1
JEE Main 2016 (Offline)
+4
-1
Out of Syllabus
$$\mathop {\lim }\limits_{n \to \infty } {\left( {{{\left( {n + 1} \right)\left( {n + 2} \right)...3n} \over {{n^{2n}}}}} \right)^{{1 \over n}}}$$ is equal to:
A
$${9 \over {{e^2}}}$$
B
$$3\,\log \,3 - 2$$
C
$${{18} \over {{e^4}}}$$
D
$${{27} \over {{e^2}}}$$
2
JEE Main 2015 (Offline)
+4
-1
The integral
$$\int\limits_2^4 {{{\log \,{x^2}} \over {\log {x^2} + \log \left( {36 - 12x + {x^2}} \right)}}dx}$$ is equal to :
A
$$1$$
B
$$6$$
C
$$2$$
D
$$4$$
3
JEE Main 2014 (Offline)
+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
$${{2\pi } \over 3} - 4 - 4\sqrt 3$$
4
JEE Main 2013 (Offline)
+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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