject to the provisions of the Act, delegate any of its powers to committees consisting of such number of members of its body as it thinks fit. Any committee so formed shall conform to any regulations that may be imposed on it by the Board in the exercise of powers delegated to it.
The resolution delegating the powers generally contains the extent of authority granted to the Committee. The Committee cannot further delegate its powers unless specifically empowered or authorised in this regard.
The provisions relating to the meetings of a committee of directors are by and large the same as those of the directors’ meetings. For example, a chairman presides over the meetings, questions arising at any meefing of a committee shall be determined by a majority of votes of members present and in case of tie, the chairman shall have a
casting vote .
Minutes of the proceedings are also to be made but these shall not be open for inspection to general public (Section 193).
© Directors’ Attendance Book
In order that the names of Directors attending a Board meeting may be properly recorded and to fix responsibility for acts done at a meeting, it is necessary to maintain
Section 289 of the Companies Act, 1956 deals with ‘resolution by circulation’. It may be noted that only the Directors and their committees are authorised to pass a resolution by circulation. Under the Act certain powers are exercisable by the Board by passing resolutions at the duly convened Board meetings only. For instance, Section 292 specifically confers certain powers on the Board to be exercised by Board only at its meetings. But where the Act is 1’ilent, the Board is empowered to take decisions by passing resolutions by circulation.
Further, Section 289 provides that no resolution shall be deemed to have been duly passed by the Board or by a Committee thereof by circulation, unless the resolution has been circulated in draft, together with necessary papers, if any, to all the Directors, or to all the members of the committee, then in India (not being less than the quorum fixed for a meeting of the Board or Committee, as the case may be), and to all other Directors or members at their usual address in India, and has been approved by such
. of the Directors as are then in India, or by a majority of such of them, as are entitled to
vote on the resolution.
The resolution delegating the powers generally contains the extent of authority granted to the Committee. The Committee cannot further delegate its powers unless specifically empowered or authorised in this regard.
The provisions relating to the meetings of a committee of directors are by and large the same as those of the directors’ meetings. For example, a chairman presides over the meetings, questions arising at any meefing of a committee shall be determined by a majority of votes of members present and in case of tie, the chairman shall have a
casting vote .
Minutes of the proceedings are also to be made but these shall not be open for inspection to general public (Section 193).
© Directors’ Attendance Book
In order that the names of Directors attending a Board meeting may be properly recorded and to fix responsibility for acts done at a meeting, it is necessary to maintain
Section 289 of the Companies Act, 1956 deals with ‘resolution by circulation’. It may be noted that only the Directors and their committees are authorised to pass a resolution by circulation. Under the Act certain powers are exercisable by the Board by passing resolutions at the duly convened Board meetings only. For instance, Section 292 specifically confers certain powers on the Board to be exercised by Board only at its meetings. But where the Act is 1’ilent, the Board is empowered to take decisions by passing resolutions by circulation.
Further, Section 289 provides that no resolution shall be deemed to have been duly passed by the Board or by a Committee thereof by circulation, unless the resolution has been circulated in draft, together with necessary papers, if any, to all the Directors, or to all the members of the committee, then in India (not being less than the quorum fixed for a meeting of the Board or Committee, as the case may be), and to all other Directors or members at their usual address in India, and has been approved by such
. of the Directors as are then in India, or by a majority of such of them, as are entitled to
vote on the resolution.
Explanations to the Directors
At the Meeting.
(I) To obtain signatures of the Directors present in the Directors’ Attendance Book.
(2) To help the Chairman by ascertaining whether quorum is present or not as per Articles.
(3) To read the notice of the meeting if required or if requested by the Chairman.
(4) To read the Minutes of the last Board meeting if requested by the Chairman and to obtain the signature of the Chairman to the minutes when it is
. approved by the meeting.
(5) To assist the Chairman in conducting the meeting including taking of votes.
(6) To supply necessary information and explanations to the Directors when required.
(7) to take notes of the proceedings in the agenda paper including exact terms of the resolutions passed.
