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1

### JEE Advanced 2014 Paper 2 Offline

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
$$\int\limits_0^{\log \left( {1 + \sqrt 2 } \right)} {2{{\left( {{e^u} - {e^{ - u}}} \right)}^{16}}\,du}$$
2

### JEE Advanced 2013 Paper 1 Offline

Let $$f$$ $$:\,\,\left[ {{1 \over 2},1} \right] \to R$$ (the set of all real number) be a positive,
non-constant and differentiable function such that
$$f'\left( x \right) < 2f\left( x \right)$$ and $$f\left( {{1 \over 2}} \right) = 1.$$ Then the value of $$\int\limits_{1/2}^1 {f\left( x \right)} \,dx$$ lies in the interval
A
$$\left( {2e - 1,2e} \right)$$
B
$$\left( {e - 1,\,2e - 1} \right)$$
C
$$\left( {{{e - 1} \over 2},e - 1} \right)$$
D
$$\left( {0,{{e - 1} \over 2}} \right)$$
3

### JEE Advanced 2013 Paper 1 Offline

The area enclosed by the curves $$y = \sin x + {\mathop{\rm cosx}\nolimits}$$ and $$y = \left| {\cos x - \sin x} \right|$$ over the interval $$\left[ {0,{\pi \over 2}} \right]$$ is
A
$$4\left( {\sqrt 2 - 1} \right)$$
B
$$2\sqrt 2 \left( {\sqrt 2 - 1} \right)$$
C
$$2\left( {\sqrt 2 + 1} \right)$$
D
$$2\sqrt 2 \left( {\sqrt 2 + 1} \right)$$
4

### IIT-JEE 2012 Paper 2 Offline

The value of the integral $$\int\limits_{ - \pi /2}^{\pi /2} {\left( {{x^2} + 1n{{\pi + x} \over {\pi - x}}} \right)\cos xdx}$$ is
A
$$0$$
B
$${{{\pi ^2}} \over 2} - 4$$
C
$${{{\pi ^2}} \over 2} + 4$$
D
$${{{\pi ^2}} \over 2}$$

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NEET

Class 12