Maths-

General

Easy

### Question

#### The number of bijective functions from set A to itself when a contains 106 elements-

- 106
- (106)
^{2}
- 106!
- 1
^{106}

^{2}^{106}#### The correct answer is: 106!

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### Related Questions to study

physics-

#### The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of is

Work done area under graph

= area of trapezium area of trapezium

= area of trapezium area of trapezium

#### The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of is

physics-General

Work done area under graph

= area of trapezium area of trapezium

= area of trapezium area of trapezium

physics-

#### A particle is acted upon by a force which varies with position as shown in figure. If the particle at has kinetic energy of 25 J, then the kinetic energy of the particle at is

Work done=area between the graph force displacement curve and displacement

According to work energy theorem

=20+25

=45J

According to work energy theorem

=20+25

=45J

#### A particle is acted upon by a force which varies with position as shown in figure. If the particle at has kinetic energy of 25 J, then the kinetic energy of the particle at is

physics-General

Work done=area between the graph force displacement curve and displacement

According to work energy theorem

=20+25

=45J

According to work energy theorem

=20+25

=45J

physics-

#### A vertical spring with force constant is fixed on a table. A ball of mass at a height above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance . The net work done in the process is

Gravitational potential energy of ball gets converted into elastic potential energy of the spring

Net work done

Net work done

#### A vertical spring with force constant is fixed on a table. A ball of mass at a height above the free upper end of the spring falls vertically on the spring so that the spring is compressed by a distance . The net work done in the process is

physics-General

Gravitational potential energy of ball gets converted into elastic potential energy of the spring

Net work done

Net work done

physics-

#### Figure shows the -graph. Where is the force applied and is the distance covered

By the body along a straight line path. Given that is in and in , what is the work done?

Work done =area under curve and displacement axis

#### Figure shows the -graph. Where is the force applied and is the distance covered

By the body along a straight line path. Given that is in and in , what is the work done?

physics-General

Work done =area under curve and displacement axis

maths-

#### Range of function f(x) = , is given by -

]

(C)

(C)

#### Range of function f(x) = , is given by -

maths-General

]

(C)

(C)

physics-

#### A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses and . Taking , find the work done (in joules) by the string on the block of mass during the first second after the system is released from rest

In the given condition tension in the string

And acceleration of each block

Let ‘S’ is the distance covered by block of mass in first sec

Work done by the string

And acceleration of each block

Let ‘S’ is the distance covered by block of mass in first sec

Work done by the string

#### A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses and . Taking , find the work done (in joules) by the string on the block of mass during the first second after the system is released from rest

physics-General

In the given condition tension in the string

And acceleration of each block

Let ‘S’ is the distance covered by block of mass in first sec

Work done by the string

And acceleration of each block

Let ‘S’ is the distance covered by block of mass in first sec

Work done by the string

physics-

#### An object of mass is tied to a string of length and a variable horizontal force is applied on it which starts at zero and gradually increases until the string makes an angel with the vertical. Work done by the force is

or

(Since, change in kinetic energy is zero)

Here, work done by tension = 0

work done by fore of gravity

(Since, change in kinetic energy is zero)

Here, work done by tension = 0

work done by fore of gravity

#### An object of mass is tied to a string of length and a variable horizontal force is applied on it which starts at zero and gradually increases until the string makes an angel with the vertical. Work done by the force is

physics-General

or

(Since, change in kinetic energy is zero)

Here, work done by tension = 0

work done by fore of gravity

(Since, change in kinetic energy is zero)

Here, work done by tension = 0

work done by fore of gravity

physics-

#### A block of mass kg sliding on a smooth horizontal surface with a velocity meets the spring of spring constant fixed at one end as shown in figure. The maximum compression of the spring and velocity of block as is returns to the original position respectively are

When block strikes the spring, the kinetic energy of block converts into potential energy of spring ie,

Or

When block returns to the original position, again potential energy converts into kinetic energy of the blocks, so velocity of the block is same as before but its sign changes as it goes to mean position.

Or

When block returns to the original position, again potential energy converts into kinetic energy of the blocks, so velocity of the block is same as before but its sign changes as it goes to mean position.

#### A block of mass kg sliding on a smooth horizontal surface with a velocity meets the spring of spring constant fixed at one end as shown in figure. The maximum compression of the spring and velocity of block as is returns to the original position respectively are

physics-General

When block strikes the spring, the kinetic energy of block converts into potential energy of spring ie,

Or

When block returns to the original position, again potential energy converts into kinetic energy of the blocks, so velocity of the block is same as before but its sign changes as it goes to mean position.

Or

When block returns to the original position, again potential energy converts into kinetic energy of the blocks, so velocity of the block is same as before but its sign changes as it goes to mean position.

physics-

#### The relationship between the force F and position of a body is as shown in figure. The work done in displacing the body from to m will be

Work done=area enclosed by graph

=area of ABNM + area of CDEN - area of EFGH + area of HIJ

=

=area of ABNM + area of CDEN - area of EFGH + area of HIJ

=

#### The relationship between the force F and position of a body is as shown in figure. The work done in displacing the body from to m will be

physics-General

Work done=area enclosed by graph

=area of ABNM + area of CDEN - area of EFGH + area of HIJ

=

=area of ABNM + area of CDEN - area of EFGH + area of HIJ

=

physics-

#### Three objects and are kept in a straight line on a frictionless horizontal surface. These have masses and respectively. The object moves towards with a speed and makes an elastic collision with it. Thereafter, makes completely inelastic collision with . All motions occur on the same straight line. Find the final speed (in ) of the object

After elastic collision strikes to with velocity of . Now collision between and is perfectly inelastic

By the law of conservation of momentum

#### Three objects and are kept in a straight line on a frictionless horizontal surface. These have masses and respectively. The object moves towards with a speed and makes an elastic collision with it. Thereafter, makes completely inelastic collision with . All motions occur on the same straight line. Find the final speed (in ) of the object

physics-General

After elastic collision strikes to with velocity of . Now collision between and is perfectly inelastic

By the law of conservation of momentum

physics-

#### The relation between the displacement of an object produced by the application of the variable force is represented by a graph shown in the figure. If the object undergoes a displacement from to the work done will be approximately equal to

Work done = Area under curve and displacement axis

= Area of trapezium

As the area actually is not trapezium so work done will be more than approximately

= Area of trapezium

As the area actually is not trapezium so work done will be more than approximately