Application of Derivatives PYQs - Last 10 Years
WB JEE / Mathematics / Calculus / 52 recent questions
MathematicsCalculus2017-2026
Practice 52 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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2017-2026
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Last 10 Years Application of Derivatives Questions
Showing 50 of 52 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
30Application Of Derivatives
The greatest and least value of \(f(x) = {\tan ^{ - 1}} - {1 \over 2}\,ln \,x\,on\,\left[ {{1 \over {\sqrt 3 }},\sqrt 3 } \right]\) are
MCQM+2 / -02021
31Application Of Derivatives
If the tangent at the point P with co-ordinates (h, k) on the curve y2 = 2x3 is perpendicular to the straight line 4x = 3y, then
MCQ+2 / -0.52021
32Application Of Derivatives
Two particles A and B move from rest along a straight line with constant accelerations f and f' respectively. If A takes m sec. more than that of B and describes n units more than that of B in acquiring the same velocity, then
MCQ+1 / -0.252021
33Application Of Derivatives
Let f : R \(\to\) R be such that f(0) = 0 and \(\left| {f'(x)} \right| \le 5\) for all x. Then f(1) is in
MCQ+1 / -0.252021
34Application Of Derivatives
Let \(f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 12\).Then
MCQ+1 / -0.252020
35Application Of Derivatives
Tangent is drawn at any point P(x, y) on a curve, which passes through (1, 1). The tangent cuts X-axis and Y-axis at A and B respectively. If AP : BP = 3 : 1, then
MCQM+2 / -02020
36Application Of Derivatives
A particle is projected vertically upwards. If it has to stay above the ground for 12 sec, then
MCQM+2 / -02020
37Application Of Derivatives
If the function \(f(x) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1\) [a > 0] attains its maximum and minimum at p and q respectively such that p2 = q, then a is equal to
MCQ+1 / -0.252020
38Application Of Derivatives
Consider the curve \(y = b{e^{ - x/a}}\), where a and b are non-zero real numbers. Then
MCQ+2 / -0.52020
39Application Of Derivatives
In open interval \(\left( {0,\,{\pi \over 2}} \right)\)
MCQ+2 / -0.52020
40Application Of Derivatives
If the tangent to the curve y2 = x3 at (m2, m3) is also a normal to the curve at (m2, m3), then the value of mM is
MCQ+1 / -0.252020
41Application Of Derivatives
If the radius of a spherical balloon increases by 0.1%, then its volume increases approximately by
MCQ+1 / -0.252019
42Application Of Derivatives
Two particles A and B move from rest along a straight line with constant accelerations f and h, respectively. If A takes m seconds more than B and describes n units more than that of B acquiring the same speed, then
MCQM+2 / -02019
43Application Of Derivatives
Let \(f(x) = \cos \left( {{\pi \over x}} \right),x \ne 0\), then assuming k as an integer,
MCQM+2 / -02018
44Application Of Derivatives
The law of motion of a body moving along a straight line is x = \({1 \over 2}\) vt. x being its distance from a fixed point on the line at time t and v is its velocity there. Then
MCQ+1 / -0.252018
45Application Of Derivatives
The normal to the curve \(y = {x^2} - x + 1\), drawn at the points with the abscissa \({x_1} = 0\), \({x_2} = - 1\) and \({x_3} = {5 \over 2}\)
MCQ+2 / -0.52018
46Application Of Derivatives
A particle is in motion along a curve 12y = x3. The rate of change of its ordinate exceeds that of abscissa in
MCQM+2 / -02018
47Application Of Derivatives
A ladder 20 ft long leans against a vertical wall. The top end slides downwards at the rate of 2 ft per second. The rate at which the lower end moves on a horizontal floor when it is 12 ft from the wall is
MCQ+2 / -0.52018
48Application Of Derivatives
If the line ax + by + c = 0, ab \(\ne\) 0, is a tangent to the curve xy = 1 \(-\) 2x, then
MCQM+2 / -02017
49Application Of Derivatives
Two particles move in the same straight line starting at the same moment from the same point in the same direction. The first moves with constant velocity u and the second starts from rest with constant acceleration f. Then,
MCQM+2 / -02017
50Application Of Derivatives
Let, \(F(x) = {e^x},G(x) = {e^{ - x}}\) and \(H(x) = G(F(x))\), where x is a real variable. Then, \({{dH} \over {dx}}\) at x = 0 is
MCQ+1 / -0.252017