1
WB JEE 2026
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Given $P(x)=x^4+a x^3+b x^2+c x+d$ such that $x=0$ is the only real root of $P^{\prime}(x)=0$. If $P(-1) < P(1)$, then in the interval $[-1,1]$.

A

$P(-1)$ is the minimum but $P(1)$ is not the maximum of $P$

B

$P(-1)$ is not minimum but $P(1)$ is the maximum of $P$

C

neither $P(1)$ is the minimum nor $P(1)$ is the maximum of P

D

$P(-1)$ is the minimum and $P(1)$ is the maximum of $P$.

2
WB JEE 2026
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Which of the following statements is always true?

A

If $f(x)$ is decreasing, then $\frac{1}{f(x)}$ is increasing

B

If $f(x)$ is decreasing, then $\frac{1}{f(x)}$ is also decreasing

C

If both $f$ and $g$ are positive functions such that $f$ is decreasing and $g$ is increasing, then $\frac{f}{g}$ is a decreasing function

D

If both $f$ and $g$ are positive functions such that $f$ is increasing and $g$ is decreasing then $\frac{f}{g}$ is a decreasing furnction

3
WB JEE 2026
MCQ (Single Correct Answer)
+1
-0.25
Change Language

Let domain and range of $f(x)$ and $g(x)$ is $[0, \infty)$. If $f(x)$ is an increasing function, $g(x)$ is a decreasing function, $h(x)= f\{g(x)\}, h(0)=0$ and $p(x)=h\left(x^3-2 x^2+2 x\right)-h(4)$, then for all $x \in(0,2)$

A

$p(x)=-3$

B

$\mathrm{p}(\mathrm{x})=0$

C

$0< p(x)<-h(4)$

D

$0 \leq p(x) \leq-h(4)$

4
WB JEE 2026
MCQ (Single Correct Answer)
+2
-0.5
Change Language

A figure is bounded by the curves $y=x^2+1, y=0, x=0$ and $x=1$. The point at which a tangent should be drawn to the curve $y=x^2+1$ for it to cut off trapezium of the greatest area from the figure is

A

$(1,2)$

B

$(-1,2)$

C

$\left(\frac{1}{2}, \frac{5}{4}\right)$

D

$(0,1)$

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