After the meeting.
(I) To prepare the minutes from his own and Chairman’s agenda notes and enter the same in the Minutes Book within 30 days of the meeting.
(2) To circulate the minutes amongst the Directors.
(3) In case of a Board meeting held to approve the draft profit and loss account and balance sheet, appropriation suggested by the Board, etc., to allow inspection of the draft by the Auditors.
(4) Where some agreement has been approved, to arrange for the sealing of the agreement with the Common Seal, after entering the same in the Seal Book.
(5) To carry out the instructions issued to him by the Board meeting and to carry out the statutory duties specifically imposed on him.
(6) To start collecting and preparing materials for the next
Board meeting.
(a) Disinterested Quorum
As per Section 287 of the Companies Act, the Quorum of a Board meeting shall be 1/3rd of the total strength of the Board or two Directors, whichever is higher. In computing the total strength, the nun;tber of Directors whose places are vacant at the time as well as interested Directors shall be excluded. If at any time the number of interested Directors exceeds or is equal to 2/3rd of the total strength, then the remaining disinterested directors (not being less than two) shall be the quorum.
(b) Committee of Directors.
Directors must, as a general rule, act at Board meetings. The maxim ‘Delegatus non-protest delegare’, that is, a delegatee cannot further delegate, applies to Directors, the Directors being agents enjoying delegated authority of the company. However, the rule is not inflexible. Delegation as per the provisions of the Articles will be proper and valid. A delegation may be made by the Board of any of its powers to a committee consisting of its own members if it is authorised by Articles or the Act.
Section 292 specifically empowers the Board to delegate the following powers to
a committee of Directors, etc.:
(a) to borrow moneys otherwise than on debentures;
(b) to invest the funds of the company; and
© to make loans.
(I) To obtain signatures of the Directors present in the Directors’ Attendance Book.
(2) To help the Chairman by ascertaining whether quorum is present or not as per Articles.
(3) To read the notice of the meeting if required or if requested by the Chairman.
(4) To read the Minutes of the last Board meeting if requested by the Chairman and to obtain the signature of the Chairman to the minutes when it is
. approved by the meeting.
(5) To assist the Chairman in conducting the meeting including taking of votes.
(6) To supply necessary information and explanations to the Directors when required.
(7) to take notes of the proceedings in the agenda paper including exact terms of the resolutions passed.
After the meeting.
(I) To prepare the minutes from his own and Chairman’s agenda notes and enter the same in the Minutes Book within 30 days of the meeting.
(2) To circulate the minutes amongst the Directors.
(3) In case of a Board meeting held to approve the draft profit and loss account and balance sheet, appropriation suggested by the Board, etc., to allow inspection of the draft by the Auditors.
(4) Where some agreement has been approved, to arrange for the sealing of the agreement with the Common Seal, after entering the same in the Seal Book.
(5) To carry out the instructions issued to him by the Board meeting and to carry out the statutory duties specifically imposed on him.
(6) To start collecting and preparing materials for the next
Board meeting.
(a) Disinterested Quorum
As per Section 287 of the Companies Act, the Quorum of a Board meeting shall be 1/3rd of the total strength of the Board or two Directors, whichever is higher. In computing the total strength, the nun;tber of Directors whose places are vacant at the time as well as interested Directors shall be excluded. If at any time the number of interested Directors exceeds or is equal to 2/3rd of the total strength, then the remaining disinterested directors (not being less than two) shall be the quorum.
(b) Committee of Directors.
Directors must, as a general rule, act at Board meetings. The maxim ‘Delegatus non-protest delegare’, that is, a delegatee cannot further delegate, applies to Directors, the Directors being agents enjoying delegated authority of the company. However, the rule is not inflexible. Delegation as per the provisions of the Articles will be proper and valid. A delegation may be made by the Board of any of its powers to a committee consisting of its own members if it is authorised by Articles or the Act.
Section 292 specifically empowers the Board to delegate the following powers to
a committee of Directors, etc.:
(a) to borrow moneys otherwise than on debentures;
(b) to invest the funds of the company; and
© to make loans.
