1
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Let f : R $$\to$$ R be a continuous function. Then $$\mathop {\lim }\limits_{x \to {\pi \over 4}} {{{\pi \over 4}\int\limits_2^{{{\sec }^2}x} {f(x)\,dx} } \over {{x^2} - {{{\pi ^2}} \over {16}}}}$$ is equal to :
A
f (2)
B
2f (2)
C
2f $$\left( {\sqrt 2 } \right)$$
D
4f (2)
2
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
The area, enclosed by the curves $$y = \sin x + \cos x$$ and $$y = \left| {\cos x - \sin x} \right|$$ and the lines $$x = 0,x = {\pi \over 2}$$, is :
A
$$2\sqrt 2 (\sqrt 2 - 1)$$
B
$$2(\sqrt 2 + 1)$$
C
$$4(\sqrt 2 - 1)$$
D
$$2\sqrt 2 (\sqrt 2 + 1)$$
3
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
The function f(x), that satisfies the condition
$$f(x) = x + \int\limits_0^{\pi /2} {\sin x.\cos y\,f(y)\,dy} $$, is :
A
$$x + {2 \over 3}(\pi - 2)\sin x$$
B
$$x + (\pi + 2)\sin x$$
C
$$x + {\pi \over 2}\sin x$$
D
$$x + (\pi - 2)\sin x$$
4
JEE Main 2021 (Online) 31st August Evening Shift
MCQ (Single Correct Answer)
+4
-1
If [x] is the greatest integer $$\le$$ x, then

$${\pi ^2}\int\limits_0^2 {\left( {\sin {{\pi x} \over 2}} \right)(x - [x]} {)^{[x]}}dx$$ is equal to :
A
2($$\pi$$ $$-$$ 1)
B
4($$\pi$$ $$-$$ 1)
C
4($$\pi$$ + 1)
D
2($$\pi$$ + 1)
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