1
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
$$\int_{a + 1}^{b + 1} {f(x)dx}$$
2
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
$$-{1 \over 2}$$
3
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
$${1 \over 2}$$
4
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
Let f : R $$\to$$ R be a continuously differentiable function such that f(2) = 6 and f'(2) = $${1 \over {48}}$$. If $$\int\limits_6^{f\left( x \right)} {4{t^3}} dt$$ = (x - 2)g(x), then $$\mathop {\lim }\limits_{x \to 2} g\left( x \right)$$ is equal to :
A
18
B
36
C
12
D
24
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