State the provisions relating
Where minutes of proceedings of any Board meeting have been properly kept,
until the contrary is proved:
(i) the meeting shall be deemed to have been duly called and held;
(ii) all proceedings thereat to have duly taken place;
(iii) all appointments of Directors made at the meeting shall be deemed to be
valid (Section 195).
State the provisions relating to signing of minutes of a Board meeting.
Explain the duties of a company secretary in connection with Board meetings.
Duties of Company Secretary with respect to Board Meetings
The Secretary plays an important role in the holding of Board meetings. As the principal officer of the company, he must ensure that every Board meeting is properly convened and duly constituted and that the provisions of the Act, Articles and standing orders are complied with in the conduct of these meetings. The principal duties of the Secretary relating to Board meetings may be outlined as follows:
Before the Meeting.
(I) If the date, time and place of the Board meeting have not been fixed by the preceding meeting, to fix the same in consultation with the Chairman of the Board.
(2) To prepare the agenda in consultation with the chairman or as directed by the authority convening Board meetings. In the absence of such provision, to ‘prepare and issue notice of the meeting as per directions of the Chairman or the Board. Also to ensure that the length of the notice is as per Articles.
(3) To send notice of the meeting alongwith the agenda to all Directors in India and at the usual addresses in India of all directors not in India.
(4) To receive resolutions from Directors proposed to be discussed at the meeting and circulate them among other Directors.
(5) To issue invitation letters to Solicitors, Auditors, etc., who are required to attend the meeting by special invitation.
(6) To prepare and keep in readiness statements and reports regarding the company’s trading activities, documents including cheques, contracts, transfer instruments, etc., for sealing and signatures, and other materials likely to be required at the meeting.
(7) To keep ready the Bank pass book and certificate of cash balances, the Minutes Book of Board Meetings, indexed copies of Memorandum and Articles, the company’s seal, etc.
(8) To arrange for the seating arrangement, stationery and other equipment necessary for holding the meeting.
until the contrary is proved:
(i) the meeting shall be deemed to have been duly called and held;
(ii) all proceedings thereat to have duly taken place;
(iii) all appointments of Directors made at the meeting shall be deemed to be
valid (Section 195).
State the provisions relating to signing of minutes of a Board meeting.
Explain the duties of a company secretary in connection with Board meetings.
Duties of Company Secretary with respect to Board Meetings
The Secretary plays an important role in the holding of Board meetings. As the principal officer of the company, he must ensure that every Board meeting is properly convened and duly constituted and that the provisions of the Act, Articles and standing orders are complied with in the conduct of these meetings. The principal duties of the Secretary relating to Board meetings may be outlined as follows:
Before the Meeting.
(I) If the date, time and place of the Board meeting have not been fixed by the preceding meeting, to fix the same in consultation with the Chairman of the Board.
(2) To prepare the agenda in consultation with the chairman or as directed by the authority convening Board meetings. In the absence of such provision, to ‘prepare and issue notice of the meeting as per directions of the Chairman or the Board. Also to ensure that the length of the notice is as per Articles.
(3) To send notice of the meeting alongwith the agenda to all Directors in India and at the usual addresses in India of all directors not in India.
(4) To receive resolutions from Directors proposed to be discussed at the meeting and circulate them among other Directors.
(5) To issue invitation letters to Solicitors, Auditors, etc., who are required to attend the meeting by special invitation.
(6) To prepare and keep in readiness statements and reports regarding the company’s trading activities, documents including cheques, contracts, transfer instruments, etc., for sealing and signatures, and other materials likely to be required at the meeting.
(7) To keep ready the Bank pass book and certificate of cash balances, the Minutes Book of Board Meetings, indexed copies of Memorandum and Articles, the company’s seal, etc.
(8) To arrange for the seating arrangement, stationery and other equipment necessary for holding the meeting.
