1
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
$${3 \over {20}}\left( {4\pi - 3} \right)$$
2
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
If  $$\int\limits_0^x \,$$f(t) dt = x2 + $$\int\limits_x^1 \,$$ t2f(t) dt then f '$$\left( {{1 \over 2}} \right)$$ is -
A
$${{18} \over {25}}$$
B
$${{6} \over {25}}$$
C
$${{24} \over {25}}$$
D
$${{4} \over {5}}$$
3
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
Let  $${\rm I} = \int\limits_a^b {\left( {{x^4} - 2{x^2}} \right)} dx.$$  If I is minimum then the ordered pair (a, b) is -
A
$$\left( {\sqrt 2 , - \sqrt 2 } \right)$$
B
$$\left( {0,\sqrt 2 } \right)$$
C
$$\left( { - \sqrt 2 ,\sqrt 2 } \right)$$
D
$$\left( { - \sqrt 2 ,0} \right)$$
4
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
Let f be a differentiable function from

R to R such that $$\left| {f\left( x \right) - f\left( y \right)} \right| \le 2{\left| {x - y} \right|^{{3 \over 2}}},$$

for all  $$x,y \in$$ R.

If   $$f\left( 0 \right) = 1$$

then   $$\int\limits_0^1 {{f^2}} \left( x \right)dx$$  is equal to :
A
1
B
2
C
$${1 \over 2}$$
D
0
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