Maths-

General

Easy

### Question

#### If is defined by then

one-one and not onto

one-one and onto

not one-one but onto

neither one-one nor onto

one-one and not onto

one-one and onto

not one-one but onto

neither one-one nor onto

### Hint:

In this question, we have to find the type of function if is defined by . A function is said to be one-one if different elements of A have different images in B, and a function is said to be onto if for all , there exists such that f (x) = y.

#### The correct answer is: not one-one but onto

## Book A Free Demo

+91

Grade*

Select Grade

### Related Questions to study

physics-

#### Two long parallel conductors carry currents in opposite directions as shown. One conductor carries a current of 10 A and the distance between the wires is d=10cm Current I is adjusted, so that the magnetic field at P is zero. P is at a distance of 5 cm to the right of the 10 A current. Value of I is

From Biot-Savart’s law the magnetic field due to a conductor carrying current at a distance is

Magnetic field at due to current in second conductor is

From Fleming’s right hands rule the fields at are directed opposite.

Given,

Magnetic field at due to current in second conductor is

From Fleming’s right hands rule the fields at are directed opposite.

Given,

#### Two long parallel conductors carry currents in opposite directions as shown. One conductor carries a current of 10 A and the distance between the wires is d=10cm Current I is adjusted, so that the magnetic field at P is zero. P is at a distance of 5 cm to the right of the 10 A current. Value of I is

physics-General

From Biot-Savart’s law the magnetic field due to a conductor carrying current at a distance is

Magnetic field at due to current in second conductor is

From Fleming’s right hands rule the fields at are directed opposite.

Given,

Magnetic field at due to current in second conductor is

From Fleming’s right hands rule the fields at are directed opposite.

Given,

physics-

#### Two long straight wires are set parallel to each other. Each carries a current in the opposite direction and the separation between them is 2R. The intensity of the magnetic field midway between them is

Magnetic field at mid-point due to wire

Magnetic field at mid-point due to wire

Resultant of Magnetic field

Magnetic field at mid-point due to wire

Resultant of Magnetic field

#### Two long straight wires are set parallel to each other. Each carries a current in the opposite direction and the separation between them is 2R. The intensity of the magnetic field midway between them is

physics-General

Magnetic field at mid-point due to wire

Magnetic field at mid-point due to wire

Resultant of Magnetic field

Magnetic field at mid-point due to wire

Resultant of Magnetic field

physics-

#### A current of 10 A is passing through a long wire which has semicircular loop of the radius 20 cm as shown in the figure. Magnetic field produced at the centre of the loop is

#### A current of 10 A is passing through a long wire which has semicircular loop of the radius 20 cm as shown in the figure. Magnetic field produced at the centre of the loop is

physics-General

physics-

#### In the figure shown, the magnetic field induction at the point will be

Field due to a straight wire of infinite length is if the point is on a line perpendicular to its length while at the centre of a semicircular coil is .

out of the page

out of the page

#### In the figure shown, the magnetic field induction at the point will be

physics-General

Field due to a straight wire of infinite length is if the point is on a line perpendicular to its length while at the centre of a semicircular coil is .

out of the page

out of the page

physics-

#### PQ and RS are long parallel conductors separated by certain distance. M is the mid-point between them (see the figure). The net magnetic field at M is B. Now, the current 2A is switched off. The field at M now becomes

Magnetic field at mid-point in first case is

When the current 2 A is switched off, the net magnetic field at is due to current 1 A

When the current 2 A is switched off, the net magnetic field at is due to current 1 A

#### PQ and RS are long parallel conductors separated by certain distance. M is the mid-point between them (see the figure). The net magnetic field at M is B. Now, the current 2A is switched off. The field at M now becomes

physics-General

Magnetic field at mid-point in first case is

When the current 2 A is switched off, the net magnetic field at is due to current 1 A

