1
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1
The value of
$$\int\limits_0^{2\pi } {{{x{{\sin }^8}x} \over {{{\sin }^8}x + {{\cos }^8}x}}} dx$$ is equal to :
A
4$$\pi$$
B
2$$\pi$$
C
$$\pi$$2
D
2$$\pi$$2
2
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1
If for all real triplets (a, b, c), ƒ(x) = a + bx + cx2; then $$\int\limits_0^1 {f(x)dx}$$ is equal to :
A
$${1 \over 6}\left\{ {f(0) + f(1) + 4f\left( {{1 \over 2}} \right)} \right\}$$
B
$$2\left\{ 3{f(1) + 2f\left( {{1 \over 2}} \right)} \right\}$$
C
$${1 \over 3}\left\{ {f(0) + f\left( {{1 \over 2}} \right)} \right\}$$
D
$${1 \over 2}\left\{ {f(1) + 3f\left( {{1 \over 2}} \right)} \right\}$$
3
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
If $$I = \int\limits_1^2 {{{dx} \over {\sqrt {2{x^3} - 9{x^2} + 12x + 4} }}}$$, then :
A
$${1 \over 16} < {I^2} < {1 \over 9}$$
B
$${1 \over 8} < {I^2} < {1 \over 4}$$
C
$${1 \over 9} < {I^2} < {1 \over 8}$$
D
$${1 \over 6} < {I^2} < {1 \over 2}$$
4
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
$$\mathop {\lim }\limits_{x \to 0} {{\int_0^x {t\sin \left( {10t} \right)dt} } \over x}$$ is equal to
A
$$- {1 \over 5}$$
B
$$- {1 \over 10}$$
C
0
D
$${1 \over 10}$$
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