1
JEE Main 2021 (Online) 20th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
The value of the integral $$\int\limits_{ - 1}^1 {{{\log }_e}(\sqrt {1 - x} + \sqrt {1 + x} )dx} $$ is equal to:
A
$${1 \over 2}{\log _e}2 + {\pi \over 4} - {3 \over 2}$$
B
$$2{\log _e}2 + {\pi \over 4} - 1$$
C
$${\log _e}2 + {\pi \over 2} - 1$$
D
$$2{\log _e}2 + {\pi \over 2} - {1 \over 2}$$
2
JEE Main 2021 (Online) 18th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
The area bounded by the curve 4y2 = x2(4 $$-$$ x)(x $$-$$ 2) is equal to :
A
$${\pi \over {16}}$$
B
$${\pi \over {8}}$$
C
$${3\pi \over {2}}$$
D
$${3\pi \over {8}}$$
3
JEE Main 2021 (Online) 18th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Let g(x) = $$\int_0^x {f(t)dt} $$, where f is continuous function in [ 0, 3 ] such that $${1 \over 3}$$ $$ \le $$ f(t) $$ \le $$ 1 for all t$$\in$$ [0, 1] and 0 $$ \le $$ f(t) $$ \le $$ $${1 \over 2}$$ for all t$$\in$$ (1, 3]. The largest possible interval in which g(3) lies is :
A
$$\left[ { - 1, - {1 \over 2}} \right]$$
B
$$\left[ { - {3 \over 2}, - 1} \right]$$
C
[1, 3]
D
$$\left[ {{1 \over 3},2} \right]$$
4
JEE Main 2021 (Online) 17th March Evening Shift
MCQ (Single Correct Answer)
+4
-1
Let f : R $$ \to $$ R be defined as f(x) = e$$-$$xsinx. If F : [0, 1] $$ \to $$ R is a differentiable function with that F(x) = $$\int_0^x {f(t)dt} $$, then the value of $$\int_0^1 {(F'(x) + f(x)){e^x}dx} $$ lies in the interval
A
$$\left[ {{{331} \over {360}},{{334} \over {360}}} \right]$$
B
$$\left[ {{{330} \over {360}},{{331} \over {360}}} \right]$$
C
$$\left[ {{{335} \over {360}},{{336} \over {360}}} \right]$$
D
$$\left[ {{{327} \over {360}},{{329} \over {360}}} \right]$$
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