List of top Questions asked in ICAR AIEEA (PG)- 2020

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):

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:

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

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:

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

In a completely randomized design with 5 treatments, treatments 1 and 2 are replicated 4 times each and treatments 3, 4 and 5 are replicated 3 times each. The degrees of freedom for error will be:

The principle of replication:

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:

Which of the following is NOT true?

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:

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

For testing goodness of fit, suppose the observed frequencies for two classes are 28 and 12. It is expected that these occur in the ratio 3:1. The value of Chi-square statistic for testing this is:

In a random sample of 100 voters in an area, 59 voters were in favour of a candidate A. The value of the test statistic for testing \(H_0: P = 0.5\) against \(H_0: P \neq 0.5\) is:

Let X be a normally distributed random variable with mean \(\mu = 50\) and variance \(\sigma^2 = 9\). The probability that X is greater than \(\mu + \sigma\) is:

In normal distribution with mean \(\mu\) and variance \(\sigma^2\), the area under the normal curve between \(\mu \pm \sigma\) is:

Which of the following statements is correct?

Which of the following is a simple hypothesis?

Which of the following is a central difference operator?

Let \(X\) follows a binomial \((n, p)\) distribution, the skewness of the distribution will be zero if:

The coefficient of variation of Poisson distribution with mean 9 is:

Which of the following is the experimental condition in case of binomial distribution?

Integrating factor for the differential equation \((x^2 + y^2 + x) \, dx + xy \, dy = 0\) is:

For the function \(f(x, y) = x^3 + x^2 y^2\), the values of \(f_x(-1, -1)\) and \(f_y(-1, -1)\) are respectively:

Number of first order equations in a system equivalent to the equation \(x''' + 3x'' + 2x' - 5x = \sin 2t\) is:

The total differential \(df\) for the function \(f(x, y, z) = x^2 y^3 z^4\) is: