1
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
The value of the integral $$\int\limits_{ - 2}^2 {{{{{\sin }^2}x} \over { \left[ {{x \over \pi }} \right] + {1 \over 2}}}} \,dx$$ (where [x] denotes the greatest integer less than or equal to x) is
A
0
B
4
C
4$$-$$ sin 4
D
sin 4
2
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
If  $$\int {{{\sqrt {1 - {x^2}} } \over {{x^4}}}}$$ dx = A(x)$${\left( {\sqrt {1 - {x^2}} } \right)^m}$$ + C, for a suitable chosen integer m and a function A(x), where C is a constant of integration, then (A(x))m equals :
A
$${1 \over {27{x^6}}}$$
B
$${{ - 1} \over {27{x^9}}}$$
C
$${1 \over {9{x^4}}}$$
D
$${1 \over {3{x^3}}}$$
3
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
The area (in sq. units) of the region bounded by the curve x2 = 4y and the straight line x = 4y – 2 is :
A
$${3 \over 4}$$
B
$${5 \over 4}$$
C
$${7 \over 8}$$
D
$${9 \over 8}$$
4
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
The value of   $$\int\limits_{ - \pi /2}^{\pi /2} {{{dx} \over {\left[ x \right] + \left[ {\sin x} \right] + 4}}} ,$$  where [t] denotes the greatest integer less than or equal to t, is
A
$${1 \over {12}}\left( {7\pi - 5} \right)$$
B
$${1 \over {12}}\left( {7\pi + 5} \right)$$
C
$${3 \over {10}}\left( {4\pi - 3} \right)$$
D
$${3 \over {20}}\left( {4\pi - 3} \right)$$
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