1
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
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
Change Language
$${\cos ^{ - 1}}(\cos ( - 5)) + {\sin ^{ - 1}}(\sin (6)) - {\tan ^{ - 1}}(\tan (12))$$ is equal to :

(The inverse trigonometric functions take the principal values)
A
3$$\pi$$ $$-$$ 11
B
4$$\pi$$ $$-$$ 9
C
4$$\pi$$ $$-$$ 11
D
3$$\pi$$ + 1
3
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Consider the system of linear equations

$$-$$x + y + 2z = 0

3x $$-$$ ay + 5z = 1

2x $$-$$ 2y $$-$$ az = 7

Let S1 be the set of all a$$\in$$R for which the system is inconsistent and S2 be the set of all a$$\in$$R for which the system has infinitely many solutions. If n(S1) and n(S2) denote the number of elements in S1 and S2 respectively, then
A
n(S1) = 2, n(S2) = 2
B
n(S1) = 1, n(S2) = 0
C
n(S1) = 2, n(S2) = 0
D
n(S1) = 0, n(S2) = 2
4
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Let the acute angle bisector of the two planes x $$-$$ 2y $$-$$ 2z + 1 = 0 and 2x $$-$$ 3y $$-$$ 6z + 1 = 0 be the plane P. Then which of the following points lies on P?
A
$$\left( {3,1, - {1 \over 2}} \right)$$
B
$$\left( { - 2,0, - {1 \over 2}} \right)$$
C
(0, 2, $$-$$4)
D
(4, 0, $$-$$2)
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