Application of Derivatives PYQs - Last 5 Years
WB JEE / Mathematics / Calculus / 29 recent questions
MathematicsCalculus2022-2026
Practice 29 WB JEE Mathematics questions from Application of Derivatives. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
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2022-2026
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Last 5 Years Application of Derivatives Questions
Showing 29 of 29 filtered questions.
1Application Of Derivatives
The quantities $a_1, a_2, a_3, \ldots$ form an infinite decreasing G.P. If $a_1=1$, then the common ratio of the progression for which the expression $6 a_5-16 a_4-3 a_3+12 a_2$ is at a maximum is
MCQ+2 / -0.52026
2Application Of Derivatives
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 $[-1,1]$.
MCQ+1 / -0.252026
3Application Of Derivatives
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
MCQ+2 / -0.52026
4Application Of Derivatives
Tangent at a point $P_1$ (other than $(0,0)$ ) on the curve $y=x^3$ meets the curve again at $P_2$. The tangent at $P_2$ meets the curve at $\mathrm{P}_3$ and so on. Then the abscissae of $\mathrm{P}_1, \mathrm{P}_2, \mathrm{P}_3, \ldots, \...
MCQ+2 / -0.52026
5Application Of Derivatives
Let $f(x)$ be a twice differentiable function in $[1,3]$ and $f(1)=f(3)$. Further if $\left|f^{\prime \prime}(x)\right| \leq 2$, then for all $x$ in $[1,3]$
MCQ+2 / -0.52026
6Application Of Derivatives
Which of the following statements is always true?
MCQ+1 / -0.252026
7Application Of Derivatives
Consider the curve $x=1-3 t^2, y=t-3 t^3$. The tangent to the curve at the point $t$ is inclined at an angle $\phi$ to OX and the tangent at $\mathrm{P}(-2,2)$ meets the curve again at Q . Then
MCQM+2 / -02026
8Application Of Derivatives
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 $x \in(0,2)$
MCQ+1 / -0.252026
9Application Of Derivatives
The maximum number of common normals of $y^2=4 a x$ and $x^2=4 b y$ is equal to :
MCQ+2 / -0.52025
10Application Of Derivatives
The function $f(x)=2 x^3-3 x^2-12 x+4, x \in \mathbb{R}$ has
MCQ+1 / -0.252025
11Application Of Derivatives
Let $f(\theta)=\left|\begin{array}{ccc}1 & \cos \theta & -1 \\ -\sin \theta & 1 & -\cos \theta \\ -1 & \sin \theta & 1\end{array}\right|$.
Suppose $A$ and $B$ are respectively maximum and minimum values of $f(\theta)$.Then $(A,B)$ is equal ...
Suppose $A$ and $B$ are respectively maximum and minimum values of $f(\theta)$.Then $(A,B)$ is equal ...
MCQ+2 / -0.52025
12Application Of Derivatives
Let $f(x)=x^3, x \in[-1,1]$. Then which of the following are correct?
MCQM+2 / -02025
13Application Of Derivatives
Let $\phi(x)=f(x)+f(2 a-x), x \in[0,2 a]$ and $f^{\prime \prime}(x)>0$ for all $x \in[0, a]$. Then $\phi(x)$ is
MCQ+1 / -0.252025
14Application Of Derivatives
Let $f$ be a function which is differentiable for all real $x$. If $f(2)=-4$ and $f^{\prime}(x) \geq 6$ for all $x \in[2,4]$, then
MCQ+1 / -0.252025
15Application Of Derivatives
If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha \log |x|+\beta x^2+x,(x \neq 0)$, then
MCQ+1 / -0.252025
16Application Of Derivatives
Let $p(x)$ be a real polynomial of least degree which has a local maximum at $x=1$ and a local minimum at $x=3$. If $p(1)=6$ and $p(3)=2$, then $p^{\prime}(0)$ is equal to :
MCQ+1 / -0.252025
17Application Of Derivatives
The acceleration f \(\mathrm{ft} / \mathrm{sec}^2\) of a particle after a time \(\mathrm{t}\) sec starting from rest is given by \(\mathrm{f}=6-\sqrt{1.2 \mathrm{t}}\). Then the maximum velocity \(\mathrm{v}\) and time \(\mathrm{T}\) to att...
MCQM+2 / -02024
18Application Of Derivatives
Consider the function \(\mathrm{f}(x)=x(x-1)(x-2) \ldots(x-100)\). Which one of the following is correct?
MCQ+2 / -0.52024
19Application Of Derivatives
Let \(\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}\) be given by \(\mathrm{f}(x)=\left|x^2-1\right|\), then
MCQ+1 / -0.252024
20Application Of Derivatives
If a particle moves in a straight line according to the law \(x=a \sin (\sqrt{\lambda} t+b)\), then the particle will come to rest at two points whose distance is [symbols have their usual meaning]
MCQ+1 / -0.252024
21Application Of Derivatives
Let \(\mathrm{y}=\mathrm{f}(x)\) be any curve on the \(\mathrm{X}-\mathrm{Y}\) plane & \(\mathrm{P}\) be a point on the curve. Let \(\mathrm{C}\) be a fixed point not on the curve. The length \(\mathrm{PC}\) is either a maximum or a minimum...
MCQ+1 / -0.252024
22Application Of Derivatives
\(f(x)=\cos x-1+\frac{x^2}{2!}, x \in \mathbb{R}\) Then \(\mathrm{f}(x)\) is
MCQ+1 / -0.252024
23Application Of Derivatives
If \(f(x) = 3\root 3 \of {{x^2}} - {x^2}\), then
MCQM+2 / -02023
24Application Of Derivatives
A balloon starting from rest is ascending from ground with uniform acceleration of 4 ft/sec\(^2\). At the end of 5 sec, a stone is dropped from it. If T be the time to reach the stone to the ground and H be the height of the balloon when th...
MCQM+2 / -02023
25Application Of Derivatives
Given \(f(x) = {e^{\sin x}} + {e^{\cos x}}\). The global maximum value of \(f(x)\)
MCQ+2 / -0.52023
26Application Of Derivatives
The portion of the tangent to the curve \({x^{{2 \over 3}}} + {y^{{2 \over 3}}} = {a^{{2 \over 3}}},a > 0\) at any point of it, intercepted between the axes
MCQ+2 / -0.52023
27Application Of Derivatives
A missile is fired from the ground level rises x meters vertically upwards in t sec, where \(x = 100t - {{25} \over 2}{t^2}\). The maximum height reached is
MCQ+1 / -0.252023
28Application Of Derivatives
From a balloon rising vertically with uniform velocity v ft/sec a piece of stone is let go. The height of the balloon above the ground when the stone reaches the ground after 4 sec is [g = 32 ft/sec2]
MCQM+2 / -02022
29Application Of Derivatives
A particle moving in a straight line starts from rest and the acceleration at any time t is \(a - k{t^2}\) where a and k are positive constants. The maximum velocity attained by the particle is
MCQ+1 / -0.252022