1
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
$${1 \over 2}$$
2
JEE Main 2019 (Online) 12th April Morning Slot
+4
-1
If the area (in sq. units) of the region {(x, y) : y2 $$\le$$ 4x, x + y $$\le$$ 1, x $$\ge$$ 0, y $$\ge$$ 0} is a $$\sqrt 2$$ + b, then a – b is equal to :
A
$${8 \over 3}$$
B
$$- {2 \over 3}$$
C
6
D
$${{10} \over 3}$$
3
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
4
JEE Main 2019 (Online) 10th April Evening Slot
+4
-1
The area (in sq.units) of the region bounded by the curves y = 2x and y = |x + 1|, in the first quadrant is :
A
$${1 \over 2}$$
B
$${3 \over 2}$$
C
$${3 \over 2} - {1 \over {\log _e^2}}$$
D
$$\log _e^2 + {3 \over 2}$$
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