If $\displaystyle \int \frac{2x+5}{\sqrt{7-6x-x^{2}}},dx = A\sqrt{7-6x-x^{2}} + B\sin^{-1}!\left(\frac{x+3}{4}\right) + C$ (where $C$ is a constant of integration), then the ordered pair $(A,B)$ is equal to :

1

The curve satisfying the differential equation $(x^{2}-y^{2}),dx + 2xy,dy = 0$ and passing through the point $(1,1)$ is…

Topic: JEE Main 2018 (15 April Evening Shift)

2

The sides of a rhombus $ABCD$ are parallel to the lines, $x - y + 2 = 0$ and $7x - y + 3 = 0$. If the diagonals of the …

Topic: JEE Main 2018 (15 April Evening Shift)

3

The foot of the perpendicular drawn from the origin, on the line, $3x + y = \lambda\ (\lambda \ne 0)$ is $P$. If the li…

Topic: JEE Main 2018 (15 April Evening Shift)

4

Tangents drawn from the point $(-8,0)$ to the parabola $y^{2} = 8x$ touch the parabola at $P$ and $Q$. If $F$ is the fo…

Topic: JEE Main 2018 (15 April Evening Shift)

5

An angle between the lines whose direction cosines are given by the equations $l + 3m + 5n = 0$ and $5lm - 2mn + 6nl = …

Topic: JEE Main 2018 (15 April Evening Shift)

6

A player $X$ has a biased coin whose probability of showing heads is $p$ and a player $Y$ has a fair coin. They start p…

Topic: JEE Main 2018 (15 April Evening Shift)

7

If the mean of the data $7, 8, 9, 7, 8, 7, \lambda, 8$ is $8$, then the variance of this data is :

Topic: JEE Main 2018 (15 April Evening Shift)

8

If the position vectors of the vertices $A$, $B$ and $C$ of a $\triangle ABC$ are respectively $4\hat{i}+7\hat{j}+8\hat…

Topic: JEE Main 2018 (15 April Evening Shift)

9

If $f(x)$ is a quadratic expression such that $f(1)+f(2)=0$, and $-1$ is a root of $f(x)=0$, then the other root of $f(…

Topic: JEE Main 2018 (15 April Evening Shift)

10

Let $f\colon A\to B$ be a function defined as $f(x)=\dfrac{x-1}{x-2}$, where $A=\mathbb{R}-{2}$ and $B=\mathbb{R}-{1}$.…

Topic: JEE Main 2018 (15 April Evening Shift)

1

If $I_1=\displaystyle\int_{0}^{1} e^{-x}\cos^{2}x,dx$; $I_2=\displaystyle\int_{0}^{1} e^{-x^{2}}\cos^{2}x,dx$ and $I_3=…

Topic: JEE Main 2018 (15 April Evening Shift)

2

The value of the integral $\displaystyle\int_{\pi/4}^{3\pi/4}\frac{x}{1+\sin x},dx$ is :

Topic: JEE Main 2018 (15 April Evening Shift)

3

Let $f(x)$ be a polynomial of degree $4$ having extreme values at $x=1$ and $x=2$. If $\lim_{x\to 0}\left(\dfrac{f(x)}{…

Topic: JEE Main 2018 (15 April Evening Shift)

4

If $f(x)=\sin^{-1}\left(\dfrac{2x^{3}}{1+9x^{2}}\right)$, then $f'!\left(-\dfrac{1}{2}\right)$ equals

Topic: JEE Main 2018 (15 April Evening Shift)

5

Let f(x) = $\left\{ {\matrix{ {{{\left( {x - 1} \right)}^{{1 \over {2 - x}}}},} & {x > 1,x \ne 2} \cr {k…

Topic: JEE Main 2018 (15 April Evening Shift)

6

$\displaystyle \lim_{x\to 0} \frac{x\tan 2x - 2x\tan x}{(1-\cos 2x)^{2}}$ equals :

Topic: JEE Main 2018 (15 April Evening Shift)