Proceedings of Board meetings
“RESOLVED that the following powers be and are hereby delegated to Sarvashri X, Y and Z and they are empowered to exercise the power so long’ as they are in the service of the company and notwithstanding change in their designations.”
(a) State the provisions of the companies Act, 1956 regarding the recording and
signing of minutes of proceedings of Board meetings.
(b) What matters must be contained in the minutes of a Board meeting?
(e) Can a Director insist that his dissent be recorded in the minutes of Board
meeting on a particular decision?
(d) What presumptions are to be drawn from the minutes of a Board meeting?
J2Lns .
(a)
As per Section 193 of the Companies Act, 1956, every company must cause minutes of all proceedings of every meeting of its Board of Directors to be entered in the book kept for the purpose, within 30 days of the conclusion of such meeting. The pages of the book are to be consecutively numbered and each page is to be initialled or signed and the last page of the record of proceedings of each meeting must be dated and signed by the chairman of the said meeting or the chairman of the next succeeding meeting. In no case the minutes are to be attached to the minutes book by pasting or otherwise.
(b) The minutes of each Board meeting must contain a fair and correct summary of the proceedings thereat, including all appointments of officers. They must also contain the names of the Directors present at the meeting. In respect of each resolution passed at the meeting, the names of the Directors, if any, dissenting from, or not concurring in, the resolution must be stated (Section 193).
© As stated above, the minutes of Board meeting must contain the names of the
Directors, if any, dissenting from any resolution passed at the meeting. Accordingly, a Director can insist that his dissent be recorded in the minutes. However, the Chairman of the meeting may, in his discretion, not include any matter in the minutes which in his opinion is, or could reasonably be regarded as, defamatory of any person or is irrelevant or immaterial to the proceedings or is detrimental to the interests of the company, The chairman of the meeting shall exercise an absolute discretion in regard to the inclusion or non-inclusion of any matter in the minutes on the grounds specified above.
(a) State the provisions of the companies Act, 1956 regarding the recording and
signing of minutes of proceedings of Board meetings.
(b) What matters must be contained in the minutes of a Board meeting?
(e) Can a Director insist that his dissent be recorded in the minutes of Board
meeting on a particular decision?
(d) What presumptions are to be drawn from the minutes of a Board meeting?
J2Lns .
(a)
As per Section 193 of the Companies Act, 1956, every company must cause minutes of all proceedings of every meeting of its Board of Directors to be entered in the book kept for the purpose, within 30 days of the conclusion of such meeting. The pages of the book are to be consecutively numbered and each page is to be initialled or signed and the last page of the record of proceedings of each meeting must be dated and signed by the chairman of the said meeting or the chairman of the next succeeding meeting. In no case the minutes are to be attached to the minutes book by pasting or otherwise.
(b) The minutes of each Board meeting must contain a fair and correct summary of the proceedings thereat, including all appointments of officers. They must also contain the names of the Directors present at the meeting. In respect of each resolution passed at the meeting, the names of the Directors, if any, dissenting from, or not concurring in, the resolution must be stated (Section 193).
© As stated above, the minutes of Board meeting must contain the names of the
Directors, if any, dissenting from any resolution passed at the meeting. Accordingly, a Director can insist that his dissent be recorded in the minutes. However, the Chairman of the meeting may, in his discretion, not include any matter in the minutes which in his opinion is, or could reasonably be regarded as, defamatory of any person or is irrelevant or immaterial to the proceedings or is detrimental to the interests of the company, The chairman of the meeting shall exercise an absolute discretion in regard to the inclusion or non-inclusion of any matter in the minutes on the grounds specified above.
Minutes of Board Meetings
Minutes of Board Meetings
While preparing minutes of the proceedings of the meetings of the Board of Directors of a company, !here are certain important statutory requirements, which should be taken care of. These are:
(a) Minutes of the meeting may be drafted in the form of a series of paragraphs
numbered consecutively with relevant headings;
(b) Minutes should give contents of the item giving serial number of the item in
the Agenda, brief subject heading, full terms of the resolutions adopted
including the statistical details, etc.
