1
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 _______________.

2
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 ___________.

3
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 _______________.

4
JEE Main 2022 (Online) 24th June Evening Shift
Numerical
+4
-1
Out of Syllabus

In an examination, there are 10 true-false type questions. Out of 10, a student can guess the answer of 4 questions correctly with probability $${3 \over 4}$$ and the remaining 6 questions correctly with probability $${1 \over 4}$$. If the probability that the student guesses the answers of exactly 8 questions correctly out of 10 is $${{{{27}k}} \over {{4^{10}}}}$$, then k is equal to ___________.