Maths-

General

Easy

Question

Let $A$ be a set containing 10 distinct elements, then the total number of distinct functions from $A$ to $A$ is-

$10!$
$10^{10}$
$2^{10}$
$2^{10} - 1$

hint Hint:

First, from the given that we have” A” be a set containing $10$ distinct elements. Distinct elements mean all the elements in that function are different elements, which means no identical elements.
We also need to know about the concept of domain and co-domain as well, which is also known as the mapping in the range functions.

The correct answer is: $10 to the power of 10 end exponent$

Complete step-by-step solution:

Since from the given question, we have A be a set containing 10 distinct elements and the total number of distinct functions from A to A is the requirement.
Let us assume the set A with the elements like $A subscript 1 comma space A subscript 2 comma space......... comma space A subscript 10$
Then by using the function definition of the domain and co-domain we have a function from A to A which means itself : $f left parenthesis A subscript m right parenthesis space equals space A subscript m$ where m and n are the ranges from 1,2, ...... 10
Therefore, the total number of distinct function for number 1 is 1,2, ...... 10( it can be represented in any ten numbers) and the number 2 is 1,2, ..... 10 and proceeding like this we also get the number 10 as 1,2, ..... 10
Thus, we get for all the ten numbers we have 1, 2, ..... 10
Hence we have in total
$10 space cross times space 10 space cross times 10 space cross times space 10 space cross times 10 space cross times space 10 space cross times 10 space cross times space 10 space cross times 10 cross times 10 space equals space space 10 to the power of 10 space w a y s.$

The domain is defined as the set which is to input in a function. We say that input values satisfy a function. The range is defined as the actual output supposed to be obtained by entering the domain of the function.
Co-domain is defined as the values that are present in the right set that is set Y, possible values expected to come out after entering domain values.

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

maths-General

General

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 $20 blank m$ is

physics-General

General

physics-

A particle is acted upon by a force $F$ which varies with position $x$ as shown in figure. If the particle at $x equals 0$ has kinetic energy of 25 J, then the kinetic energy of the particle at $x equals 16 blank m$ is

physics-General

General

physics-

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

physics-General

General

physics-

Figure shows the $F$ - $x$ graph. Where $F$ is the force applied and $x$ is the distance covered

By the body along a straight line path. Given that $F$ is in $n e w t o n$ and $x blank$ in $m e t r e$ , what is the work done?

physics-General

General

maths-

Range of function f(x) = $fraction numerator x to the power of 2 end exponent plus 2 x plus 3 over denominator x end fraction$ , $x element of times R$ is given by -

maths-General

General

physics-

A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of masses $0.36 blank k g$ and $0.72 blank k g$ . Taking $g equals 10 blank m divided by s to the power of 2 end exponent$ , find the work done (in joules) by the string on the block of mass $0.36 blank k g$ during the first second after the system is released from rest

physics-General

General

physics-

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

physics-General

General

physics-

A block of mass $m equals 25$ kg sliding on a smooth horizontal surface with a velocity $v equals 3 m s to the power of negative 1 end exponent$ meets the spring of spring constant $k equals 100 N m to the power of negative 1 end exponent$ 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

General

physics-

The relationship between the force F and position $x$ of a body is as shown in figure. The work done in displacing the body from $x equals 1 m$ to $x equals 5$ m will be

physics-General

General

physics-

Three objects $A comma B$ and $C$ are kept in a straight line on a frictionless horizontal surface. These have masses $m comma blank 2 m$ and $m$ respectively. The object $A$ moves towards $B$ with a speed $9 blank m divided by s$ and makes an elastic collision with it. Thereafter, $B$ makes completely inelastic collision with $C$ . All motions occur on the same straight line. Find the final speed (in $m divided by s$ ) of the object $C$

physics-General

General

physics-

The relation between the displacement $X$ of an object produced by the application of the variable force $F$ is represented by a graph shown in the figure. If the object undergoes a displacement from $X equals 0.5 blank m$ to $X equals 2.5 blank m$ the work done will be approximately equal to

Have a query? Ask a Tutor!!

Can’t find what you’re looking for?

Let $A$ be a set containing 10 distinct elements, then the total number of distinct functions from $A$ to $A$ is-

$10!$
$10^{10}$
$2^{10}$
$2^{10} - 1$

The correct answer is: $10 to the power of 10 end exponent$

Related Questions to study

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

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

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 $20 blank m$ is

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 $20 blank m$ is

A particle is acted upon by a force $F$ which varies with position $x$ as shown in figure. If the particle at $x equals 0$ has kinetic energy of 25 J, then the kinetic energy of the particle at $x equals 16 blank m$ is

A particle is acted upon by a force $F$ which varies with position $x$ as shown in figure. If the particle at $x equals 0$ has kinetic energy of 25 J, then the kinetic energy of the particle at $x equals 16 blank m$ is

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

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

Figure shows the $F$ - $x$ graph. Where $F$ is the force applied and $x$ is the distance covered

By the body along a straight line path. Given that $F$ is in $n e w t o n$ and $x blank$ in $m e t r e$ , what is the work done?

