List of top Mathematics Questions on Probability and Statistics asked in JEE Main

If the mean and the variance of the data

are $\mu$ and 19 respectively, then the value of $\lambda + \mu$ is

Let the mean and variance of 7 observations 2, 4, 10, x, 12, 14, y, where x>y, be 8 and 16 respectively. Two numbers are chosen from $\{1, 2, 3, x-4, y, 5\}$ one after another without replacement, then the probability, that the smaller number among the two chosen numbers is less than 4, is:

Let $ A = [a_{ij}] $ be a 2 $\times$ 2 matrix such that $a_{ij} \in \{0, 1\}$ for all $i$ and $j$. Let the random variable X denote the possible values of the determinant of the matrix A. Then, the variance of X is:

A coin is tossed three times. Let X denote the number of times a tail follows a head. If $\mu$ and $\sigma^2$ denote the mean and variance of X, then the value of $64(\mu + \sigma^2)$ is:

Let $ \mathbf{a} = 3\hat{i} - \hat{j} + 2\hat{k} $, $ \mathbf{b} = \mathbf{a} \times (\hat{i} - 2\hat{k}) $ and $ \mathbf{c} = \mathbf{b} \times \hat{k} $. Then the projection of $ \mathbf{c} - 2\hat{j} $ on $ \mathbf{a} $ is:

Let $ f: (0, \infty) \to \mathbb{R} $ be a function which is differentiable at all points of its domain and satisfies the condition $ x^2 f'(x) = 2f(x) + 3 $, with $ f(1) = 4 $. Then $ 2f(2) $ is equal to:

Two numbers $k_1$ and $k_2$ are randomly chosen from the set of natural numbers. Then, the probability that the value of $i^{k_1} + i^{k_2}$ (where $i = \sqrt{-1}$) is non-zero equals:

Three defective oranges are accidentally mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If $ x $ denotes the number of defective oranges, then the variance of $ x $ is:

One die has two faces marked 1, two faces marked 2, one face marked 3, and one face marked 4. Another die has one face marked 1, two faces marked 2, two faces marked 3, and one face marked 4. The probability of getting the sum of numbers to be 4 or 5 when both the dice are thrown together is:

Let $ \mathbf{a} = 3\hat{i} - \hat{j} + 2\hat{k} $, $ \mathbf{b} = \mathbf{a} \times (\hat{i} - 2\hat{k}) $ and $ \mathbf{c} = \mathbf{b} \times \hat{k} $. Then the projection of $ \mathbf{c} - 2\hat{j} $ on $ \mathbf{a} $ is:

Let $ f: (0, \infty) \to \mathbb{R} $ be a function which is differentiable at all points of its domain and satisfies the condition $ x^2 f'(x) = 2f(x) + 3 $, with $ f(1) = 4 $. Then $ 2f(2) $ is equal to:

Let $ y = y(x) $ be the solution of the differential equation \[ \cos(x \log_e (\cos x))^2 \, dy + (\sin x - 3 \sin x \log_e (\cos x)) \, dx = 0, \, x \in \left( 0, \frac{\pi}{2} \right) \] If $ y \left( \frac{\pi}{4} \right) = -1 $, then $ y \left( \frac{\pi}{6} \right) $ is equal to:

Two numbers $k_1$ and $k_2$ are randomly chosen from the set of natural numbers. Then, the probability that the value of $i^{k_1} + i^{k_2}$ (where $i = \sqrt{-1}$) is non-zero equals:

Three defective oranges are accidentally mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If $ x $ denotes the number of defective oranges, then the variance of $ x $ is: