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JEE Advanced

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.

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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. 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 3. 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 4. Consider an electric field {tex} \vec { E } = E _ { 0 } \hat { x } {/tex} where {tex} \mathrm { E } _ { 0 } {/tex} is a constant. The flux through the shaded area (as shown in the figure) due to this field is

A

{tex} 2 E _ { 0 } a _ { 2 } {/tex}

B

{tex} \sqrt { 2 } E _ { 0 } a ^ { 2 } {/tex}

{tex} E _ { 0 } \mathrm { a } ^ { 2 } {/tex}

D

{tex} \frac { E _ { 0 } a ^ { 2 } } { \sqrt { 2 } } {/tex}

Explanation



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Q 5. A parallel plate capacitor of area {tex} A , {/tex} plate separation {tex} d {/tex} and capacitance {tex} C {/tex} is filled with three different dielectric materials having dielectric constants {tex} K _ { 1 } , K _ { 2 } {/tex} and {tex} K _ { 3 } {/tex} as shown. If a single dieletric material is to be used to have the same capacitance {tex} C {/tex} is this capacitors, then its dielectric constant {tex} K {/tex} is given by

A

{tex} \frac { 1 } { K } = \frac { 1 } { K _ { 1 } } + \frac { 1 } { K _ { 2 } } + \frac { 1 } { 2 K _ { 3 } } {/tex}

{tex} \frac { 1 } { K } = \frac { 1 } { K _ { 1 } + K _ { 2 } } + \frac { 1 } { 2 K _ { 3 } } {/tex}

C

{tex} K = \frac { K _ { 1 } K _ { 2 } } { K _ { 1 } + K _ { 2 } } + 2 K _ { 3 } {/tex}

D

{tex} K = K _ { 1 } + K _ { 2 } + 2 K _ { 3 } {/tex}

Explanation


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Q 6. 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 7. Three identical metallic uncharged spheres {tex} A , B {/tex} and {tex} C {/tex} each of radius {tex} a {/tex}, are kept at the corners of an equilateral triangle of side {tex} d ( d \gg a ) {/tex} as shown in Fig. The fourth sphere (of radius {tex} a {/tex} ), which has a charge {tex} q {/tex}, touches {tex} A {/tex} and is then removed to a position far away. {tex} B {/tex} is earthed and then the earth connection is removed. {tex}C {/tex} is then earthed. The charge on {tex} C {/tex} is

A

{tex} \frac { q a } { 2 d } \left( \frac { 2 d - a } { 2 d } \right) {/tex}

B

{tex} \frac { q a } { 2 d } \left( \frac { 2 d - a } { d } \right) {/tex}

{tex} - \frac { q a } { 2 d } \left( \frac { d - a } { d } \right) {/tex}

D

{tex} \frac { 2 q a } { d } \left( \frac { d - a } { 2 d } \right) {/tex}

Explanation

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Q 8. Two copper spheres of same radii, one hollow and the other solid, are charged to same potential. Then, which, if any, of the two will have more charge?

A

Hollow

B

Solid

Both will have the same charge

D

Nothing can be predicted

Explanation

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Q 9. 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 10. 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 11. 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 12. 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 13. 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 14. Three infinite planes have a uniform surface charge distribution {tex} \sigma {/tex} on its surface. All charges are fixed. On each of the three infinite planes, parallel to the {tex} y - z {/tex} plane placed at {tex} x = - a , x = 0 {/tex} and {tex} x = a {/tex}. There is a uniform surface charge of the same density, {tex} \sigma {/tex}

The potential difference between {tex} A {/tex} and {tex} C {/tex} is

A

{tex} \frac { \sigma } { 2 \varepsilon _ { 0 } } a {/tex}

B

{tex} \frac { \sigma } { \varepsilon _ { 0 } } a {/tex}

C

{tex} \frac { \sigma a } { 2 \varepsilon _ { 0 } } {/tex}

None of the above

Explanation

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Q 15. 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

Made of metal

Explanation



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Q 16. 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 17. Three infinitely long charge sheets are placed as shown in figure. The electric field at point {tex} P {/tex} is

A

{tex} \frac { 2 \sigma } { \varepsilon _ { 0 } } \widehat { k } {/tex}

{tex} - \frac { 2 \sigma } { \varepsilon _ { 0 } } \widehat { k } {/tex}

C

{tex} \frac { 4 \sigma } { \varepsilon _ { 0 } } \widehat { k } {/tex}

D

{tex} - \frac { 4 \sigma } { \varepsilon _ { 0 } } \widehat { k } {/tex}

Explanation

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Q 18. 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

Explanation

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Q 19. Find the electric field vector at {tex} P ( a , a , a ) {/tex} due to three infinitely long lines of charges along the {tex} x - , y- {/tex} and {tex} z - {/tex} axis, respectively. The charge density, i.e., charge per unit length of each wire is {tex} \lambda {/tex}

A

{tex} \frac { \lambda } { 3 \pi \varepsilon _ { 0 } a } ( \hat { \imath } + \hat { \jmath } + \hat { k } ) {/tex}

{tex} \frac { \lambda } { 2 \pi \varepsilon _ { 0 } a } ( \hat { \imath } + \hat { \jmath } + \hat { k } ) {/tex}