© Place, date and time of the meeting should be stated.
(d) Give names of the Directors present at the meeting [Section 193(4)(a)].
(e) Give names of the Directors absent and asking for the grant of leave of absence
by Board.
(j) Give names of the Directors, if any, dissenting from or not concurring in the
resolutions under respective items of business.
(g) Mention notice given by Directors, if any, with regard to their directorships
in other companies and their shareholdings as per Section 299 (3) of the Act.
(h) Ref:::rence about interested directors abstaining from volting is necessary. (i) Mention the fact of unanimity of decisions of Directors as contemplated in
Sees. 316, 372A and 386. (j) Incorporate the appointments of officers made at the Board meetings. (k) Chairman’s initials on every page and full signatures along with date on the
last page is necessary .
While drafting minutes of the Board meeting with regard to the delegation of powers, both financial and administrative, to officers, care should be taken to so draft the resolutions as to provide for automatic cancellation of the power delegated when the delegatee ceases to be in employment of the company. Likewise, during the course of employment of a person in the company, the designation of delegatees is frequently change on promotion or otherwise. Care should be taken so that necessity of going to the ‘Board too often may be ayoided. In such cases, it will be useful to adopt the following type of a resolution:
While preparing minutes of the proceedings of the meetings of the Board of Directors of a company, !here are certain important statutory requirements, which should be taken care of. These are:
(a) Minutes of the meeting may be drafted in the form of a series of paragraphs
numbered consecutively with relevant headings;
(b) Minutes should give contents of the item giving serial number of the item in
the Agenda, brief subject heading, full terms of the resolutions adopted
including the statistical details, etc.
© Place, date and time of the meeting should be stated.
(d) Give names of the Directors present at the meeting [Section 193(4)(a)].
(e) Give names of the Directors absent and asking for the grant of leave of absence
by Board.
(j) Give names of the Directors, if any, dissenting from or not concurring in the
resolutions under respective items of business.
(g) Mention notice given by Directors, if any, with regard to their directorships
in other companies and their shareholdings as per Section 299 (3) of the Act.
(h) Ref:::rence about interested directors abstaining from volting is necessary. (i) Mention the fact of unanimity of decisions of Directors as contemplated in
Sees. 316, 372A and 386. (j) Incorporate the appointments of officers made at the Board meetings. (k) Chairman’s initials on every page and full signatures along with date on the
last page is necessary .
While drafting minutes of the Board meeting with regard to the delegation of powers, both financial and administrative, to officers, care should be taken to so draft the resolutions as to provide for automatic cancellation of the power delegated when the delegatee ceases to be in employment of the company. Likewise, during the course of employment of a person in the company, the designation of delegatees is frequently change on promotion or otherwise. Care should be taken so that necessity of going to the ‘Board too often may be ayoided. In such cases, it will be useful to adopt the following type of a resolution:
Quorum at the time of transacting the business
Quorum need not be present throughout the Board meeting.
The transactions at a Board meeting, the notice of which was not sent to one
of the Directors.
(a)Section 287 of the Companies Act, 1956 provides that quorum for a meeting of the Board of Directors shall be 1/3rd of its total strength or two Directors, whichever is higher.
‘Total strength’ means the total strength as determined in pursuance of the Act, after deducting therefrom the number of the Directors, if any, whose places may be vacant at the time. It further provides that where the number of interested Directors exceeds or is equal to 2!3rds of the total strength, the number of the remaining Directors, who are not interested being not less than two, shall be the quorum during that time.
In the Board meeting, no business can be transacted unless a quorum is present at the time of transacting the business. Even if a quorum was present when the meeting began, a resolution, passed after the quorum ceased to be there, is invalid. It is required to be present throughout the meeting.
However, if the Articles of Association of a company contain an article on the lines of Regulation 75 of Table A, as given below, the acts of the Board shall be valid for certain purposes although the members present were less than the specified minimum.
