1
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
The intercepts on $$x$$-axis made by tangents to the curve,
$$y = \int\limits_0^x {\left| t \right|dt,x \in R,} $$ which are parallel to the line $$y=2x$$, are equal to :
A
$$ \pm 1$$
B
$$ \pm 2$$
C
$$ \pm 3$$
D
$$ \pm 4$$
2
JEE Main 2013 (Offline)
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
If $$P = \left[ {\matrix{ 1 & \alpha & 3 \cr 1 & 3 & 3 \cr 2 & 4 & 4 \cr } } \right]$$ is the adjoint of a $$3 \times 3$$ matrix $$A$$ and
$$\left| A \right| = 4,$$ then $$\alpha $$ is equal to :
A
$$4$$
B
$$11$$
C
$$5$$
D
$$0$$
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
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.
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