1
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1

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

A
$$10(\pi+4)$$
B
$$10(\pi+2)$$
C
$$20(\pi-2)$$
D
$$20(\pi+2)$$
2
JEE Main 2022 (Online) 26th July Evening Shift
+4
-1

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

A
$$\frac{2}{3}(\sqrt{2}+1)$$
B
$$\frac{4}{3}(\sqrt{2}-1)$$
C
$$2(\sqrt{2}-1)$$
D
$$\frac{8}{3}(\sqrt{2}-1)$$
3
JEE Main 2022 (Online) 26th July Morning Shift
+4
-1

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

A
3
B
5
C
7
D
9
4
JEE Main 2022 (Online) 26th July Morning Shift
+4
-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 :

A
$$2\sqrt 2 f\left( {{a \over 2}} \right) = f'\left( {{a \over 2}} \right)$$
B
$$f\left( {{a \over 2}} \right)f'\left( {{a \over 2}} \right) = \sqrt 2$$
C
$$\sqrt 2 f\left( {{a \over 2}} \right) = f'\left( {{a \over 2}} \right)$$
D
$$f\left( {{a \over 2}} \right) = \sqrt 2 f'\left( {{a \over 2}} \right)$$
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