1
JEE Main 2021 (Online) 25th July Evening Shift
+4
-1
The value of the

integral $$\int\limits_{ - 1}^1 {\log \left( {x + \sqrt {{x^2} + 1} } \right)dx}$$ is :
A
2
B
0
C
$$-$$1
D
1
2
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
The value of the definite integral $$\int\limits_{\pi /24}^{5\pi /24} {{{dx} \over {1 + \root 3 \of {\tan 2x} }}}$$ is :
A
$${\pi \over 3}$$
B
$${\pi \over 6}$$
C
$${\pi \over {12}}$$
D
$${\pi \over {18}}$$
3
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
The area (in sq. units) of the region, given by the set $$\{ (x,y) \in R \times R|x \ge 0,2{x^2} \le y \le 4 - 2x\}$$ is :
A
$${8 \over 3}$$
B
$${{17} \over 3}$$
C
$${{13} \over 3}$$
D
$${7 \over 3}$$
4
JEE Main 2021 (Online) 25th July Morning Shift
+4
-1
Let $$f:[0,\infty ) \to [0,\infty )$$ be defined as $$f(x) = \int_0^x {[y]dy}$$

where [x] is the greatest integer less than or equal to x. Which of the following is true?
A
f is continuous at every point in $$[0,\infty )$$ and differentiable except at the integer points.
B
f is both continuous and differentiable except at the integer points in $$[0,\infty )$$.
C
f is continuous everywhere except at the integer points in $$[0,\infty )$$.
D
f is differentiable at every point in $$[0,\infty )$$.
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