Trigonometry
Inverse Trigonometric Functions
MCQ (Single Correct Answer)Subjective
1
WB JEE 2011
MCQ (Single Correct Answer)
+1
-0.25

If f(x + 2y, x $$-$$ 2y) = xy, then f(x, y) is equal to

A
$${1 \over 4}xy$$
B
$${1 \over 4}({x^2} - {y^2})$$
C
$${1 \over 8}({x^2} - {y^2})$$
D
$${1 \over 2}({x^2} + {y^2})$$
2
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25

If $g(f(x))=|\sin x|$ and $f(g(x))=(\sin \sqrt{x})^2$, then

A
$f(x)=\sin ^2 x, g(x)=\sqrt{x}$
B
$f(x)=\sin x, g(x)=|x|$
C
$f(x)=x^2, g(x)=\sin \sqrt{x}$
D
$f(x)=|x|, g(x)=\sin x$
3
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5

If $f(x)=\frac{3 x-4}{2 x-3}$, then $f(f(f(x)))$ will be

A
$x$
B
$2 x$
C
$\frac{2 x-3}{3 x-4}$
D
$\frac{3 x-4}{2 x-3}$
4
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5

Let $u+v+w=3, u, v, w \in \mathbb{R}$ and $f(x)=u x^2+v x+w$ be such that $f(x+y)=f(x)+f(y)+x y$, $\forall x, y \in \mathbb{R}$. Then $f(1)$ is equal to

A
$\frac{5}{2}$
B
$\frac{1}{2}$
C
$\frac{1}{\sqrt{2}}$
D
$3$
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