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Previous year question hub

Application Of Integration - Calculus - Mathematics Previous Year Questions

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

9Papers
9Years
21Questions
1Topics

Application Of Integration question pattern

Every graph below is calculated only from this selection.

Questions by year

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

Difficulty distribution

How the classified questions are distributed by difficulty.

Not classified 21 100%

Question type distribution

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

Multiple Choices 21 100%

Subject weightage

Top subjects by unique question coverage.

Mathematics
21 Qs

Most asked topics

Top topics across the included previous year papers.

Calculus
21 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Application Of Integration
21 Qs

Paper coverage

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

WB JEE 2024
2 Qs
WB JEE 2022
2 Qs
WB JEE 2021
2 Qs
WB JEE 2020
4 Qs
WB JEE 2019
2 Qs
WB JEE 2017
1 Qs
WB JEE 2011
2 Qs
WB JEE 2010
3 Qs
WB JEE 2008
3 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
WB JEE 202420242View paper
WB JEE 202220222View paper
WB JEE 202120212View paper
WB JEE 202020204View paper
WB JEE 201920192View paper
WB JEE 201720171View paper
WB JEE 201120112View paper
WB JEE 201020103View paper
WB JEE 200820083View paper

All Application Of Integration previous year questions

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

1
2017 · Mathematics · Calculus · Application Of Integration
WB JEE 2017
The area of the figure bounded by the parabolas x = \(-\) 2y2 and x = 1 \(-\) 3y2 is
A
\({4 \over 3}\) sq units
B
\({2 \over 3}\) sq units
C
\({3 \over 7}\) sq units
D
\({6 \over 7}\) sq units
Open complete paper
2
2019 · Mathematics · Calculus · Application Of Integration
WB JEE 2019
Let P and T be the subsets of k, y-plane defined by

P = {(x, y) : x > 0, y > 0 and x2 + y2 = 1}

T = {(x, y) : x > 0, y > 0 and x8 + y8 < 1}

Then, P \(\cap\) T is
A
the void set \(\phi\)
B
P
C
T
D
P \(-\) TC
Open complete paper
3
2019 · Mathematics · Calculus · Application Of Integration
WB JEE 2019
The area bounded by y = x + 1 and y = cos x and the X-axis, is
A
1 sq unit
B
\({3 \over 2}\) sq unit
C
\({1 \over 4}\) sq unit
D
\({1 \over 8}\) sq unit
Open complete paper
4
2020 · Mathematics · Calculus · Application Of Integration
WB JEE 2020
If \({x^2} + {y^2} = {a^2}\), then \(\int\limits_0^a {\sqrt {1 + {{\left( {{{dy} \over {dx}}} \right)}^2}} dx = }\)
A
2\(\pi a\)
B
\(\pi a\)
C
\({1 \over 2}\pi a\)
D
\({1 \over 4}\pi a\)
Open complete paper
5
2020 · Mathematics · Calculus · Application Of Integration
WB JEE 2020
The area of the figure bounded by the parabola \(x = - 2{y^2},\,x = 1 - 3{y^2}\) is
A
\({1 \over 3}\)sq unit
B
\({4 \over 3}\)sq unit
C
1 sq unit
D
2 sq units
Open complete paper
6
2020 · Mathematics · Calculus · Application Of Integration
WB JEE 2020
Area in the first quadrant between the ellipses x2 + 2y2 = a2 and 2x2 + y2 = a2 is
A
\({{{a^2}} \over {\sqrt 2 }}{\tan ^{ - 1}}{1 \over {\sqrt 2 }}\)
B
\({{3{a^2}} \over 4}{\tan ^{ - 1}}{1 \over 2}\)
C
\({{5{a^2}} \over 2}{\sin ^{ - 1}}{1 \over 2}\)
D
\({{9\pi {a^2}} \over 2}\)
Open complete paper
7
2020 · Mathematics · Calculus · Application Of Integration
WB JEE 2020
The area of the region

\(\{ (x,y):{x^2} + {y^2} \le 1 \le x + y\}\) is
A
\({{{\pi ^2}} \over 2}\)
B
\({\pi \over 4}\)
C
\({\pi \over 4}\)\(-\)\({1 \over 2}\)
D
\({{{\pi ^2}} \over 3}\)
Open complete paper
8
2021 · Mathematics · Calculus · Application Of Integration
WB JEE 2021
The straight the through the origin which divides the area formed by the curves y = 2x \(-\) x2, y = 0 and x = 1 into two equal halves is
A
y = x
B
y = 2x
C
y = \({3 \over 2}\) x
D
y = \({2 \over 3}\) x
Open complete paper
9
2021 · Mathematics · Calculus · Application Of Integration
WB JEE 2021
The area bounded by the parabolas \(y = 4{x^2},y = {{{x^2}} \over 9}\) and the straight line y = 2 is
A
\({{20\sqrt 2 } \over 3}\) sq. unit
B
\(10\sqrt 5\) sq. unit
C
\({{10\sqrt 3 } \over 7}\) sq. unit
D
\(10\sqrt 2\) sq. unit
Open complete paper
10
2022 · Mathematics · Calculus · Application Of Integration
WB JEE 2022

