List of top Questions asked in ICAR AIEEA (PG)- 2024

The annual precipitation data of a city is normally distributed with mean 1200 mm and standard deviation 200 mm. The probability that annual precipitation will be more than 1400 mm is

A die is thrown 100 times. Getting an even number is considered a success. The variance of the number of successes is

If \(X\) is a normal random variable with mean 50 and variance 25, then \(P(X \le 55)\) is

The probability that an individual is left-handed is 0.16. In a class of 10 students, what is the mean and standard deviation of the number of left-handed students?

The coefficient of variation of Poisson distribution with mean 36 is

In a binomial distribution, the mean is 8 and variance is 6. Then the mode is

Two events, A and B, are mutually exclusive and each have a nonzero probability. If event A is known to occur, the probability of the occurrence of event B is:

For a random variable \(X\) with mean \(\mu\) and variance \(\sigma^2\), the coefficient of variation is:

The value of the integral \(I = \int_{0}^{1} \frac{1}{1+x} dx\) by using Simpson's one-third rule with \(h = 0.5\) is

The mean of 21 numbers is 9. One of the numbers, 19, is deleted. What is the mean of the remaining 20 numbers?

The probability of rejecting null hypothesis when it is true is known as

The line \(y = L\) is a horizontal asymptote of the graph of the function \(f\) if

Find the interval in which the graph of the function given by \(f(x) = x^4 - 4x^3 + 10\) is concave up.

The value of \(\int_{0}^{\infty} x^7 e^{-x^2} dx\) is

The point at which the tangent to the curve \(y = x^3 - 3x^2 - 9x + 7\) is parallel to the x-axis is

Find constants a and b so that \(\lim_{x \to 0} \left( \frac{a}{2x} + \frac{a}{2} + b \right) = 1\)

The annual precipitation data of a city is normally distributed with mean \(1200\text{mm}\) and standard deviation \(200\text{mm}\), respectively. The probability that annual precipitation will be more than \(1400\text{mm}\)

A random variable \(X\) has the following pdf:
\[ f(x) = \frac{1}{\sqrt{12\pi}} e^{-\frac{(x-1)^2}{6}}; \quad -\infty < x < \infty \]
\(= 0\), otherwise.
Then \(\int_{1}^{\infty} f(x)dx = ?\)

A bowl contains eight chips. Three of the chips are red and the remaining five are blue. Two chips are to be drawn successively, at random and without replacement. What is the probability that the first draw results in a red chip and that the second draw results in a blue chip?

Find the value of \(\int_{-1}^{2} |x| \, dx\)

Which is the following statement is true?

In a binomial distribution the mean is 8 and variance is 6. Then the mode is:

A die is thrown 100 times. Getting an even number is considered a success. The variance of the number of successes is:

The probability of occurrence of two events \(A\) and \(B\) are 0.25 and 0.50 respectively. The probability of their simultaneous occurrence is 0.14. The probability that neither \(A\) occurs nor \(B\) occurs is:

The coefficient of variation of Poisson distribution with mean 36 is: