Javascript is required
1
JEE Main 2021 (Online) 20th July Morning Shift
MCQ (Single Correct Answer)  +4  -1
Let a be a positive real number such that $$\int_0^a {{e^{x - [x]}}} dx = 10e - 9$$ where [ x ] is the greatest integer less than or equal to x. Then a is equal to:
A
$$10 - {\log _e}(1 + e)$$
B
$$10 + {\log _e}2$$
C
$$10 + {\log _e}3$$
D
$$10 + {\log _e}(1 + e)$$
2
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
$$2{\log _e}2 + {\pi \over 2} - {1 \over 2}$$
3
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
$${3\pi \over {8}}$$
4
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
$$\left[ {{1 \over 3},2} \right]$$
JEE Main Subjects
© 2023 ExamGOAL