JEE Main 2021 (Online) 25th July Evening Shift | Definite Integrals and Applications of Integrals Question 134 | Mathematics

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JEE Main 2021 (Online) 25th July Evening Shift

MCQ (Single Correct Answer)

-1

The value of the

integral $$\int\limits_{ - 1}^1 {\log \left( {x + \sqrt {{x^2} + 1} } \right)dx} $$ is :

$$-$$1

JEE Main 2021 (Online) 25th July Morning Shift

MCQ (Single Correct Answer)

-1

The value of the definite integral $$\int\limits_{\pi /24}^{5\pi /24} {{{dx} \over {1 + \root 3 \of {\tan 2x} }}} $$ is :

$${\pi \over 3}$$

$${\pi \over 6}$$

$${\pi \over {12}}$$

$${\pi \over {18}}$$

JEE Main 2021 (Online) 25th July Morning Shift

MCQ (Single Correct Answer)

-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 :

$${8 \over 3}$$

$${{17} \over 3}$$

$${{13} \over 3}$$

$${7 \over 3}$$

JEE Main 2021 (Online) 25th July Morning Shift

MCQ (Single Correct Answer)

-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?

f is continuous at every point in $$[0,\infty )$$ and differentiable except at the integer points.

f is both continuous and differentiable except at the integer points in $$[0,\infty )$$.

f is continuous everywhere except at the integer points in $$[0,\infty )$$.

f is differentiable at every point in $$[0,\infty )$$.

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