1
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
If $$\theta$$1 and $$\theta$$2 be respectively the smallest and the largest values of $$\theta$$ in (0, 2$$\pi$$) - {$$\pi$$} which satisfy the equation,
2cot2$$\theta$$ - $${5 \over {\sin \theta }}$$ + 4 = 0, then
$$\int\limits_{{\theta _1}}^{{\theta _2}} {{{\cos }^2}3\theta d\theta }$$ is equal to :
A
$${\pi \over 9}$$
B
$${{2\pi } \over 3}$$
C
$${{\pi } \over 3}$$
D
$${\pi \over 3} + {1 \over 6}$$
2
JEE Main 2020 (Online) 7th January Morning Slot
+4
-1
If ƒ(a + b + 1 - x) = ƒ(x), for all x, where a and b are fixed positive real numbers, then

$${1 \over {a + b}}\int_a^b {x\left( {f(x) + f(x + 1)} \right)} dx$$ is equal to:
A
$$\int_{a - 1}^{b - 1} {f(x+1)dx}$$
B
$$\int_{a + 1}^{b + 1} {f(x + 1)dx}$$
C
$$\int_{a - 1}^{b - 1} {f(x)dx}$$
D
$$\int_{a + 1}^{b + 1} {f(x)dx}$$
3
JEE Main 2019 (Online) 12th April Evening Slot
+4
-1
A value of $$\alpha$$ such that
$$\int\limits_\alpha ^{\alpha + 1} {{{dx} \over {\left( {x + \alpha } \right)\left( {x + \alpha + 1} \right)}}} = {\log _e}\left( {{9 \over 8}} \right)$$ is :
A
2
B
- 2
C
$${1 \over 2}$$
D
$$-{1 \over 2}$$
4
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
If $$\int\limits_0^{{\pi \over 2}} {{{\cot x} \over {\cot x + \cos ecx}}} dx$$ = m($$\pi$$ + n), then m.n is equal to
A
- 1
B
1
C
$$- {1 \over 2}$$
D
$${1 \over 2}$$
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