The value of $\int\limits_{ - {\pi \over 2}}^{{\pi \over 2}} {\left( {{{1 + {{\sin }^2}x} \over {1 + {\pi ^{\sin x}}}}} \right)} \,dx$

1

If ${\left( {\sqrt 3 + i} \right)^{100}} = {2^{99}}(p + iq)$, then p and q are roots of the equation :

Topic: JEE Main 2021 (26 August Evening Shift)

2

The value of $2\sin \left( {{\pi \over 8}} \right)\sin \left( {{{2\pi } \over 8}} \right)\sin \left( {{{3\pi } \over 8…

Topic: JEE Main 2021 (26 August Evening Shift)

3

The locus of the mid points of the chords of the hyperbola x2 $-$ y2 = 4, which touch the parabola y2 = 8x, is :

Topic: JEE Main 2021 (26 August Evening Shift)

4

Two fair dice are thrown. The numbers on them are taken as $\lambda$ and $\mu$, and a system of linear equations, x + y…

Topic: JEE Main 2021 (26 August Evening Shift)

5

If $\sum\limits_{r = 1}^{50} {{{\tan }^{ - 1}}{1 \over {2{r^2}}} = p} $, then the value of tan p is :

Topic: JEE Main 2021 (26 August Evening Shift)

6

A fair die is tossed until six is obtained on it. Let x be the number of required tosses, then the conditional probabil…

Topic: JEE Main 2021 (26 August Evening Shift)

7

The domain of the function ${{\mathop{\rm cosec}\nolimits} ^{ - 1}}\left( {{{1 + x} \over x}} \right)$ is :

Topic: JEE Main 2021 (26 August Evening Shift)

8

Let y(x) be the solution of the differential equation 2x2 dy + (ey $-$ 2x)dx = 0, x > 0. If y(e) = 1, then y(1) is …

Topic: JEE Main 2021 (26 August Evening Shift)

9

If the value of the integral $\int\limits_0^5 {{{x + [x]} \over {{e^{x - [x]}}}}dx = \alpha {e^{ - 1}} + \beta } $, wh…

Topic: JEE Main 2021 (26 August Evening Shift)

10

The local maximum value of the function $f(x) = {\left( {{2 \over x}} \right)^{{x^2}}}$, x > 0, is

Topic: JEE Main 2021 (26 August Evening Shift)

1

A circle C touches the line x = 2y at the point (2, 1) and intersects the circle C1 : x2 + y2 + 2y $-$ 5 = 0 at two poi…

Topic: JEE Main 2021 (26 August Evening Shift)

2

$\mathop {\lim }\limits_{x \to 2} \left( {\sum\limits_{n = 1}^9 {{x \over {n(n + 1){x^2} + 2(2n + 1)x + 4}}} } \right)$…

Topic: JEE Main 2021 (26 August Evening Shift)