Area of the figure bounded by the parabola \({y^2} + 8x = 16\) and \({y^2} - 24x = 48\) is

A
\({{11} \over 9}\) sq. unit
B
\({{32} \over 3}\sqrt 6\) sq. unit
C
\({{16} \over 3}\) sq. unit
D
\({{24} \over 5}\) sq. unit
Open complete paper
11
2022 · Mathematics · Calculus · Application Of Integration
WB JEE 2022

Let f be a non-negative function defined in \([0,\pi /2]\), f' exists and be continuous for all x and \(\int\limits_0^x {\sqrt {1 - {{(f'(t))}^2}} dt = \int\limits_0^x {f(t)dt} }\) and f (0) = 0. Then

A
\(f\left( {{1 \over 2}} \right) < {1 \over 2}\) and \(f\left( {{1 \over 3}} \right) < {1 \over 3}\)
B
\(f\left( {{1 \over 2}} \right) > {1 \over 2}\) and \(f\left( {{1 \over 3}} \right) < {1 \over 3}\)
C
\(f\left( {{4 \over 3}} \right) < {4 \over 3}\) and \(f\left( {{2 \over 3}} \right) < {2 \over 3}\)
D
\(f\left( {{4 \over 3}} \right) > {4 \over 3}\) and \(f\left( {{2 \over 3}} \right) > {2 \over 3}\)
Open complete paper
12
2024 · Mathematics · Calculus · Application Of Integration
WB JEE 2024

Consider the function \(\mathrm{f}(x)=(x-2) \log _{\mathrm{e}} x\). Then the equation \(x \log _{\mathrm{e}} x=2-x\)

A
has at least one root in \((1,2)\)
B
has no root in \((1,2)\)
C
is not at all solvable
D
has infinitely many roots in \((-2,1)\)
Open complete paper
13
2024 · Mathematics · Calculus · Application Of Integration
WB JEE 2024

The area bounded by the curves \(x=4-y^2\) and the Y-axis is

A
16 sq. unit
B
\(\frac{32}{3}\) sq. unit
C
\(\frac{16}{3}\) sq. unit
D
32 sq. unit
Open complete paper
14
2008 · Mathematics · Calculus · Application Of Integration
WB JEE 2008

The area enclosed between the curve y = 1 + x2, the y-axis, and the straight line y = 5 is given by

A
\({{14} \over 3}\) square units
B
\({{7} \over 3}\) square units
C
5 square units
D
\({{16} \over 3}\) square units
Open complete paper
15
2008 · Mathematics · Calculus · Application Of Integration
WB JEE 2008

The area included between the parabolas y2 = 4x and x2 = 4y is

A
\({8 \over 3}\) sq. units
B
8 sq. units
C
\({16 \over 3}\) sq. units
D
12 sq. units
Open complete paper
16
2008 · Mathematics · Calculus · Application Of Integration
WB JEE 2008

The line which is parallel to x-axis and crosses the curve y = \(\sqrt x\) at an angle 45\(^\circ\) is

A
y = \({1 \over 4}\)
B
y = \({1 \over 2}\)
C
y = 1
D
y = 4
Open complete paper
17
2010 · Mathematics · Calculus · Application Of Integration
WB JEE 2010

The area of the region bounded by y2 = x and y = | x | is

A
\({1 \over 3}\) sq. unit
B
\({1 \over 6}\) sq. unit
C
\({2 \over 3}\) sq. unit
D
1 sq. unit
Open complete paper
18
2010 · Mathematics · Calculus · Application Of Integration
WB JEE 2010

The area enclosed by y = 3x \(-\) 5, y = 0, x = 3 and x = 5 is

A
12 sq. units
B
13 sq. units
C
13\({1 \over 2}\) sq. units
D
14 sq. units
Open complete paper
19
2010 · Mathematics · Calculus · Application Of Integration
WB JEE 2010

The area bounded by the parabolas y = 4x2, \(y = {{{x^2}} \over 9}\) and the line y = 2 is

A
\({{5\sqrt 2 } \over 3}\) sq. units
B
\({{10\sqrt 2 } \over 3}\) sq. units
C
\({{15\sqrt 2 } \over 3}\) sq. units
D
\({{20\sqrt 2 } \over 3}\) sq. units
Open complete paper
20
2011 · Mathematics · Calculus · Application Of Integration
WB JEE 2011

The area bounded by y2 = 4x and x2 = 4y is

A
\({{20} \over 3}\) sq. units
B
\({{16} \over 3}\) sq. units
C
\({{14} \over 3}\) sq. units
D
\({{10} \over 3}\) sq. units
Open complete paper

Showing 20 of 21 questions