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

## Chemistry

Differential Calculus

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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}