The coefficient of x¹⁰¹ in the expression ${(5 + x)^{500}} + x{(5 + x)^{499}} + {x^2}{(5 + x)^{498}} + \,\,.....\,\, + \,\,{x^{500}}$, x > 0, is

1

The area of the region enclosed between the parabolas y2 = 2x $-$ 1 and y2 = 4x $-$ 3 is

Topic: JEE Main 2022 (25 June Evening Shift)

2

$\mathop {\lim }\limits_{x \to {\pi \over 2}} \left( {{{\tan }^2}x\left( {{{(2{{\sin }^2}x + 3\sin x + 4)}^{{1 \over 2…

Topic: JEE Main 2022 (25 June Evening Shift)

3

The system of equations$ - kx + 3y - 14z = 25$$ - 15x + 4y - kz = 3$$ - 4x + y + 3z = 4$is consistent for all k in the …

Topic: JEE Main 2022 (25 June Evening Shift)

4

Let z1 and z2 be two complex numbers such that ${\overline z _1} = i{\overline z _2}$ and $\arg \left( {{{{z_1}} \over …

Topic: JEE Main 2022 (25 June Evening Shift)

5

Let a, b $\in$ R be such that the equation $a{x^2} - 2bx + 15 = 0$ has a repeated root $\alpha$. If $\alpha$ and $\beta…

Topic: JEE Main 2022 (25 June Evening Shift)

6

Let $A = \{ x \in R:|x + 1| < 2\} $ and $B = \{ x \in R:|x - 1| \ge 2\} $. Then which one of the following statements i…

Topic: JEE Main 2022 (25 June Evening Shift)

1

Water is being filled at the rate of 1 cm3 / sec in a right circular conical vessel (vertex downwards) of height 35 cm …

Topic: JEE Main 2022 (25 June Evening Shift)

2

If ${b_n} = \int_0^{{\pi \over 2}} {{{{{\cos }^2}nx} \over {\sin x}}dx,\,n \in N} $, then

Topic: JEE Main 2022 (25 June Evening Shift)

3

If $y = y(x)$ is the solution of the differential equation $2{x^2}{{dy} \over {dx}} - 2xy + 3{y^2} = 0$ such that $y(e)…

Topic: JEE Main 2022 (25 June Evening Shift)

4

The value of 2sin (12$^\circ$) $-$ sin (72$^\circ$) is :

Topic: JEE Main 2022 (25 June Evening Shift)

5

A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n …

Topic: JEE Main 2022 (25 June Evening Shift)

6

The value of ${\tan ^{ - 1}}\left( {{{\cos \left( {{{15\pi } \over 4}} \right) - 1} \over {\sin \left( {{\pi \over 4}}…

Topic: JEE Main 2022 (25 June Evening Shift)

7

The line y = x + 1 meets the ellipse ${{{x^2}} \over 4} + {{{y^2}} \over 2} = 1$ at two points P and Q. If r is the rad…

Topic: JEE Main 2022 (25 June Evening Shift)