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Previous year question hub

Application Of Derivatives - Calculus - Mathematics Previous Year Questions

Practice Application Of Derivatives - Calculus - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

15Papers
14Years
64Questions
1Topics

Application Of Derivatives question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Application Of Derivatives. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Not classified 64 100%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 61 95.3%
Subjective 3 4.7%

Subject weightage

Top subjects by unique question coverage.

Mathematics
64 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
64 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Application Of Derivatives
64 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

WB JEE 2025
8 Qs
VITEEE 2025
3 Qs
WB JEE 2024
6 Qs
WB JEE 2023
5 Qs
WB JEE 2022
2 Qs
WB JEE 2021
4 Qs
WB JEE 2020
7 Qs
WB JEE 2019
2 Qs
WB JEE 2018
5 Qs
WB JEE 2017
5 Qs
WB JEE 2016
2 Qs
WB JEE 2011
2 Qs
WB JEE 2010
5 Qs
WB JEE 2009
7 Qs
WB JEE 2008
1 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
VITEEE 202520253View paper
WB JEE 202520258View paper
WB JEE 202420246View paper
WB JEE 202320235View paper
WB JEE 202220222View paper
WB JEE 202120214View paper
WB JEE 202020207View paper
WB JEE 201920192View paper
WB JEE 201820185View paper
WB JEE 201720175View paper
WB JEE 201620162View paper
WB JEE 201120112View paper
WB JEE 201020105View paper
WB JEE 200920097View paper
WB JEE 200820081View paper

All Application Of Derivatives previous year questions

Practice every matching question in batches of 20, with every available option.

1
2016 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2016
Time period T of a simple pendulum of length l is given by \(T = 2\pi \sqrt {{l \over g}}\). If the length is increased by 2%, then an approximate change in the time period is
A
2%
B
1%
C
\({1 \over 2}\)%
D
None of these
Open complete paper
2
2016 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2016
If f(x) is a function such that f'(x) = (x \(-\) 1)2(4 \(-\) x), then
A
f(0) = 0
B
f(x) is increasing in (0, 3)
C
x = 4 is a critical point of f(x)
D
f(x) is decreasing in (3, 5)
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3
2017 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2017
If the line ax + by + c = 0, ab \(\ne\) 0, is a tangent to the curve xy = 1 \(-\) 2x, then
A
a > 0, b < 0
B
a > 0, b > 0
C
a < 0, b > 0
D
a < 0, b < 0
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4
2017 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2017
The value of K in order that f(x) = sin x \(-\) cos x \(-\) kx + 5 decreases for all positive real values of x is given by
A
K < 1
B
K \(\ge\) 1
C
K > \(\sqrt 2\)
D
K < \(\sqrt 2\)
Open complete paper
5
2017 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2017
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
A
1
B
\(-\)1
C
\(- {1 \over e}\)
D
\(-\) e
Open complete paper
6
2017 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2017
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,
A
they will be at the greatest distance at the end of time \({u \over {2f}}\) from the start
B
they will be at the greatest distance at the end of time \({u \over f}\) from the start
C
their greatest distance is \({{{u^2}} \over {2f}}\)
D
their greatest distance is \({{{u^2}} \over f}\)
Open complete paper
7
2017 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2017
The chord of the curve \(y = {x^2} + 2ax + b\), joining the points where x = \(\alpha\) and x = \(\beta\), is parallel to the tangent to the curve at abscissa x is equal to
A
\({{a + b} \over 2}\)
B
\({{2a + b} \over 3}\)
C
\({{2\alpha + \beta } \over 3}\)
D
\({{\alpha + \beta } \over 2}\)
Open complete paper
8
2018 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2018
A particle is in motion along a curve 12y = x3. The rate of change of its ordinate exceeds that of abscissa in
A
\(-\) 2 < x < 2
B
x = \(\pm\) 2
C
x < \(-\)2
D
x > 2
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9
2018 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2018
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
A
acceleration f varies directly with x
B
acceleration f varies inversely with x
C
acceleration f is constant
D
acceleration f varies directly with t
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10
2018 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2018
The normal to the curve \(y = {x^2} - x + 1\), drawn at the points with the abscissa \({x_1} = 0\), \({x_2} = - 1\) and \({x_3} = {5 \over 2}\)
A
are parallel to each other
B
are pairwise perpendicular
C
are concurrent
D
are not concurrent
Open complete paper
11
2018 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2018
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
A
\({{ - 8} \over 3}\)
B
\({6 \over 5}\)
C
\({3 \over 2}\)
D
\({17 \over 4}\)
Open complete paper
12
2018 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2018
Let \(f(x) = \cos \left( {{\pi \over x}} \right),x \ne 0\), then assuming k as an integer,
A
f(x) increases in the interval \(\left( {{1 \over {2k + 1}},{1 \over {2k}}} \right)\)
B
f(x) decreases in the interval \(\left( {{1 \over {2k + 1}},{1 \over {2k}}} \right)\)
C
f(x) decreases in the interval \(\left( {{1 \over {2k + 2}},{1 \over {2k + 1}}} \right)\)
D
f(x) increases in the interval \(\left( {{1 \over {2k + 2}},{1 \over {2k + 1}}} \right)\)
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13
2019 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2019
If the radius of a spherical balloon increases by 0.1%, then its volume increases approximately by
A
0.2%
B
0.3%
C
0.4%
D
0.05%
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14
2019 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2019
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
A
\((f + h){m^2} = fhn\)
B
\((f - h){m^2} = fhn\)
C
\((h - f)n = {1 \over 2}fh{m^2}\)
D
\({1 \over 2}(f + h)n = fh{m^2}\)
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15
2020 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2020
In open interval \(\left( {0,\,{\pi \over 2}} \right)\)
A
cos x + x sin x < 1
B
cos x + x sin x >1
C
no specific order relation can be ascertained between cos x + x sin x and 1
D
\(\cos \,x + x\,\sin \,x < {1 \over 2}\)
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16
2020 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2020
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
A
2
B
\({1 \over 2}\)
C
\({1 \over 4}\)
D
3
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17
2020 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2020
A particle is projected vertically upwards. If it has to stay above the ground for 12 sec, then
A
velocity of projection is 192 ft/sec
B
greatest height attained is 600 ft
C
velocity of projection is 196 ft/sec
D
greatest height attained is 576 ft
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18
2020 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2020
Let \(f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 12\).

Then
A
f(x) has 13 non-zero real roots
B
f(x) has exactly one real root
C
f(x) has exactly one pair of imaginary roots
D
f(x) has no real root
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19
2020 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2020
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
A
\(- {1 \over 9}\)
B
\(- {2 \over 9}\)
C
\(- {1 \over 3}\)
D
\(- {4 \over 9}\)
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20
2020 · Mathematics · Calculus · Application Of Derivatives
WB JEE 2020
Consider the curve \(y = b{e^{ - x/a}}\), where a and b are non-zero real numbers. Then
A
\({x \over a} + {y \over b}\) = 1 is tangent to the curve at (0, 0)
B
\({x \over a} + {y \over b}\) = 1 is tangent to the curve, where the curve crosses the axis of y
C
\({x \over a} + {y \over b}\) = 1 is tangent to the curve at (a, 0)
D
\({x \over a} + {y \over b}\) = 1 is tangent to the curve at (2a, 0)
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Showing 20 of 64 questions