If $\int f(x)\,dx=\psi(x)$, then $\int x^{5}f(x^{3})\,dx$ is equal to

1

Statement-1 : The value of the integral $\displaystyle \int_{\pi/6}^{\pi/3}\frac{dx}{1+\sqrt{\tan x}}$ is equal to $\pi…

Topic: JEE Main 2013 (Offline)

2

The area (in square units) bounded by the curves $y=\sqrt{x}$, $2y-x+3=0$, $x$-axis, and lying in the first quadrant is…

Topic: JEE Main 2013 (Offline)

3

At present, a firm is manufacturing $2000$ items. It is estimated that the rate of change of production $P$ w.r.t. addi…

Topic: JEE Main 2013 (Offline)

4

$\displaystyle \lim_{x\to 0}\frac{(1-\cos 2x)(3+\cos x)}{x\tan 4x}$ is equal to :

Topic: JEE Main 2013 (Offline)

5

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of…

Topic: JEE Main 2013 (Offline)

6

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of AXB having 3 or mor…

Topic: JEE Main 2013 (Offline)

1

If $x,y,z$ are in A.P. and $\tan^{-1}x,\tan^{-1}y$ and $\tan^{-1}z$ are also in A.P., then :

Topic: JEE Main 2013 (Offline)

2

If $y=\sec(\tan^{-1}x)$, then $\dfrac{dy}{dx}$ at $x=1$ is equal to :

Topic: JEE Main 2013 (Offline)

3

The equation of the circle passing through the foci of the ellipse $\dfrac{x^{2}}{16}+\dfrac{y^{2}}{9}=1$, and having c…

Topic: JEE Main 2013 (Offline)

4

The $x$-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as $(0,1)$, $(1,…

Topic: JEE Main 2013 (Offline)

5

A ray of light along $x+\sqrt{3}\,y=\sqrt{3}$ gets reflected upon reaching $X$-axis, the equation of the reflected ray …

Topic: JEE Main 2013 (Offline)

6

The term independent of $x$ in expansion of $\left(\dfrac{x+1}{x^{2/3}-x^{1/3}+1}-\dfrac{x-1}{x-x^{1/2}}\right)^{10}$ is

Topic: JEE Main 2013 (Offline)

7

Let $T_{n}$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{…

Topic: JEE Main 2013 (Offline)

8

If the equations $x^{2}+2x+3=0$ and $ax^{2}+bx+c=0$, $a,b,c\in\mathbb{R}$, have a common root, then $a:b:c$ is

Topic: JEE Main 2013 (Offline)

9

The real number $k$ for which the equation $2x^{3}+3x+k=0$ has two distinct real roots in $[0,1]$

Topic: JEE Main 2013 (Offline)

10

The number of values of $k$, for which the system of equations : $\matrix{ {\left( {k + 1} \right)x + 8y = 4k} \cr …

Topic: JEE Main 2013 (Offline)