1
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.
2
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
$${{27} \over 4}$$
3
AIEEE 2012
MCQ (Single Correct Answer)
+4
-1
The area between the parabolas $${x^2} = {y \over 4}$$ and $${x^2} = 9y$$ and the straight line $$y=2$$ is :
A
$$20\sqrt 2 $$
B
$${{10\sqrt 2 } \over 3}$$
C
$${{20\sqrt 2 } \over 3}$$
D
$$10\sqrt 2 $$
4
AIEEE 2011
MCQ (Single Correct Answer)
+4
-1
The value of $$\int\limits_0^1 {{{8\log \left( {1 + x} \right)} \over {1 + {x^2}}}} dx$$ is
A
$${\pi \over 8}\log 2$$
B
$${\pi \over 2}\log 2$$
C
$$\log 2$$
D
$$\pi \log 2$$
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