If $\displaystyle \int_{0}^{\pi/2} \dfrac{\cot x}{\cot x + \cos \csc x} , dx = m(\pi + n)$, then $m \cdot n$ is equal to

1

The equation $|z - i| = |z - 1|$, where $i = \sqrt{-1}$, represents :

Topic: JEE Main 2019 (12 April Morning Shift)

2

If $\alpha$ and $\beta$ are the roots of the equation $375x^2 - 25x - 2 = 0$, then $\displaystyle \lim_{n \to \infty} \…

Topic: JEE Main 2019 (12 April Morning Shift)

3

If $e^y + xy = e$, the ordered pair $\left(\dfrac{dy}{dx}, \dfrac{d^2y}{dx^2}\right)$ at $x=0$ is equal to:

Topic: JEE Main 2019 (12 April Morning Shift)

1

For $x \in (0, 3/2)$, let $f(x) = \sqrt{x}$, $g(x) = \tan x$ and $h(x) = \dfrac{1 - x^2}{1 + x^2}$. If $\phi(x) = (h \c…

Topic: JEE Main 2019 (12 April Morning Shift)

2

The integral $\displaystyle \int \dfrac{2x^3 - 1}{x^4 + x} , dx$ is equal to : (Here $C$ is a constant of integration)

Topic: JEE Main 2019 (12 April Morning Shift)

3

. The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distin…

Topic: JEE Main 2019 (12 April Morning Shift)

4

If $B = \left[ {\matrix{ 5 & {2\alpha } & 1 \cr 0 & 2 & 1 \cr \alpha & 3 & { - 1}…

Topic: JEE Main 2019 (12 April Morning Shift)

5

If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed w…

Topic: JEE Main 2019 (12 April Morning Shift)

6

The value of $\sin^{-1}\left(\dfrac{12}{13}\right)-\sin^{-1}\left(\dfrac{3}{5}\right)$ is equal to:

Topic: JEE Main 2019 (12 April Morning Shift)

7

Let $S_n$ denote the sum of the first $n$ terms of an A.P. If $S_4=16$ and $S_6=-48$, then $S_{10}$ equals:

Topic: JEE Main 2019 (12 April Morning Shift)

8

Let f : R $ \to $R be a continuously differentiable function such that f(2) = 6 and f'(2) = ${1 \over {48}}$. If $\int\…

Topic: JEE Main 2019 (12 April Morning Shift)

9

The equation $y = \sin x \sin (x + 2) - \sin^2 (x + 1)$ represents a straight line lying in:

Topic: JEE Main 2019 (12 April Morning Shift)

10

A 2m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate of 25 cm/…

Topic: JEE Main 2019 (12 April Morning Shift)