1
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
Out of Syllabus
If    $$\mathop {\lim }\limits_{n \to \infty } \,\,{{{1^a} + {2^a} + ...... + {n^a}} \over {{{(n + 1)}^{a - 1}}\left[ {\left( {na + 1} \right) + \left( {na + 2} \right) + ..... + \left( {na + n} \right)} \right]}} = {1 \over {60}}$$

for some positive real number a, then a is equal to :
A
7
B
8
C
$${{15} \over 2}$$
D
$${{17} \over 2}$$
2
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
$${{13} \over {256}}$$
3
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
4
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
$${1 \over 3}$$
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