1
JEE Main 2022 (Online) 26th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

$$16\sin (20^\circ )\sin (40^\circ )\sin (80^\circ )$$ is equal to :

A
$$\sqrt 3 $$
B
2$$\sqrt 3 $$
C
3
D
4$$\sqrt 3 $$
2
JEE Main 2022 (Online) 26th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

If the inverse trigonometric functions take principal values then

$${\cos ^{ - 1}}\left( {{3 \over {10}}\cos \left( {{{\tan }^{ - 1}}\left( {{4 \over 3}} \right)} \right) + {2 \over 5}\sin \left( {{{\tan }^{ - 1}}\left( {{4 \over 3}} \right)} \right)} \right)$$ is equal to :

A
0
B
$${\pi \over 4}$$
C
$${\pi \over 3}$$
D
$${\pi \over 6}$$
3
JEE Main 2022 (Online) 26th June Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let r $$\in$$ {p, q, $$\sim$$p, $$\sim$$q} be such that the logical statement

r $$\vee$$ ($$\sim$$p) $$\Rightarrow$$ (p $$\wedge$$ q) $$\vee$$ r

is a tautology. Then r is equal to :

A
p
B
q
C
$$\sim$$p
D
$$\sim$$q
4
JEE Main 2022 (Online) 26th June Evening Shift
Numerical
+4
-1
Change Language

Let f : R $$\to$$ R satisfy $$f(x + y) = {2^x}f(y) + {4^y}f(x)$$, $$\forall$$x, y $$\in$$ R. If f(2) = 3, then $$14.\,{{f'(4)} \over {f'(2)}}$$ is equal to ____________.

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