“Regulation 75. The continuing Directors may act notwithstanding any vacan .
cy in the Board but if and so long as their number is reduced below the quorum fixed by the Act for a meeting of the Board, the continuing Directors may act for the purpose of increasing the number of Directors to that fixed for the quorum, or for summoning a general meeting but for no other purpose.”
(M As per Section 286 of the Companies Act, 1956 notice of every meeting of the
Board of Directors of a company shall be given in writing to all the Directors
for the time being in India. If notice of the meeting is not given to one of the
Directors, meeting of the Board of Directors is invalid and the resolution
passed at such meeting is inoperative. In Parmeshwari Pd. Gupta Vs. Union of
India (1974), the Supreme Court held that notice to all directors was essential
for the validity of any resolution passed at the meeting. Where, however,
notice is not given as required but all the Directors attend the meeting and do
not object to the absence of notice, the proceedings of the meeting will not be
invalid.
The transactions at a Board meeting, the notice of which was not sent to one
of the Directors.
(a)Section 287 of the Companies Act, 1956 provides that quorum for a meeting of the Board of Directors shall be 1/3rd of its total strength or two Directors, whichever is higher.
‘Total strength’ means the total strength as determined in pursuance of the Act, after deducting therefrom the number of the Directors, if any, whose places may be vacant at the time. It further provides that where the number of interested Directors exceeds or is equal to 2!3rds of the total strength, the number of the remaining Directors, who are not interested being not less than two, shall be the quorum during that time.
In the Board meeting, no business can be transacted unless a quorum is present at the time of transacting the business. Even if a quorum was present when the meeting began, a resolution, passed after the quorum ceased to be there, is invalid. It is required to be present throughout the meeting.
However, if the Articles of Association of a company contain an article on the lines of Regulation 75 of Table A, as given below, the acts of the Board shall be valid for certain purposes although the members present were less than the specified minimum.
“Regulation 75. The continuing Directors may act notwithstanding any vacan .
cy in the Board but if and so long as their number is reduced below the quorum fixed by the Act for a meeting of the Board, the continuing Directors may act for the purpose of increasing the number of Directors to that fixed for the quorum, or for summoning a general meeting but for no other purpose.”
(M As per Section 286 of the Companies Act, 1956 notice of every meeting of the
Board of Directors of a company shall be given in writing to all the Directors
for the time being in India. If notice of the meeting is not given to one of the
Directors, meeting of the Board of Directors is invalid and the resolution
passed at such meeting is inoperative. In Parmeshwari Pd. Gupta Vs. Union of
India (1974), the Supreme Court held that notice to all directors was essential
for the validity of any resolution passed at the meeting. Where, however,
notice is not given as required but all the Directors attend the meeting and do
not object to the absence of notice, the proceedings of the meeting will not be
invalid.
Board of Directors
The company can recover the amount of Rs. 5 lakhG paid on the ground that
Mr. Doubtful is not entitled to any compensation, because he is guilty of corrupt
practices
According to Section 318, compensation can be paid for loss of office but only to a managing director or manager-director or a whole-time director. The compensation payable is limited to the average remuneration actually earned by such director during the three years period immediately preceding the date on which he ceased to hold the office and multiplied for the unexpired period of his term or for three years, whichever is shorter. Further, no compensation will be payable to such a director if the company goes into winding up within a period of 12 months from the date of cessation of his office.
Proviso to sub-section (4) of Section 318] Again, the company is not bound to pay compensation to Mr. Doubtful if he had been found guilty of any fraud or breach of trust or gross negligence and mismanagement of the affairs of the company [Section 318 (3) (e)]. However, it is not proper for the company to withhold the payment of compensation on the basis of allegations alone unless there is a proper
Deepika, one of the directors in XYZ Company Limited, did not attend the Board of Directors’ meetings from January 1 to March 31, 1992, without obtaining leave from the Board, though the company had sent her notices for the meetings. Two meetings were held between, 1st January 1992 and 31st March, 1992. There were five meetings of the Board of Directors, held during the financial year 1991-92, out of which Deepika had attended three meetings. The last meeting attended by her was held on 1st December, 1991. There were no further meetings of the Board of Directors in Derember, 1991. After the commencement of the new financia year 1992-93 (commencing 1st April 1992), the company called a meeting of the Board of Directors on 1st May, 1992, for which no notice was sent to Deepika, on the ground that she had ceased to be a director under the Companies Act. The meeting was held as scheduled and certain important decisions were taken thereat. Deepika, on coming to know of the meeting on 1st May, 1992, challenges the company’s calling of the Board of Directors’ meeting and decisions taken thereat, on the ground of omission on the part of the company to send notice for the meeting to her, and wants to restrain fuecompany from implementing the decisions taken at the meeting. Decide, giving reasons:
(i)Whether Deepika would succeed in restraining the company from im
plementing the decisions taken at the meeting of the Board of Directors?
(ii)Would your answer be still the same in case Deepika had attended only
two of the five meetings prior to 1st }anu:uy, 1992? (May, 1992)
XYZ Company Limited calls a meeting of the Board of Directors without giving notice to Directors as required under the Companies Act, 1956. The meeting is attended by all the Directors. None of the Directors of the company objected to the absence of notice. The proceedings of the meeting are ratified later”by the Board of Directors at a regularly constituted meeting.
Decide giving reasons for your answer whether:
(i)The meeting and the proceedings are valid?
(ii) The Board of Directors is competent to ratify at a later meeting the above
Mr. Doubtful is not entitled to any compensation, because he is guilty of corrupt
practices
According to Section 318, compensation can be paid for loss of office but only to a managing director or manager-director or a whole-time director. The compensation payable is limited to the average remuneration actually earned by such director during the three years period immediately preceding the date on which he ceased to hold the office and multiplied for the unexpired period of his term or for three years, whichever is shorter. Further, no compensation will be payable to such a director if the company goes into winding up within a period of 12 months from the date of cessation of his office.
Proviso to sub-section (4) of Section 318] Again, the company is not bound to pay compensation to Mr. Doubtful if he had been found guilty of any fraud or breach of trust or gross negligence and mismanagement of the affairs of the company [Section 318 (3) (e)]. However, it is not proper for the company to withhold the payment of compensation on the basis of allegations alone unless there is a proper
Deepika, one of the directors in XYZ Company Limited, did not attend the Board of Directors’ meetings from January 1 to March 31, 1992, without obtaining leave from the Board, though the company had sent her notices for the meetings. Two meetings were held between, 1st January 1992 and 31st March, 1992. There were five meetings of the Board of Directors, held during the financial year 1991-92, out of which Deepika had attended three meetings. The last meeting attended by her was held on 1st December, 1991. There were no further meetings of the Board of Directors in Derember, 1991. After the commencement of the new financia year 1992-93 (commencing 1st April 1992), the company called a meeting of the Board of Directors on 1st May, 1992, for which no notice was sent to Deepika, on the ground that she had ceased to be a director under the Companies Act. The meeting was held as scheduled and certain important decisions were taken thereat. Deepika, on coming to know of the meeting on 1st May, 1992, challenges the company’s calling of the Board of Directors’ meeting and decisions taken thereat, on the ground of omission on the part of the company to send notice for the meeting to her, and wants to restrain fuecompany from implementing the decisions taken at the meeting. Decide, giving reasons:
(i)Whether Deepika would succeed in restraining the company from im
plementing the decisions taken at the meeting of the Board of Directors?
(ii)Would your answer be still the same in case Deepika had attended only
two of the five meetings prior to 1st }anu:uy, 1992? (May, 1992)
XYZ Company Limited calls a meeting of the Board of Directors without giving notice to Directors as required under the Companies Act, 1956. The meeting is attended by all the Directors. None of the Directors of the company objected to the absence of notice. The proceedings of the meeting are ratified later”by the Board of Directors at a regularly constituted meeting.
Decide giving reasons for your answer whether:
(i)The meeting and the proceedings are valid?
(ii) The Board of Directors is competent to ratify at a later meeting the above
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