1
JEE Main 2020 (Online) 7th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
The value of $$\alpha $$ for which
$$4\alpha \int\limits_{ - 1}^2 {{e^{ - \alpha \left| x \right|}}dx} = 5$$, is:
A
$${\log _e}2$$
B
$${\log _e}\sqrt 2 $$
C
$${\log _e}\left( {{4 \over 3}} \right)$$
D
$${\log _e}\left( {{3 \over 2}} \right)$$
2
JEE Main 2020 (Online) 7th January Evening Slot
MCQ (Single Correct Answer)
+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
$${\pi \over 3} + {1 \over 6}$$
3
JEE Main 2020 (Online) 7th January Morning Slot
MCQ (Single Correct Answer)
+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
$$\int_{a + 1}^{b + 1} {f(x)dx} $$
4
JEE Main 2019 (Online) 12th April Evening Slot
MCQ (Single Correct Answer)
+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
$$-{1 \over 2}$$
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