List of top Questions asked in ICAR AIEEA (PG)

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:

Which of the following is NOT true?

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:

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

Which of the following is a simple hypothesis?

Which of the following statements is correct?

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:

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

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 a central difference operator?

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

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

For the system \(x' = y; \, y' = -x\), the solution curve has the form:

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

The equations of asymptotes for the hyperbola \(xy - 3x - 2y = 0\) are:

A solution to the difference equation \(u_{x+3} - 3u_{x+1} - 2u_x = 0\) is of the form:

A solution to the differential equation \(\left(y - x \frac{dy}{dx}\right) = a \left(y^2 + \frac{dy}{dx}\right)\) is:

Which of the following equations is exact?

Solution of the differential equation \(x \sin \frac{y}{x} \, dy = \left( y \sin \frac{y}{x} - x \right) dx\) is: