# JEE Main > Calculus

Explore popular questions from Calculus for JEE Main. This collection covers Calculus previous year JEE Main questions hand picked by popular teachers.

Physics
Chemistry
Maths

Q 1.

Correct4

Incorrect-1

The area enclosed between the curves {tex} y ^ { 2 } = x {/tex} and {tex} y = | x | {/tex} is

A

2{tex} / 3 {/tex}

B

1

1{tex} / 6 {/tex}

D

1{tex} / 3 {/tex}

##### Explanation

Q 2.

Correct4

Incorrect-1

The area of the plane region bounded by the curves {tex} x + 2 y ^ { 2 } = 0 {/tex} and {tex} x + 3 y ^ { 2 } = 1 {/tex} is equal to

A

{tex} \frac { 5 } { 3 } {/tex}

B

{tex} \frac { 1 } { 3 } {/tex}

C

{tex} \frac { 2 } { 3 } {/tex}

{tex} \frac { 4 } { 3 } {/tex}

##### Explanation

Q 3.

Correct4

Incorrect-1

The area of the region bounded by the parabola {tex} ( y - 2 ) ^ { 2 } = x - 1 {/tex} , the tangent to the parabola at the point {tex} ( 2,3 ) {/tex} and the {tex} x {/tex} -axis is

A

13

B

6

9

D

12

##### Explanation

Q 4.

Correct4

Incorrect-1

The area bounded by the curves {tex} y = \cos x {/tex} and {tex} y = \sin x {/tex} between the ordinates {tex} x = 0 {/tex} and {tex} x = \frac { 3 \pi } { 2 } {/tex} is

A

{tex} 4 \sqrt { 2 } + 2 {/tex}

B

{tex} 4 \sqrt { 2 } - 1 {/tex}

C

{tex} 4 \sqrt { 2 } + 1 {/tex}

{tex} 4 \sqrt { 2 } - 2 {/tex}

##### Explanation

Q 5.

Correct4

Incorrect-1

The area of the region enclosed by the curves {tex} y = x , x = e , y = \frac { 1 } { x } {/tex} and the positive {tex} x {/tex}-axis is

A

{tex} 1 {/tex} sq. units

{tex} \frac { 3 } { 2 } {/tex} sq. units

C

{tex} \frac { 5 } { 2 } {/tex} sq.units

D

{tex} \frac { 1 } { 2 } {/tex} sq.units

##### Explanation

Q 6.

Correct4

Incorrect-1

The area bounded between the parabolas {tex} x ^ { 2 } = \frac { y } { 4 } {/tex} and {tex} x ^ { 2 } = 9 y {/tex} and the straight line {tex} y = 2 {/tex} is

A

20{tex} \sqrt { 2 } {/tex}

B

{tex} \frac { 10 \sqrt { 2 } } { 3 } {/tex}

{tex} \frac { 20 \sqrt { 2 } } { 3 } {/tex}

D

10{tex} \sqrt { 2 } {/tex}

##### Explanation

Q 7.

Correct4

Incorrect-1

The area (in square units) bounded by the curves {tex} y = \sqrt { x } {/tex} , {tex} 2 y - x + 3 = 0 , x {/tex}-axis, and lying in the first quadrant is

A

36

B

18

C

{tex} \frac { 27 } { 4 } {/tex}

9

##### Explanation

Q 8.

Correct4

Incorrect-1

The area of the region described by {tex} A = \left\{ ( x , y ) : x ^ { 2 } + y ^ { 2 } \leq 1 \text { and } \right. {/tex} {tex} y ^ { 2 } \leq 1 - x \} {/tex} is

A

{tex} \frac { \pi } { 2 } - \frac { 2 } { 3 } {/tex}

B

{tex} \frac { \pi } { 2 } + \frac { 2 } { 3 } {/tex}

{tex} \frac { \pi } { 2 } + \frac { 4 } { 3 } {/tex}

D

{tex} \frac { \pi } { 2 } - \frac { 4 } { 3 } {/tex}

##### Explanation

Q 9.

