Application Of Integration - Calculus - Mathematics Previous Year Questions

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

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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 \(-\) T^C

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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

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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

\({1 \over 4}\pi a\)

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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

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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

\({{9\pi {a^2}} \over 2}\)

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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

\({{{\pi ^2}} \over 3}\)

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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

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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

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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

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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 \(f\left( {{2 \over 3}} \right) > {2 \over 3}\)

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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 \((-2,1)\)

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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

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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

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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

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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

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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

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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

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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

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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

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