JEE Main 2022 (Online) 26th July Evening Shift | Definite Integrals and Applications of Integrals Question 56 | Mathematics

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JEE Main 2022 (Online) 26th July Evening Shift

MCQ (Single Correct Answer)

-1

$$ \int\limits_{0}^{20 \pi}(|\sin x|+|\cos x|)^{2} d x \text { is equal to } $$

$$10(\pi+4)$$

$$10(\pi+2)$$

$$20(\pi-2)$$

$$20(\pi+2)$$

JEE Main 2022 (Online) 26th July Evening Shift

MCQ (Single Correct Answer)

-1

The area bounded by the curves $$y=\left|x^{2}-1\right|$$ and $$y=1$$ is

$$\frac{2}{3}(\sqrt{2}+1)$$

$$\frac{4}{3}(\sqrt{2}-1)$$

$$2(\sqrt{2}-1)$$

$$\frac{8}{3}(\sqrt{2}-1)$$

JEE Main 2022 (Online) 26th July Morning Shift

MCQ (Single Correct Answer)

-1

The odd natural number a, such that the area of the region bounded by y = 1, y = 3, x = 0, x = y^a is $${{364} \over 3}$$, is equal to :

JEE Main 2022 (Online) 26th July Morning Shift

MCQ (Single Correct Answer)

-1

If $$a = \mathop {\lim }\limits_{n \to \infty } \sum\limits_{k = 1}^n {{{2n} \over {{n^2} + {k^2}}}} $$ and $$f(x) = \sqrt {{{1 - \cos x} \over {1 + \cos x}}} $$, $$x \in (0,1)$$, then :

$$2\sqrt 2 f\left( {{a \over 2}} \right) = f'\left( {{a \over 2}} \right)$$

$$f\left( {{a \over 2}} \right)f'\left( {{a \over 2}} \right) = \sqrt 2 $$

$$\sqrt 2 f\left( {{a \over 2}} \right) = f'\left( {{a \over 2}} \right)$$

$$f\left( {{a \over 2}} \right) = \sqrt 2 f'\left( {{a \over 2}} \right)$$

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