Let X be a random variable such that the probability function of a distribution is given by $P(X = 0) = {1 \over 2},P(X = j) = {1 \over {{3^j}}}(j = 1,2,3,...,\infty )$. Then the mean of the distribution and P(X is positive and even) respectively are :

1

If $P = \begin{bmatrix} 1 & 0 \\ \tfrac{1}{2} & 1 \end{bmatrix}$, then $P^{50}$ is :

Topic: JEE Main 2021 (25 July Evening Shift)

2

Consider function f : A $\to$ B and g : B $\to$ C (A, B, C $ \subseteq $ R) such that (gof)$-$1 exists, then :

Topic: JEE Main 2021 (25 July Evening Shift)

3

The number of real solutions of the equation, x2 $-$ |x| $-$ 12 = 0 is :

Topic: JEE Main 2021 (25 July Evening Shift)

4

If $\left| {\overrightarrow a } \right| = 2,\left| {\overrightarrow b } \right| = 5$ and $\left| {\overrightarrow a \t…

Topic: JEE Main 2021 (25 July Evening Shift)

5

The number of distinct real roots of $\left| {\matrix{ {\sin x} & {\cos x} & {\cos x} \cr {\cos x} & …

Topic: JEE Main 2021 (25 July Evening Shift)

6

If [x] be the greatest integer less than or equal to x, then $\sum\limits_{n = 8}^{100} {\left[ {{{{{( - 1)}^n}n} \over…

Topic: JEE Main 2021 (25 July Evening Shift)

7

Let a, b and c be distinct positive numbers. If the vectors $a\widehat i + a\widehat j + c\widehat k,\widehat i+\wideha…

Topic: JEE Main 2021 (25 July Evening Shift)

8

The value of the integral $\int\limits_{ - 1}^1 {\log \left( {x + \sqrt {{x^2} + 1} } \right)dx} $ is :

Topic: JEE Main 2021 (25 July Evening Shift)

9

The lowest integer which is greater than ${\left( {1 + {1 \over {{{10}^{100}}}}} \right)^{{{10}^{100}}}}$ is _________…

Topic: JEE Main 2021 (25 July Evening Shift)

10

The value of $\cot \dfrac{\pi}{24}$ is :

Topic: JEE Main 2021 (25 July Evening Shift)

1

If ${}^n{P_r} = {}^n{P_{r + 1}}$ and ${}^n{C_r} = {}^n{C_{r - 1}}$, then the value of r is equal to :

Topic: JEE Main 2021 (25 July Evening Shift)

2

Let y = y(x) be the solution of the differential equation xdy = (y + x3 cosx)dx with y($\pi$) = 0, then $y\left( {{\pi…

Topic: JEE Main 2021 (25 July Evening Shift)