1
JEE Advanced 2016 Paper 2 Offline
+3
-1
The value of $$\int\limits_{-{\pi \over 2}}^{{\pi \over 2}} {{{{x^2}\cos x} \over {1 + {e^x}}}dx}$$ is equal to
A
$${{{\pi ^2}} \over 4} - 2$$
B
$${{{\pi ^2}} \over 4} + 2$$
C
$${\pi ^2} - {e^{{\pi \over 2}}}$$
D
$${\pi ^2} + {e^{{\pi \over 2}}}$$
2
JEE Advanced 2015 Paper 2 Offline
+4
-1
Let $$f'\left( x \right) = {{192{x^3}} \over {2 + {{\sin }^4}\,\pi x}}$$ for all $$x \in R\,\,$$ with $$f\left( {{1 \over 2}} \right) = 0$$.
If $$m \le \int\limits_{1/2}^1 {f\left( x \right)dx \le M,}$$ then the possible values of $$m$$ and $$M$$ are
A
$$m=13,$$ $$M=24$$
B
$$\,m = {1 \over 4},M = {1 \over 2}$$
C
$$m=-11,$$ $$M=0$$
D
$$m=1,$$ $$M=12$$
3
JEE Advanced 2014 Paper 2 Offline
+3
-1
The following integral $$\int\limits_{{\pi \over 4}}^{{\pi \over 2}} {{{\left( {2\cos ec\,\,x} \right)}^{17}}dx}$$ is equal to
A
$$\int\limits_0^{\log \left( {1 + \sqrt 2 } \right)} {2{{\left( {{e^u} + {e^{ - u}}} \right)}^{16}}\,du}$$
B
$$\int\limits_0^{\log \left( {1 + \sqrt 2 } \right)} {{{\left( {{e^u} + {e^{ - u}}} \right)}^{17}}\,du}$$
C
$$\int\limits_0^{\log \left( {1 + \sqrt 2 } \right)} {{{\left( {{e^u} - {e^{ - u}}} \right)}^{17}}\,du}$$
D
$$\int\limits_0^{\log \left( {1 + \sqrt 2 } \right)} {2{{\left( {{e^u} - {e^{ - u}}} \right)}^{16}}\,du}$$
4
JEE Advanced 2014 Paper 2 Offline
+3
-1
List - $$I$$
P.$$\,\,\,\,$$ The number of polynomials $$f(x)$$ with non-negative integer coefficients of degree $$\le 2$$, satisfying $$f(0)=0$$ and $$\int_0^1 {f\left( x \right)dx = 1,}$$ is
Q.$$\,\,\,\,$$ The number of points in the interval $$\left[ { - \sqrt {13} ,\sqrt {13} } \right]$$
at which $$f\left( x \right) = \sin \left( {{x^2}} \right) + \cos \left( {{x^2}} \right)$$ attains its maximum value, is
R.$$\,\,\,\,$$ $$\int\limits_{ - 2}^2 {{{3{x^2}} \over {\left( {1 + {e^x}} \right)}}dx}$$ equals
S.$$\,\,\,\,$$ $${{\left( {\int\limits_{ - {1 \over 2}}^{{1 \over 2}} {\cos 2x\log \left( {{{1 + x} \over {1 - x}}} \right)dx} } \right)} \over {\left( {\int\limits_0^{{1 \over 2}} {\cos 2x\log \left( {{{1 + x} \over {1 - x}}} \right)dx} } \right)}}$$

List $$II$$
1.$$\,\,\,\,$$ $$8$$
2.$$\,\,\,\,$$ $$2$$
3.$$\,\,\,\,$$ $$4$$
4.$$\,\,\,\,$$ $$0$$

A
$$P = 3,Q = 2,R = 4,S = 1$$
B
$$P = 2,Q = 3,R = 4,S = 1$$
C
$$P = 3,Q = 2,R = 1,S = 4$$
D
$$P = 2,Q = 3,R = 1,S = 4$$
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