Correct4

Incorrect-1

Let {tex} A = \left\{ ( x , y ) : y ^ { 2 } \leq 4 x , y - 2 x \geq - 4 \right\} . {/tex} Then the area (in square units) of the region {tex} A {/tex} is

A

8

9

C

10

D

11

##### Explanation

Q 10.

Correct4

Incorrect-1

The area of the region above the {tex} x {/tex} -axis bounded by the curve {tex} y = \tan x , 0 \leq x \leq \frac { \pi } { 2 } {/tex} and the tangent to the curve at {tex} x = \frac { \pi } { 4 } {/tex} is

{tex} \frac { 1 } { 2 } \left( \log 2 - \frac { 1 } { 2 } \right) {/tex}

B

{tex} \frac { 1 } { 2 } \left( \log 2 + \frac { 1 } { 2 } \right) {/tex}

C

{tex} \frac { 1 } { 2 } ( 1 - \log 2 ) {/tex}

D

{tex} \frac { 1 } { 2 } ( 1 + \log 2 ) {/tex}

##### Explanation

Q 11.

Correct4

Incorrect-1

The area (in sq. units) of the region described by {tex} \left\{ ( x , y ) : y ^ { 2 } \leq 2 x \right. {/tex} and {tex} y \geq 4 x - 1 \} {/tex} is

A

{tex} \frac { 5 } { 64 } {/tex}

B

{tex} \frac { 15 } { 64 } {/tex}

{tex} \frac { 9 } { 32 } {/tex}

D

{tex} \frac { 7 } { 32 } {/tex}

##### Explanation

Q 12.

Correct4

Incorrect-1

The area (in square units) of the region bounded by the curves {tex} y + 2 x ^ { 2 } = 0 {/tex} and {tex} y + 3 x ^ { 2 } = 1 {/tex} is equal to

A

{tex} \frac { 3 } { 5 } {/tex}

B

{tex} \frac { 3 } { 4 } {/tex}

C

{tex} \frac { 1 } { 3 } {/tex}

{tex} \frac { 4 } { 3 } {/tex}

##### Explanation

Q 13.

Correct4

Incorrect-1

The area (in sq. units) of the region {tex} \left\{ ( x , y ) : y ^ { 2 } \geq 2 x \text { and } x ^ { 2 } + y ^ { 2 } \leq 4 x \right. {/tex} {tex} x \geq 0 , y \geq 0 \} {/tex} is

A

{tex} \frac { \pi } { 2 } - \frac { 2 \sqrt { 2 } } { 3 } {/tex}

B

{tex} \pi - \frac { 4 } { 3 } {/tex}

{tex} \pi - \frac { 8 } { 3 } {/tex}

D

{tex} \pi - \frac { 4 \sqrt { 2 } } { 3 } {/tex}

##### Explanation

Q 14.

Correct4

Incorrect-1

The area (in sq. units) of the region described by {tex} A = \{ ( x , y ) | y {/tex} {tex} \geq x ^ { 2 } - 5 x + 4 , x + y \geq 1 , y \leq 0 \} {/tex} is

{tex} \frac { 19 } { 6 } {/tex}

B

{tex} \frac { 17 } { 6 } {/tex}

C

{tex} \frac { 7 } { 2 } {/tex}

D

{tex} \frac { 13 } { 6 } {/tex}

##### Explanation

Q 15.

Correct4

Incorrect-1

The area of the region bounded by {tex} y = | x - 1 | {/tex} and {tex} y = 1 {/tex} is

A

2

1

C

{tex} \frac { 1 } { 2 } {/tex}

D

None of these

##### Explanation

Q 16.

Correct4

Incorrect-1

The area between the curve {tex} y ^ { 2 } = 4 a x , x {/tex}-axis and the ordinates {tex} x = 0 {/tex} and {tex} x = a {/tex} is

A

{tex} \frac { 4 } { 3 } a ^ { 2 } {/tex}

{tex} \frac { 8 } { 3 } a ^ { 2 } {/tex}

C

{tex} \frac { 2 } { 3 } a ^ { 2 } {/tex}

D

{tex} \frac { 5 } { 3 } a ^ { 2 } {/tex}

##### Explanation

Q 17.

