1
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
The value of $$\int\limits_0^{2\pi } {\left[ {\sin 2x\left( {1 + \cos 3x} \right)} \right]} dx$$,
where [t] denotes the greatest integer function is :
A
2$$\pi$$
B
$$\pi$$
C
-2$$\pi$$
D
-$$\pi$$
2
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
Out of Syllabus
$$\mathop {\lim }\limits_{n \to \infty } \left( {{{{{(n + 1)}^{1/3}}} \over {{n^{4/3}}}} + {{{{(n + 2)}^{1/3}}} \over {{n^{4/3}}}} + ....... + {{{{(2n)}^{1/3}}} \over {{n^{4/3}}}}} \right)$$
is equal to :
A
$${4 \over 3}{\left( 2 \right)^{3/4}}$$
B
$${3 \over 4}{\left( 2 \right)^{4/3}} - {3 \over 4}$$
C
$${4 \over 3}{\left( 2 \right)^{4/3}}$$
D
$${3 \over 4}{\left( 2 \right)^{4/3}} - {4 \over 3}$$
3
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
The value of the integral $$\int\limits_0^1 {x{{\cot }^{ - 1}}(1 - {x^2} + {x^4})dx}$$ is :-
A
$${\pi \over 2} - {1 \over 2}{\log _e}2$$
B
$${\pi \over 4} - {\log _e}2$$
C
$${\pi \over 4} - {1 \over 2}{\log _e}2$$
D
$${\pi \over 2} - {\log _e}2$$
4
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
If f : R $$\to$$ R is a differentiable function and f(2) = 6,
then $$\mathop {\lim }\limits_{x \to 2} {{\int\limits_6^{f\left( x \right)} {2tdt} } \over {\left( {x - 2} \right)}}$$ is :-
A
2f'(2)
B
24f'(2)
C
0
D
12f'(2)
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