When the current 2 A is switched off, the net magnetic field at is due to current 1 A

physics-

#### Current through ABC and A’ B’ C’ is I. What is the magnetic field at P? (Here C’ B’ PBC are collinear)

Magnetic field

#### Current through ABC and A’ B’ C’ is I. What is the magnetic field at P? (Here C’ B’ PBC are collinear)

physics-General

Magnetic field

physics

#### The ratio of pathlength and the respective time interval is

#### The ratio of pathlength and the respective time interval is

physicsGeneral

physics

#### A particle is thrown in upward direction with initial velocity of 60 m/s. Find average speed and average velocity after 10 seconds. [g =10 MS^{2}]

#### A particle is thrown in upward direction with initial velocity of 60 m/s. Find average speed and average velocity after 10 seconds. [g =10 MS^{2}]

physicsGeneral

physics-

#### The work done in deforming body is given by

Let

Force necessary to deform the body is

If body is deformed by a distance, then

Hence, work done for unit volume is

*L*be length of body,*A*the area of cross-section and the increase in length.Force necessary to deform the body is

If body is deformed by a distance, then

Hence, work done for unit volume is

#### The work done in deforming body is given by

physics-General

Let

Force necessary to deform the body is

If body is deformed by a distance, then

Hence, work done for unit volume is

*L*be length of body,*A*the area of cross-section and the increase in length.Force necessary to deform the body is

If body is deformed by a distance, then

Hence, work done for unit volume is

physics-

#### A wire of length and radius is stretched between and without the application of any tension. If is the Young’s modulus of the wire and it is stretched like , then the tension in the wire will be

Increase in length of one segment of wire

So,

#### A wire of length and radius is stretched between and without the application of any tension. If is the Young’s modulus of the wire and it is stretched like , then the tension in the wire will be

physics-General

Increase in length of one segment of wire

So,

physics-

#### A cube of aluminium of sides 0.1 m is subjected to a sharing force of 100 N. The top face of the cube is displaced through 0.02 cm with respect to the bottom face. The shearing strain would be

Shearing strain =

#### A cube of aluminium of sides 0.1 m is subjected to a sharing force of 100 N. The top face of the cube is displaced through 0.02 cm with respect to the bottom face. The shearing strain would be

physics-General

Shearing strain =

physics-

#### A uniform slender rod of length L, cross-sectional area A and Young’s modulus Y is acted upon by the forces shown in the figure. The elongation of the rod is

Net elongation of the rod is

#### A uniform slender rod of length L, cross-sectional area A and Young’s modulus Y is acted upon by the forces shown in the figure. The elongation of the rod is

physics-General

Net elongation of the rod is

physics-

#### The graph shows the behaviour of a length of wire in the region for which the substance obeys Hooke’s law. and represent

Graph between applied force and extension will be straight line because in elastic range

Applied force extension

But the graph between extension and stored elastic energy will be parabolic in nature

As or

Applied force extension

But the graph between extension and stored elastic energy will be parabolic in nature

As or

#### The graph shows the behaviour of a length of wire in the region for which the substance obeys Hooke’s law. and represent

physics-General

Graph between applied force and extension will be straight line because in elastic range

Applied force extension

But the graph between extension and stored elastic energy will be parabolic in nature

As or

Applied force extension

But the graph between extension and stored elastic energy will be parabolic in nature

As or

physics-

#### If the shear modulus of a wire material is 5.9 then the potential energy of a wire of in diameter and 5 cm long twisted through an angle of 10’ , is

To twist the wire through the angle it is necessary to do the work

And

And

#### If the shear modulus of a wire material is 5.9 then the potential energy of a wire of in diameter and 5 cm long twisted through an angle of 10’ , is

physics-General

To twist the wire through the angle it is necessary to do the work

And

And

physics-

#### The Young’s modulus of the material of a wire is equal to the

Young’s modulus of material

If longitudinal strain is equal unity, then

Linear stress produced

If longitudinal strain is equal unity, then

Linear stress produced

#### The Young’s modulus of the material of a wire is equal to the

physics-General

Young’s modulus of material

If longitudinal strain is equal unity, then

Linear stress produced

If longitudinal strain is equal unity, then

Linear stress produced