Correct4

Incorrect-1

The area of the curve {tex} x y ^ { 2 } = a ^ { 2 } ( a - x ) {/tex} bounded by {tex} y {/tex} -axis is

{tex} \pi a ^ { 2 } {/tex}

B

2{tex} \pi a ^ { 2 } {/tex}

C

3{tex} \pi a ^ { 2 } {/tex}

D

4{tex} \pi a ^ { 2 } {/tex}

##### Explanation

Q 18.

Correct4

Incorrect-1

The area enclosed by the parabolas {tex} y = x ^ { 2 } - 1 {/tex} and {tex} y = 1 - x ^ { 2 } {/tex} is

A

1{tex} / 3 {/tex}

B

2{tex} / 3 {/tex}

C

4{tex} / 3 {/tex}

8{tex} / 3 {/tex}

##### Explanation

Q 19.

Correct4

Incorrect-1

The area of the smaller segment cut off from the circle {tex} x ^ { 2 } + y ^ { 2 } {/tex} {tex} = 9 {/tex} by {tex} x = 1 {/tex} is

A

{tex} \frac { 1 } { 2 } \left( 9 \sec ^ { - 1 } 3 - \sqrt { 8 } \right) {/tex}

{tex} 9 \sec ^ { - 1 } ( 3 ) - \sqrt { 8 } {/tex}

C

{tex} \sqrt { 8 } - 9 \sec ^ { - 1 } ( 3 ) {/tex}

D

None of these

##### Explanation

Q 20.

Correct4

Incorrect-1

The area of the region bounded by the curves {tex} y = | x - 2 | , x = 1 {/tex} {tex} x = 3 {/tex} and the {tex} x {/tex} -axis is

A

4

B

2

C

3

1

##### Explanation

Q 21.

Correct4

Incorrect-1

The area enclosed between the parabolas {tex} y ^ { 2 } = 4 x {/tex} and {tex} x ^ { 2 } = 4 y {/tex} is

A

{tex} \frac { 14 } { 3 } {/tex} sq. units

B

{tex} \frac { 3 } { 4 } {/tex} sq.units

C

{tex} \frac { 3 } { 16 } {/tex} sq. units

{tex} \frac { 16 } { 3 } {/tex} sq. units

##### Explanation

Q 22.

Correct4

Incorrect-1

The area bounded by the curves {tex} y ^ { 2 } = 8 x {/tex} and {tex} y = x {/tex} is

A

{tex} \frac { 128 } { 3 } {/tex} sq. units

{tex} \frac { 32 } { 3 } {/tex} sq. units

C

{tex} \frac { 64 } { 3 } {/tex} sq. units

D

{tex}32{/tex} sq.units

##### Explanation

Q 23.

Correct4

Incorrect-1

The area bounded by the curves {tex} y = \log _ { e } x {/tex} and {tex} y = \left( \log _ { e } x \right) ^ { 2 } {/tex} is

{tex} 3 - e {/tex}

B

{tex} e - 3 {/tex}

C

{tex} \frac { 1 } { 2 } ( 3 - e ) {/tex}

D

{tex} \frac { 1 } { 2 } ( e - 3 ) {/tex}

##### Explanation

Q 24.

Correct4

Incorrect-1

The area between the parabola {tex} y ^ { 2 } = 4 a x {/tex} and {tex} x ^ { 2 } = 8 a y {/tex} is

A

{tex} \frac { 8 } { 3 } a ^ { 2 } {/tex}

B

{tex} \frac { 4 } { 3 } a ^ { 2 } {/tex}

{tex} \frac { 32 } { 3 } a ^ { 2 } {/tex}

D

{tex} \frac { 16 } { 3 } a ^ { 2 } {/tex}

##### Explanation

Q 25.

Correct4

Incorrect-1

The area of the region bounded by the curves {tex} y = x ^ { 2 } {/tex} and {tex} y = | x | {/tex} is

A

1{tex} / 6 {/tex}

1{tex} / 3 {/tex}

C

{tex}5 / 6 {/tex}

D

{tex} 5/ 3 {/tex}