Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote the total number of one-one functions form the set A to the set A $\times$ B. Then :

1

A function f(x) is given by $f(x) = {{{5^x}} \over {{5^x} + 5}}$, then the sum of the series $f\left( {{1 \over {20}}} …

Topic: JEE Main 2021 (25 February Evening Shift)

1

The integral $\int {{{{e^{3{{\log }_e}2x}} + 5{e^{2{{\log }_e}2x}}} \over {{e^{4{{\log }_e}x}} + 5{e^{3{{\log }_e}x}} -…

Topic: JEE Main 2021 (25 February Evening Shift)

2

Let A be a set of all 4-digit natural numbers whose exactly one digit is 7. Then the probability that a randomly chosen…

Topic: JEE Main 2021 (25 February Evening Shift)

3

The shortest distance between the line x $-$ y = 1 and the curve x2 = 2y is :

Topic: JEE Main 2021 (25 February Evening Shift)

4

Let $\alpha$ and $\beta$ be the roots of x2 $-$ 6x $-$ 2 = 0. If an = $\alpha$$n $-$ $\beta$n for n $ \ge $ 1, then the…

Topic: JEE Main 2021 (25 February Evening Shift)

5

If 0 < x, y < $\pi$ and cosx + cosy $-$ cos(x + y) = ${3 \over 2}$, then sinx + cosy is equal to :

Topic: JEE Main 2021 (25 February Evening Shift)

6

cosec$\left[ {2{{\cot }^{ - 1}}(5) + {{\cos }^{ - 1}}\left( {{4 \over 5}} \right)} \right]$ is equal to :

Topic: JEE Main 2021 (25 February Evening Shift)

7

Let A be a 3 $\times$ 3 matrix with det(A) = 4. Let Ri denote the ith row of A. If a matrix B is obtained by performing…

Topic: JEE Main 2021 (25 February Evening Shift)

8

If $\alpha$, $\beta$ $\in$ R are such that 1 $-$ 2i (here i2 = $-$1) is a root of z2 + $\alpha$z + $\beta$ = 0, then ($…

Topic: JEE Main 2021 (25 February Evening Shift)

9

The minimum value of $f(x) = {a^{{a^x}}} + {a^{1 - {a^x}}}$, where a, $x \in R$ and a > 0, is equal to :

Topic: JEE Main 2021 (25 February Evening Shift)

10

If ${I_n} = \int\limits_{{\pi \over 4}}^{{\pi \over 2}} {{{\cot }^n}x\,dx} $, then :

Topic: JEE Main 2021 (25 February Evening Shift)