1
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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
$f(x)=|x|, g(x)=\sin x$
2
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5
Change Language

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
$\frac{3 x-4}{2 x-3}$
3
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5
Change Language

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
$3$
4
WB JEE 2025
MCQ (Single Correct Answer)
+2
-0.5
Change Language

If $f(x)$ and $g(x)$ are two polynomials such that $\phi(x)=f\left(x^3\right)+x g\left(x^3\right)$ is divisible by $x^2+x+1$, then

A
$\phi(x)$ is divisible by $(x-1)$
B
none of $f(x)$ and $g(x)$ is divisible by $(x-1)$
C
$g(x)$ is divisible by $(x-1)$ but $f(x)$ is not divisible by $(x-1)$
D
$f(x)$ io divisible hv $(x-1)$ but $g(x)$ is not divisible by $(x-1)$
WB JEE Subjects
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12