WB JEE 2011 | Application of Derivatives Question 14 | Mathematics

WB JEE 2011

MCQ (Single Correct Answer)

-0.25

The acceleration of a particle starting from rest moving in a straight line with uniform acceleration is 8m/sec². The time taken by the particle to move the second metre is

$${{\sqrt 2 - 1} \over 2}$$ sec

$${{\sqrt 2 + 1} \over 2}$$ sec

$$(1 + \sqrt 2 )$$ sec

$$(\sqrt 2 - 1)$$ sec

WB JEE 2026

MCQ (Single Correct Answer)

-0.25

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 $[-1,1]$.

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

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

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

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

WB JEE 2026

MCQ (Single Correct Answer)

-0.25

Which of the following statements is always true?

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

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

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

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

WB JEE 2026

MCQ (Single Correct Answer)

-0.25

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 $x \in(0,2)$

$p(x)=-3$

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

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

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

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