Javascript is required
1
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Let $$g(t) = \int_{ - \pi /2}^{\pi /2} {\cos \left( {{\pi \over 4}t + f(x)} \right)} dx$$, where $$f(x) = {\log _e}\left( {x + \sqrt {{x^2} + 1} } \right),x \in R$$. Then which one of the following is correct?
A
g(1) = g(0)
B
$$\sqrt 2 g(1) = g(0)$$
C
$$g(1) = \sqrt 2 g(0)$$
D
g(1) + g(0) = 0
2
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
$$10 + {\log _e}(1 + e)$$
3
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
$$2{\log _e}2 + {\pi \over 2} - {1 \over 2}$$
4
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
$${3\pi \over {8}}$$
JEE Main Subjects
© 2023 ExamGOAL