Explore popular questions for JEE Advanced. This collection includes questions from Physics, Chemistry, Mathematics. They're hand picked by top teachers from a vast pool of questions including previous year JEE Advanced questions.

## Mathematics

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Q 1. Two identical metal plates are given positive charges {tex} Q _ { 1 } {/tex} and {tex} Q _ { 2 } \left( < Q _ { 1 } \right) {/tex} respectively. If they are now brought close together to form a parallel plate capacitor with capacitance {tex} C , {/tex} the potential difference between them is

A

{tex} \left( Q _ { 1 } + Q _ { 2 } \right) / ( 2 C ) {/tex}

B

{tex} \left( Q _ { 1 } + Q _ { 2 } \right) / C {/tex}

C

{tex} \left( Q _ { 1 } - Q _ { 2 } \right) / C {/tex}

{tex} \left( Q _ { 1 } - { Q } _ { 2 } \right) / ( 2 C ) {/tex}

##### Explanation

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Q 2. Three positive charges of equal value {tex} q {/tex} are placed at the vertices of an equilateral triangle. The resulting lines of force should be sketched as in

A

B

D

##### Explanation

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Q 3. Consider the situation shown in the figure. The capacitor {tex} A {/tex} has a charge {tex} q {/tex} on it whereas {tex} B {/tex} is uncharged. The charge appearing on the capacitor {tex} B {/tex} a long time after the switch is closed is

zero

B

{tex} q / 2 {/tex}

C

{tex} q {/tex}

D

{tex} 2 q {/tex}

##### Explanation

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Q 4. In the arrangement of capacitors shown in figure, each capacitor is of {tex} 9 \mu F , {/tex} Then the equivalent capacitance between in points {tex} A {/tex} and {tex} B {/tex} is

A

{tex} 9 \mu \mathrm F {/tex}

B

{tex} 18 \mu \mathrm F {/tex}

C

{tex} 4.5 \mu \mathrm F {/tex}

{tex} 15\mu \mathrm F {/tex}

##### Explanation

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Q 5. In the electric field of a point charge {tex} q {/tex}, a certain point charges is carried from point {tex} A {/tex} to {tex} B , C , D {/tex} and {tex} E {/tex} as shown in figue The work done is

A

Least along the path {tex} A E {/tex}

B

Least along the path {tex} A C {/tex}

Zero along any one of the paths

D

Least along {tex} A B {/tex}

##### Explanation

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Q 6. Each capacitor shown in figure is {tex} 2 \mu \mathrm { F } . {/tex} Then the equivalent capacitance between points {tex} A {/tex} and {tex} B {/tex} is

{tex} 2 \mu \mathrm { F } {/tex}

B

{tex} 4\mu \mathrm F {/tex}

C

{tex} 6 \mu \mathrm F {/tex}

D

{tex} 8 \mu \mathrm { F } {/tex}

##### Explanation

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Q 7. Some equipotential surfaces are shown in Fig. The magnitude and direction of the electric field is

A

{tex} 100 \mathrm { Vm } ^ { - 1 } {/tex} making angle {tex} 120 ^ { \circ } {/tex} with the {tex} x {/tex} -axis

B

{tex} 200 \mathrm { Vm } ^ { - 1 } {/tex} making angle {tex} 60 ^ { \circ } {/tex} with the {tex} x {/tex} -axis

{tex} 200 \mathrm { Vm } ^ { - 1 } {/tex} making angle {tex} 120 ^ { \circ } {/tex} with the {tex} x {/tex} -axis

D

None of the above

##### Explanation

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Q 8. Charges {tex} 2 q , - q {/tex} and {tex} - q {/tex} lie at the vertices of a triangle. The value of {tex} E {/tex} and {tex} V {/tex} at the centroid of equilateral triangle will be

A

{tex} \mathrm { E } \neq 0 {/tex} and {tex} \mathrm { V } \neq 0 {/tex}

B

{tex} \mathrm { E } = 0 {/tex} and {tex} \mathrm { V } = 0 {/tex}

{tex} \mathrm { E } \neq 0 {/tex} and {tex} \mathrm { V } = 0 {/tex}

D

{tex} \mathrm { E } = 0 {/tex} and {tex} \mathrm { V } \neq 0 {/tex}

##### Explanation

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Q 9. For the circuit shown in figure the charge on {tex} 4 \mu \mathrm { F } {/tex} capacitor is

A

{tex} 40 \mu C {/tex}

B

{tex} 30 \mu C {/tex}

{tex} 24 \mu C {/tex}

D

{tex} 54 \mu C {/tex}

##### Explanation

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Q 10. Five balls numbered {tex} 1,2,3,4,5 {/tex} are suspended using separate threads. The balls {tex} ( 1,2 ) , ( 2,4 ) {/tex} and {tex} ( 4,1 ) {/tex} show electrostatic attraction, while balls {tex} ( 2,3 ) {/tex} and {tex} ( 4,5 ) {/tex} show repulsion. Therefore, ball {tex}1{/tex} must be

A

Negatively charged

B

Positively charged

Neutral

D

##### Explanation

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Q 11. A dielectric in the form of a sphere is introduced into a homogeneous electric field. {tex} A , B {/tex} and {tex} C {/tex} are three points as shown in fig

Then,

A

Intensity at {tex} A {/tex} increases while that at {tex} B {/tex} and {tex} C {/tex} decreases

B

Intensity at {tex} A {/tex} and {tex} B {/tex} decreases, whereas intensity at {tex} C {/tex} increases

Intensity at {tex} A {/tex} and {tex} C {/tex} increases and that {tex} B {/tex} decreases

D

Intensity at {tex} A , B {/tex} and {tex} C {/tex} decreases

##### Explanation

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Q 12. If the flux of the electric field through a closed surface is zero, then

A

The electric field must be zero everywhere on the surface

The total charge inside the surface must be zero

C

The electric field must be uniform throughout the closed surface

D

The charge outside the surface must be zero