1
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
2
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
3
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
$$2 \over 3$$
4
JEE Main 2018 (Online) 16th April Morning Slot
+4
-1
If $$f(x) = \int\limits_0^x {t\left( {\sin x - \sin t} \right)dt\,\,\,}$$ then :
A
f'''(x) + f''(x) = sinx
B
f'''(x) + f''(x) $$-$$ f'(x) = cosx
C
f'''(x) + f'(x) = cosx $$-$$ 2x sinx
D
f'''(x) $$-$$ f''(x) = cosx $$-$$ 2x sinx
EXAM MAP
Medical
NEET