1
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
The integral $$\int_{{\pi \over {12}}}^{{\pi \over 4}} {\,\,{{8\cos 2x} \over {{{\left( {\tan x + \cot x} \right)}^3}}}} \,dx$$ equals :
A
$${{15} \over {128}}$$
B
$${{15} \over {64}}$$
C
$${{13} \over {32}}$$
D
$${{13} \over {256}}$$
2
JEE Main 2017 (Offline)
+4
-1
The integral $$\int\limits_{{\pi \over 4}}^{{{3\pi } \over 4}} {{{dx} \over {1 + \cos x}}}$$ is equal to
A
2
B
4
C
$$-$$ 1
D
$$-$$ 2
3
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
The value of the integral

$$\int\limits_4^{10} {{{\left[ {{x^2}} \right]dx} \over {\left[ {{x^2} - 28x + 196} \right] + \left[ {{x^2}} \right]}}} ,$$

where [x] denotes the greatest integer less than or equal to x, is :
A
6
B
3
C
7
D
$${1 \over 3}$$
4
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
For x $$\in$$ R, x $$\ne$$ 0, if y(x) is a differentiable function such that

x $$\int\limits_1^x y$$ (t) dt = (x + 1) $$\int\limits_1^x ty$$ (t) dt,  then y (x) equals :

(where C is a constant.)
A
$${C \over x}{e^{ - {1 \over x}}}$$
B
$${C \over {{x^2}}}{e^{ - {1 \over x}}}$$
C
$${C \over {{x^3}}}{e^{ - {1 \over x}}}$$
D
$$C{x^3}\,{1 \over {{e^x}}}$$
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