1
JEE Main 2021 (Online) 24th February Morning Slot
+4
-1
$$\mathop {\lim }\limits_{x \to 0} {{\int\limits_0^{{x^2}} {\left( {\sin \sqrt t } \right)dt} } \over {{x^3}}}$$ is equal to :
A
$${1 \over {15}}$$
B
0
C
$${2 \over 3}$$
D
$${3 \over 2}$$
2
JEE Main 2021 (Online) 24th February Morning Slot
+4
-1
The area (in sq. units) of the part of the circle x2 + y2 = 36, which is outside the parabola y2 = 9x, is :
A
$$12\pi - 3\sqrt 3$$
B
$$24\pi + 3\sqrt 3$$
C
$$24\pi - 3\sqrt 3$$
D
$$12\pi + 3\sqrt 3$$
3
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
The integral $$\int\limits_1^2 {{e^x}.{x^x}\left( {2 + {{\log }_e}x} \right)} dx$$ equals :
A
e(4e + 1)
B
e(2e – 1)
C
e(4e – 1)
D
4e2 – 1
4
JEE Main 2020 (Online) 6th September Evening Slot
+4
-1
The area (in sq. units) of the region enclosed
by the curves y = x2 – 1 and y = 1 – x2 is equal to :
A
$${8 \over 3}$$
B
$${4 \over 3}$$
C
$${7 \over 2}$$
D
$${{16} \over 3}$$
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