C

{tex} \frac { \lambda } { 2 \sqrt { 2 } \pi \varepsilon _ { 0 } a } ( \hat { \imath } + \hat { \jmath } + \hat { k } ) {/tex}

D

{tex} \frac { \sqrt { 2 } \lambda } { \pi \varepsilon _ { 0 } a } ( \hat { \imath } + \hat { \jmath } + \hat { k } ) {/tex}

Explanation



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Q 20. Consider an electric field {tex} \vec { E } = E _ { 0 } \hat { x } {/tex} where {tex} \mathrm { E } _ { 0 } {/tex} is a constant. The flux through the shaded area (as shown in the figure) due to this field is

A

{tex} 2 E _ { 0 } a _ { 2 } {/tex}

B

{tex} \sqrt { 2 } E _ { 0 } a ^ { 2 } {/tex}

{tex} E _ { 0 } \mathrm { a } ^ { 2 } {/tex}

D

{tex} \frac { E _ { 0 } a ^ { 2 } } { \sqrt { 2 } } {/tex}

Explanation



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Q 21. Let {tex} E _ { 1 } ( r ) , E _ { 2 } ( r ) {/tex} and {tex} E _ { 3 } ( r ) {/tex} be the respective electric field at a distance r from a point charge {tex} Q , {/tex} an infinitely long wire with constant lines chargedensity {tex} \lambda , {/tex} and an infinite plane with uniform surface charge density {tex} \sigma , {/tex} If {tex} E _ { 1 } \left( r _ { 0 } \right) = E _ { 2 } \left( r _ { 0 } \right) = E _ { 3 } \left( r _ { 0 } \right) {/tex} at a given distance {tex} r _ { 0 } , {/tex} then

A

{tex} Q = 4 \sigma \pi \mathrm { r } _ { 0 } ^ { 2 } {/tex}

B

{tex} r _ { 0 } = \frac { \lambda } { 2 \pi \sigma } {/tex}

{tex} E _ { 1 } \left( r _ { 0 } / 2 \right) = 2 E _ { 2 } \left( r _ { 0 } / 2 \right) {/tex}

D

{tex} E _ { 2 } \left( r _ { 0 } / 2 \right) = 4 E _ { 3 } \left( r _ { 0 } / 2 \right) {/tex}

Explanation





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Q 22. A particle of charge {tex} - q {/tex} and mass {tex} m {/tex} moves in a circle of radius {tex}r{/tex} around an infinitely long line charge of linear charge density {tex} + \lambda {/tex}. Then time period will be

{tex} T = 2 \pi r \sqrt { \frac { m } { 2 k \lambda q } } {/tex}

B

{tex} T ^ { 2 } = \frac { 4 \pi ^ { 2 } m } { 2 k \lambda q } r ^ { 3 } {/tex}

C

{tex} T = \frac { 1 } { 2 \pi r } \sqrt { \frac { 2 k \lambda q } { m } } {/tex}

D

{tex} T = \frac { 1 } { 2 \pi r } \sqrt { \frac { m } { 2 \mathrm { k } \lambda q } } {/tex}

Explanation

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Q 23. The electric dipole is situated is an electric field as shown in fig {tex} 1 . {/tex} The dipole and electric field are both in the plane of the paper. The dipole is rotated about an axis perpendicular to plane of paper passing through {tex}A{/tex} in anticlockwise direction. If the angle of rotation {tex} ( \theta ) {/tex} is measured with respect to the direction of electric field, then the torque {tex} ( \tau ) {/tex} experienced by the dipole for different values of the angle of rotation {tex} \theta {/tex} will be represented in fig. {tex} 2 , {/tex} by

A

curve(1)

curve(2)

C

curve(3)

D

curve(4)

Explanation

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Q 24. A spherical conductor A contains two spherical cavities. The total charge on the conductor itself is zero. However, there is a point charge {tex} q _ { b } {/tex} at the centre of one cavity and {tex} q _ { c } {/tex} at the centre of the other.
A considerable distance {tex} r {/tex} away from the centre of the spherical conductor, there is another charge {tex} q _ { d } {/tex}, Force acting on {tex} q _ { b } , q _ { c } {/tex} and {tex} q _ { d } {/tex} are {tex} F _ { 1 } F _ { 2 } {/tex} and {tex} F _ { 3 } {/tex} respectively, then (Assume all charges are positive)

A

{tex} F _ { 1 } < F _ { 2 } < F _ { 3 } {/tex}

{tex} F _ { 1 } = F _ { 2 } < F _ { 3 } {/tex}

C

{tex} F _ { 1 } = F _ { 2 } > F _ { 3 } {/tex}

D

{tex} F _ { 1 } > F _ { 2 } > F _ { 3 } {/tex}

Explanation

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Q 25. An electron with initial kinetic energy {tex} K _ { 0 } {/tex} is ejected at point {tex} A {/tex} as shown in the figure.

The acceleration of the electron (mass {tex} = \mathrm { m } _ { \mathrm { e } } {/tex} ) along y-axis is

A

{tex} \frac { 4 \pi \sigma e ^ { 2 } } { m _ { e } } {/tex}

{tex} \frac { - 4 \pi \sigma e } { m _ { e } } {/tex}

C

{tex} \frac { - 4 \pi e \sigma ^ { 2 } } { m _ { e } } {/tex}

D

{tex} \frac { - 4 \pi \sigma } { e m _ { e } } {/tex}

Explanation