1
JEE Main 2014 (Offline)
MCQ (Single Correct Answer)
+4
-1
The integral $$\int\limits_0^\pi {\sqrt {1 + 4{{\sin }^2}{x \over 2} - 4\sin {x \over 2}{\mkern 1mu} } } dx$$ equals:
A
$$4\sqrt 3 - 4$$
B
$$4\sqrt 3 - 4 - {\pi \over 3}$$
C
$$\pi - 4$$
D
$${{2\pi } \over 3} - 4 - 4\sqrt 3 $$
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
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
$$\pi \log 2$$
4
AIEEE 2010
MCQ (Single Correct Answer)
+4
-1
Let $$p(x)$$ be a function defined on $$R$$ such that $$p'(x)=p'(1-x),$$ for all $$x \in \left[ {0,1} \right],p\left( 0 \right) = 1$$ and $$p(1)=41.$$ Then $$\int\limits_0^1 {p\left( x \right)dx} $$ equals :
A
$$21$$
B
$$41$$
C
$$42$$
D
$$\sqrt {41} $$
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