1
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+4
-1
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 :
A
$$9$$
B
$$36$$
C
$$18$$
D
$${{27} \over 4}$$
2
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+4
-1
Statement-1 : The value of the integral
$$\int\limits_{\pi /6}^{\pi /3} {{{dx} \over {1 + \sqrt {\tan \,x} }}} $$ is equal to $$\pi /6$$

Statement-2 : $$\int\limits_a^b {f\left( x \right)} dx = \int\limits_a^b {f\left( {a + b - x} \right)} dx.$$

A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
C
Statement- 1 is true; Statement-2 is False.
D
Statement-1 is false; Statement-2 is true.
3
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+4
-1
If $$\int {f\left( x \right)dx = \psi \left( x \right),} $$ then $$\int {{x^5}f\left( {{x^3}} \right)dx} $$ is equal to
A
$${1 \over 3}\left[ {{x^3}\psi \left( {{x^3}} \right) - \int {{x^2}\psi \left( {{x^3}} \right)dx} } \right] + C$$
B
$${1 \over 3}{x^3}\psi \left( {{x^3}} \right) - 3\int {{x^3}\psi \left( {{x^3}} \right)dx} + C$$
C
$${1 \over 3}{x^3}\psi \left( {{x^3}} \right) - \int {{x^2}\psi \left( {{x^3}} \right)dx} + C$$
D
$${1 \over 3}\left[ {{x^3}\psi \left( {{x^3}} \right) - \int {{x^3}\psi \left( {{x^3}} \right)dx} } \right] + C$$
4
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+4
-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 :
A
$$x=y=z$$
B
$$2x=3y=6z$$
C
$$6x=3y=2z$$
D
$$6x=4y=3z$$
JEE Main Papers
2023
2021
EXAM MAP