Figure shows the $F$ - $x$ graph. Where $F$ is the force applied and $x$ is the distance covered

By the body along a straight line path. Given that $F$ is in $n e w t o n$ and $x blank$ in $m e t r e$ , what is the work done?

Range of function f(x) = $fraction numerator x to the power of 2 end exponent plus 2 x plus 3 over denominator x end fraction$ , $x element of times R$ is given by -

Range of function f(x) = $fraction numerator x to the power of 2 end exponent plus 2 x plus 3 over denominator x end fraction$ , $x element of times R$ is given by -

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

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

The relationship between the force F and position $x$ of a body is as shown in figure. The work done in displacing the body from $x equals 1 m$ to $x equals 5$ m will be

The relationship between the force F and position $x$ of a body is as shown in figure. The work done in displacing the body from $x equals 1 m$ to $x equals 5$ m will be

The relation between the displacement $X$ of an object produced by the application of the variable force $F$ is represented by a graph shown in the figure. If the object undergoes a displacement from $X equals 0.5 blank m$ to $X equals 2.5 blank m$ the work done will be approximately equal to

The relation between the displacement $X$ of an object produced by the application of the variable force $F$ is represented by a graph shown in the figure. If the object undergoes a displacement from $X equals 0.5 blank m$ to $X equals 2.5 blank m$ the work done will be approximately equal to

Have a query? Ask a Tutor!!

Can’t find what you’re looking for?

Let be a set containing 10 distinct elements, then the total number of distinct functions from to is-

The correct answer is:

Related Questions to study

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

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

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

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

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

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

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

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

Figure shows the -graph. Where is the force applied and is the distance coveredBy the body along a straight line path. Given that is in and in , what is the work done?

Figure shows the -graph. Where is the force applied and is the distance coveredBy the body along a straight line path. Given that is in and in , what is the work done?

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

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

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

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

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

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

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

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

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

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

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

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

Let $A$ be a set containing 10 distinct elements, then the total number of distinct functions from $A$ to $A$ is-

The correct answer is: $10 to the power of 10 end exponent$

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 $20 blank m$ is

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 $20 blank m$ is

A particle is acted upon by a force $F$ which varies with position $x$ as shown in figure. If the particle at $x equals 0$ has kinetic energy of 25 J, then the kinetic energy of the particle at $x equals 16 blank m$ is

A particle is acted upon by a force $F$ which varies with position $x$ as shown in figure. If the particle at $x equals 0$ has kinetic energy of 25 J, then the kinetic energy of the particle at $x equals 16 blank m$ is

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

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

Figure shows the $F$ - $x$ graph. Where $F$ is the force applied and $x$ is the distance covered

By the body along a straight line path. Given that $F$ is in $n e w t o n$ and $x blank$ in $m e t r e$ , what is the work done?

Figure shows the $F$ - $x$ graph. Where $F$ is the force applied and $x$ is the distance covered

By the body along a straight line path. Given that $F$ is in $n e w t o n$ and $x blank$ in $m e t r e$ , what is the work done?

Range of function f(x) = $fraction numerator x to the power of 2 end exponent plus 2 x plus 3 over denominator x end fraction$ , $x element of times R$ is given by -

Range of function f(x) = $fraction numerator x to the power of 2 end exponent plus 2 x plus 3 over denominator x end fraction$ , $x element of times R$ is given by -

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

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

The relationship between the force F and position $x$ of a body is as shown in figure. The work done in displacing the body from $x equals 1 m$ to $x equals 5$ m will be

The relationship between the force F and position $x$ of a body is as shown in figure. The work done in displacing the body from $x equals 1 m$ to $x equals 5$ m will be

The relation between the displacement $X$ of an object produced by the application of the variable force $F$ is represented by a graph shown in the figure. If the object undergoes a displacement from $X equals 0.5 blank m$ to $X equals 2.5 blank m$ the work done will be approximately equal to

The relation between the displacement $X$ of an object produced by the application of the variable force $F$ is represented by a graph shown in the figure. If the object undergoes a displacement from $X equals 0.5 blank m$ to $X equals 2.5 blank m$ the work done will be approximately equal to