1
JEE Main 2022 (Online) 28th July Evening Shift
Numerical
+4
-1

A bag contains 4 white and 6 black balls. Three balls are drawn at random from the bag. Let $$\mathrm{X}$$ be the number of white balls, among the drawn balls. If $$\sigma^{2}$$ is the variance of $$\mathrm{X}$$, then $$100 \sigma^{2}$$ is equal to ________.

2
JEE Main 2022 (Online) 30th June Morning Shift
Numerical
+4
-1

The probability distribution of X is :

X 0 1 2 3
P(X) $${{1 - d} \over 4}$$ $${{1 + 2d} \over 4}$$ $${{1 - 4d} \over 4}$$ $${{1 + 3d} \over 4}$$

For the minimum possible value of d, sixty times the mean of X is equal to _______________.

3
JEE Main 2022 (Online) 27th June Evening Shift
Numerical
+4
-1

Let S = {E1, E2, ........., E8} be a sample space of a random experiment such that $$P({E_n}) = {n \over {36}}$$ for every n = 1, 2, ........, 8. Then the number of elements in the set $$\left\{ {A \subseteq S:P(A) \ge {4 \over 5}} \right\}$$ is ___________.

4
JEE Main 2022 (Online) 26th June Evening Shift
Numerical
+4
-1

If the probability that a randomly chosen 6-digit number formed by using digits 1 and 8 only is a multiple of 21 is p, then 96 p is equal to _______________.