List of top Questions asked in ICAR AIEEA (PG)

The class intervals in a grouped frequency distribution should be:
A. Exhaustive
B. Mutually exclusive
Select the correct answer from the following options:

The point of intersection of the two regression lines is:

If the arithmetic mean and geometric mean of two numbers are 36 and 30 respectively, then their harmonic mean is:

The type of survey where every unit of the population is enumerated is called:

A, B, and C are three mutually exclusive and exhaustive events associated with a random experiment. Also, \(P(B) = \frac{3{2} P(A)\) and \(P(C) = \frac{1}{2} P(B)\), then \(P(A)\) is:}

If A and B are independent events, then:

X speaks truth 4 out of 5 times. A die is tossed and X reports it to be 6. The probability that there was actually 6 is:

If the regression coefficient of X on Y is \(b_{xy}\), and the variables are transformed as \(U = \frac{X - a}{h}\), \(V = \frac{Y - b}{k}\), then the regression coefficient of U on V is:

If regression line of X on Y is linear, then the regression line of Y on X is:

If A and B are mutually exclusive events, then:

If A and B are two events, then \(P(A|B)\) is:

If \(P(A) = \frac{1{2}\), \(P(B) = \frac{1}{3}\), and \(P(A \cap B) = \frac{1}{6}\), then \(P(A \cup B)\) is:}

If \(X\) follows a uniform distribution on \([0, 1]\), then the variance of \(X\) is:

In case of Simple Random Sampling with Replacement, the sample mean:

The sum of absolute deviations is minimum when taken from:

The range of Coefficient of Variation (CV) is:

The minimum number of blocks required for 6 treatments so that the error degrees of freedom is 10 in case of a randomized complete block design is:

The Fairfield Smith's Variance law used in uniformity trials to obtain the relationship between plot size and plot variance is of the form \((V_x\) is the variance of yield per unit area from plots of size \(x\), \(V_1\) is the variance among plots of size unity and \(b\) is the coefficient representing soil characteristic):

Let the Arithmetic Mean of \(n\) observations be AM. If 5 is added to all the observations, then the new AM will be:

The sum of the deviations of the observations 3, 4, 5, 6, 7 from their mean is:

Let \(x_1, x_2, \dots, x_n\) be observations which have a variance \(\sigma_x^2\). Each \(x_i\) is changed to \(a x_i - h\), where \(a\) and \(h\) are positive constants, then the new series will have variance:

Mean, mode and variance of a given dataset are 60, 76 and 16, respectively. The value of Coefficient of Skewness of the dataset is:

If each value of variable X is multiplied by 8 and of Y is multiplied by 10, then correlation coefficient of new data is:

It is given that the standard deviation of a large population is 10. To test \(H_0: \mu = 10\) against \(H_1: \mu \neq 10\) at \(1\%\) level of significance, a sample of size 100 is taken. \(H_0\) will be rejected if:

There are 15 students in a class. Out of these 6 students failed. The marks of the passed students are 51, 67, 48, 71, 46, 45, 81, 90 and 50. The median of all the observations is: