1
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
$$\left( { - \sqrt 2 ,0} \right)$$
2
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
3
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
If   $$\int\limits_0^{{\pi \over 3}} {{{\tan \theta } \over {\sqrt {2k\,\sec \theta } }}} \,d\theta = 1 - {1 \over {\sqrt 2 }},\left( {k > 0} \right),$$ then value of k is :
A
4
B
$${1 \over 2}$$
C
1
D
2
4
JEE Main 2019 (Online) 9th January Morning Slot
+4
-1
The value of $$\int\limits_0^\pi {{{\left| {\cos x} \right|}^3}} \,dx$$ is :
A
$$4 \over 3$$
B
$$-$$ $$4 \over 3$$
C
0
D
$$2 \over 3$$
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