On account of the disruption in education due to the corona pandemic, we're are providing a 7-day Free trial of our platform to teachers. Know More →

JEE Advanced

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

Select Subject

Mathematics

Physics

Chemistry

Differential Calculus

Correct Marks 4

Incorrectly Marks -1

Q 1. If {tex} y = ( \sin x ) ^ { \tan x } , {/tex} then {tex} \frac { d y } { d x } {/tex} is equal to

{tex} ( \sin x ) ^ { \tan x } \left( 1 + \sec ^ { 2 } x \log \sin x \right) {/tex}

B

{tex} \tan x ( \sin x ) ^ { \tan x - 1 } \cdot \cos x {/tex}

C

{tex} ( \sin x ) ^ { \tan x } \sec ^ { 2 } x \log \sin x {/tex}

D

{tex} \tan x ( \sin x ) ^ { \tan x - 1 } {/tex}

Explanation

Correct Marks 4

Incorrectly Marks -1

Q 2. If {tex} a + b + c = 0 , {/tex} then the quadratic equation {tex} 3 a x ^ { 2 } + 2 b x + c = 0 {/tex} has

at least one root in {tex} [ 0,1 ] {/tex}

B

one root in {tex} [ 2,3 ] {/tex} and the other in {tex} [ - 2 , - 1 ] {/tex}

C

imaginary roots

D

none of these

Explanation


Correct Marks 4

Incorrectly Marks -1

Q 3. {tex} AB {/tex} is a diameter of a circle and {tex} C {/tex} is any point on the circumference of the circle. Then

the area of {tex} \Delta A B C {/tex} is maximum when it is isosceles

B

the area of {tex} \Delta A B C {/tex} is minimum when it is isosceles

C

the perimeter of {tex} \Delta A B C {/tex} is minimum when it is isosceles

D

none of these

Explanation


Correct Marks 4

Incorrectly Marks -1

Q 4. The function {tex} f ( x ) = \frac { \ln ( \pi + x ) } { \ln ( e + x ) } {/tex} is

A

increasing on {tex} ( 0 , \infty ) {/tex}

decreasing on {tex} ( 0 , \infty ) {/tex}

C

increasing on {tex} ( 0 , \pi / e ) , {/tex} decreasing on {tex} ( \pi / e , \infty ) {/tex}

D

decreasing on {tex} (0 , \pi / e ) , {/tex} increasing on {tex} ( \pi / e , \infty ) {/tex}

Explanation



Correct Marks 4

Incorrectly Marks -1

Q 5. The slope of the tangent to a curve {tex} y = f ( x ) {/tex} at {tex} [ x , f ( x ) ] {/tex} is {tex} 2 x + 1 . {/tex} If the curve passes through the point {tex} ( 1,2 ) , {/tex} then the area bounded by the curve, the {tex} x {/tex} -axis and the line {tex} x = 1 {/tex} is

{tex} \frac { 5 } { 6 } {/tex}

B

{tex} \frac { 6 } { 5 } {/tex}

C

{tex} \frac { 1 } { 6 } {/tex}

D

{tex}6{/tex}

Explanation


Correct Marks 4

Incorrectly Marks -1

Q 6. The point(s) on the curve {tex} y ^ { 3 } + 3 x ^ { 2 } = 12 y {/tex} where the tangent is vertical, is (are)

A

{tex} \left( \pm \frac { 4 } { \sqrt { 3 } } , - 2 \right) {/tex}

B

{tex} ( \pm \sqrt { \frac { 11 } { 3 } } , 1 ) {/tex}

C

{tex} ( 0,0 ) {/tex}

{tex} \left( \pm \frac { 4 } { \sqrt { 3 } } , 2 \right) {/tex}

Explanation

Correct Marks 3

Incorrectly Marks -1

Q 7. In certain problems, the differ- entiation of {tex} \{ f ( x ) \text { - } g ( x ) \} {/tex} appears. One student commits mistake and differentiates as {tex} \frac { d f } { d x } \cdot \frac { d g } { d x } , {/tex} but he gets correct result if {tex} f ( x ) = x ^ { 3 } {/tex} and {tex} g ( 0 ) = \frac { 1 } { 3 }. {/tex}
The function {tex} g ( x ) {/tex} is

A

{tex} \frac { 3 } { | x - 3 | ^ { 3 } } {/tex}

B

{tex} \frac { 4 } { | x - 3 | ^ { 3 } } {/tex}

{tex} \frac { 9 } { | x - 3 | ^ { 3 } } {/tex}

D

{tex} \frac { 27 } { | x - 3 | ^ { 3 } } {/tex}

Explanation


Correct Marks 3

Incorrectly Marks -1

Q 8. Derivative of {tex} \{ f ( x - 3 ) \cdot g ( x ) \} {/tex} with respect to {tex} x {/tex} at {tex} x = 100 {/tex} is

0

B

1

C

{tex} - 1 {/tex}

D

2

Explanation

Correct Marks 3

Incorrectly Marks -1

Q 9. {/tex} Let {tex} f ( x ) = \frac { 1 } { 1 + x ^ { 2 } } {/tex}. Let {tex} m {/tex} be the slope, {tex} a {/tex} be the {tex} x {/tex} -intercept and {tex} b {/tex} be the {tex} y {/tex} -intercept of a tangent to {tex} y = f ( x ) {/tex}, then
Abscissa of the point of contact of the tangent for which {tex} m {/tex} is greatest

A

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

B

1

C

-1

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

Explanation

Correct Marks 3

Incorrectly Marks -1

Q 10. The abscissa of the point of contact of tangent for which {tex} \frac { 1 } { a } {/tex} is qreatest, is

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

B

1

C

{tex} - 1 {/tex}

D

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

Explanation