Maths-

General

Easy

Question

# If then y satisfies

Hint:

### In this question we have to differentiate the function twice to get the required result.

## The correct answer is:

### Related Questions to study

physics-

### In the figure, a proton moves a distance d in a uniform electric field E as shown in the figure. Does the electric field do a positive or negative work on the proton? Does the electric potential energy of the proton increase or decrease?

Since, the proton is moving against the direction of electric field so, work is done by the proton against electric field. It implies that electric field does negative work on the proton.

Again, proton is moving in electric field from low potential region to high potential region hence, its potential energy increases.

Again, proton is moving in electric field from low potential region to high potential region hence, its potential energy increases.

### In the figure, a proton moves a distance d in a uniform electric field E as shown in the figure. Does the electric field do a positive or negative work on the proton? Does the electric potential energy of the proton increase or decrease?

physics-General

Since, the proton is moving against the direction of electric field so, work is done by the proton against electric field. It implies that electric field does negative work on the proton.

Again, proton is moving in electric field from low potential region to high potential region hence, its potential energy increases.

Again, proton is moving in electric field from low potential region to high potential region hence, its potential energy increases.

maths-

### Solution of is

### Solution of is

maths-General

physics-

### Two charges and are placed 30 cm apart, as shown in the figure. A third charge is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is where k is

When charge is at , then its potential energy is

Where charge is at , then

Hence, change in potential energy

Where charge is at , then

Hence, change in potential energy

### Two charges and are placed 30 cm apart, as shown in the figure. A third charge is moved along the arc of a circle of radius 40 cm from C to D. The change in the potential energy of the system is where k is

physics-General

When charge is at , then its potential energy is

Where charge is at , then

Hence, change in potential energy

Where charge is at , then

Hence, change in potential energy

physics-

### Figure shows three spherical and equipotential surfaces A, B and C round a point charge q. The potential difference. If and be the distance between them. Then

Potential difference between two equipotential surfaces A and B.

Or

Or

Similarly,

Since,

therefore

Or

Or

Similarly,

Since,

therefore

### Figure shows three spherical and equipotential surfaces A, B and C round a point charge q. The potential difference. If and be the distance between them. Then

physics-General

Potential difference between two equipotential surfaces A and B.

Or

Or

Similarly,

Since,

therefore

Or

Or

Similarly,

Since,

therefore

physics-

### Charges +q and –q are placed at points A and B respectively which are a distance apart, C is the mid-point between A and B. The work done in moving a charge+ along the semicircle CRD is

In Ist case, when charge is situated at C

Electric potential energy of system

In IInd case, when charge is moved from C to D.

Electric potential energy of system in that case

Electric potential energy of system

In IInd case, when charge is moved from C to D.

Electric potential energy of system in that case

### Charges +q and –q are placed at points A and B respectively which are a distance apart, C is the mid-point between A and B. The work done in moving a charge+ along the semicircle CRD is

physics-General

In Ist case, when charge is situated at C

Electric potential energy of system

In IInd case, when charge is moved from C to D.

Electric potential energy of system in that case

Electric potential energy of system

In IInd case, when charge is moved from C to D.

Electric potential energy of system in that case

physics-

### Consider three concentric shells of metal A, B and C are having radii a, b and c respectively as shown in the figure Their surface charge densities are respectively. Calculate the electric potential on the surface of shell A

The electric potential on the surface of shell

Or

Or

### Consider three concentric shells of metal A, B and C are having radii a, b and c respectively as shown in the figure Their surface charge densities are respectively. Calculate the electric potential on the surface of shell A

physics-General

The electric potential on the surface of shell

Or

Or

physics-

### Work required to set up the four charge configuration (as shown in the figure) is

Work is required to set up the four charge configuration

### Work required to set up the four charge configuration (as shown in the figure) is

physics-General

Work is required to set up the four charge configuration

physics-

### The points resembling equal potentials are

The points S and R are inside the uniform electric field, so these will be at equal potential.

### The points resembling equal potentials are

physics-General

The points S and R are inside the uniform electric field, so these will be at equal potential.

physics-

### In the following diagram the work done in moving a point charge from point P to point A, B and C is respectively as then

When a positive charge is moved from one point to another in an electric of magnetic field, then under the influence of the field force acts on the particle and an external agent will have to do work against this force. But in the given case the charge moves under influence of no field, hence it does not experience any force therefore, no work is done.

### In the following diagram the work done in moving a point charge from point P to point A, B and C is respectively as then

physics-General

When a positive charge is moved from one point to another in an electric of magnetic field, then under the influence of the field force acts on the particle and an external agent will have to do work against this force. But in the given case the charge moves under influence of no field, hence it does not experience any force therefore, no work is done.

physics-

### Three charges and are placed at the vertices of an isosceles right angle triangle as in the figure. The net electrostatic potential energy is zero if is equal to

Here total electrostatic potential energy is zero

On solving,

On solving,

### Three charges and are placed at the vertices of an isosceles right angle triangle as in the figure. The net electrostatic potential energy is zero if is equal to

physics-General

Here total electrostatic potential energy is zero

On solving,

On solving,

physics-

### A hollow conducting sphere is placed in an electric field produced by a point charge placed at P as shown in figure. be the potentials at points A, B and C respectively. Then

At each point on the surface of a conducting sphere the potential is equal.

So,

So,

### A hollow conducting sphere is placed in an electric field produced by a point charge placed at P as shown in figure. be the potentials at points A, B and C respectively. Then

physics-General

At each point on the surface of a conducting sphere the potential is equal.

So,

So,

physics-

### The figure shows electric potential V as a function of . Rank the four regions according to the magnitude of -component of the electric field E within them, greatest first

Electric field

For I region, =constant

For II region,

For III region.

=constant

For IV region,

From these values, we have

For I region, =constant

For II region,

For III region.

=constant

For IV region,

From these values, we have

### The figure shows electric potential V as a function of . Rank the four regions according to the magnitude of -component of the electric field E within them, greatest first

physics-General

Electric field

For I region, =constant

For II region,

For III region.

=constant

For IV region,

From these values, we have

For I region, =constant

For II region,

For III region.

=constant

For IV region,

From these values, we have

maths-

### The general solution of the equation is

### The general solution of the equation is

maths-General

Maths-

### Solution of is given by

### Solution of is given by

Maths-General

Maths-

### Equation of the curve passing through (3, 9) which satisfies the differential equation is

### Equation of the curve passing through (3, 9) which satisfies the differential equation is

Maths-General