Let A be a 3 $\times$ 3 matrix with det(A) = 4. Let R_i denote the i^th row of A. If a matrix B is obtained by performing the operation R₂ $ \to $ 2R₂ + 5R₃ on 2A, then det(B) is equal to :

1

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)

2

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)

3

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)

4

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

Topic: JEE Main 2021 (25 February Evening Shift)

5

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)

6

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)

7

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…

Topic: JEE Main 2021 (25 February Evening Shift)

8

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

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)

2

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)

3

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

Topic: JEE Main 2021 (25 February Evening Shift)

4

In a group of 400 people, 160 are smokers and non-vegetarian; 100 are smokers and vegetarian and the remaining 140 are …

Topic: JEE Main 2021 (25 February Evening Shift)

5

If for the matrix, $A = \left[ {\matrix{ 1 & { - \alpha } \cr \alpha & \beta \cr } } \right]$, $A{A^T…

Topic: JEE Main 2021 (25 February Evening Shift)

6

If the curve x2 + 2y2 = 2 intersects the line x + y = 1 at two points P and Q, then the angle subtended by the line seg…

Topic: JEE Main 2021 (25 February Evening Shift)

7

The following system of linear equations :- 2x + 3y + 2z = 9, 3x + 2y + 2z = 9, x $-$ y + 4z = 8

Topic: JEE Main 2021 (25 February Evening Shift)

8

A hyperbola passes through the foci of the ellipse ${{{x^2}} \over {25}} + {{{y^2}} \over {16}} = 1$ and its transverse…

Topic: JEE Main 2021 (25 February Evening Shift)