Number of Functions Possible from Set A to Set B

Q. Set 'A' has 3 elements and set 'B' has 4 elements. The number of injection that can be defined from 'A' to 'B' is

1. 144
2. 12
3. 24
4. 64

Q. Five balls are to be placed in three boxes. Each box can hold all the five balls. In how many different ways can we place the balls so that no box remains empty, if balls are identical and boxes are different is

Q. The number of $5$ digits palindrome numbers is

1. $1000$
2. $990$
3. $900$
4. $999$

Q.

There are four parcels and five pos offices. In how many different ways can tl parcels be sent by registered post ?

Q. Let $A=\{1,2,3,4,5,6\}$ and $B=\{a,b,c,d\}$, then the total number of possible functions from $A$ to $B$

1. without any restriction is $6^4$
2. such that every element in $B$ has atleast one pre-image is $1560$
3. such that all the elements in $B$ should not have pre-image is $2536$
4. without any restriction is $4^6$

Q. Number of functions from a set $A$ containing $6$ elements to a set $B$ containing $3$ elements such that every element in $B$ has atleast one preimage is

1. $3^6-{}^3{C}_1-{}^3{C}_2(2^6+2)$
2. $534$
3. $540$
4. $3^6-{}^3{C}_1-{}^3{C}_2\left(2^6\right)$

Q.

In how many ways can an examinee answer a set of ten true/false type questions?

Q. The number of ways in which $20$ letters $a_1,a_2,a_3,\dots ,a_{10},b_1,b_2,b_3,\dots ,b_{10}$ can be arranged in a line so that suffixes of the letters $a$ and also those of $b$ are respectively in ascending order of magnitude is

1. $\frac{20!}{10!}$
2. $\frac{20!}{{(10!)}^2}$
3. $2^{20}$
4. $20!-10!\cdot 10!$

Q.

In how many ways can 7 letters posted in 4 letter boxes?

Q. If the number of ways in which four distinct balls can be put into two identical boxes so that no box remains empty is equal to $k$, then $k$ is

Q. The number of bijections of a set consisting of 10 elements to itself is :

1. 
2. 
3. 
4. 

Q. There are $20$ points lying on a circle, distance between two consecutive points is same. Three points are selected at random. $X$ represents number of ways to select them. $Y$ represents number of ways to select them such that no two adjacent points are selected and $Z$ represents number of ways to select them such that chosen points are not diametrically opposite. Which of the following is/are CORRECT?

1. $X=1140$
2. $Y=800$
3. $Z=960$
4. $Y\cap Z=660$

Q. Number of linear arrangements of $4$ alike of one kind and $5$ alike of another kind is NOT equal to

1. number of $5-$digit numbers whose digits are in increasing order from left to right.
2. number of linear arrangements of $8$ identical apples and $4$ identical oranges if no two oranges are together.
3. number of ways of distribution of $9$ distinct toys between two children when one is having exactly one toy more than the other.
4. number of ways in which $8$ students can be divided into two teams, that need not necessarily be of equal size.

Q. Consider the letters of the word $MATHEMATICS$.
The possible number of words in which no two vowels are together is

1. $7!\cdot {}^8{C}_4\cdot \frac{4!}{2!}$
2. $\frac{7!}{2!}\cdot {}^8{C}_4\cdot \frac{4!}{2!}$
3. $\frac{7!}{2!2!}\cdot {}^8{C}_4\cdot \frac{4!}{2!}$
4. $\frac{7!}{2!2!2!}\cdot {}^8{C}_4\cdot \frac{4!}{2!}$

Q. How many $3-$ digit even numbers can be made using the digits $1,2,3,4,6,7,$ if no digit is repeated?

Q. Set 'A' has 3 elements and set 'B' has 4 elements. The number of injection that can be defined from 'A' to 'B' is

1. 64
2. 144
3. 12
4. 24

Q. If $R$ is a relation from a finite set $A$ having $m$ elements to a finite set $B$ having $n$ elements, then the number of relations from $A$ to $B$ is:

1. $2^{mn}$
2. $2^{mn}-1$
3. $2mn$
4. $m^n$

Q. The number of ways in which $12$ different books can be put in three shelves with four on each shelf is

1. $\frac{12!}{(4!{)}^3}$
2. $\frac{12!}{(3!)(4!{)}^3}$
3. $\frac{12!}{(3!{)}^{3}4!}$
4. none of these

Q. Two numbers $x$ and $y$ are such that when divided by $6$ they leave remainders $4$ and $5$, respectively. Find the remainder when $(x^2+y^2)$ is divided by $6$.

Q.

In the given figure, observe the matchstick pattern and fill in the table that follows:

Q.

In how many ways can 5 different balls be distributed among three boxes ?

Q.

Determine the number of $5$ card combinations out of a deck of $52$ cards, If there is exactly one ace in each combination.

Q. The number of injections that can be defined from a set A consisting 5 elements to a set B consisting 6 elements is

1. 720
2. 360
3. 180
4. 90

Q. There are 'mn' letters and n post boxes. The number of ways in which these letters can be posted is:

1. $(mn{)}^n$
2. $(mn{)}^m$
3. $m{}^m{}^n$
4. $n{}^m{}^n$

Q. There are $4$ parcels and $5$ post-offices. In how many different ways the registration of parcel can be made.

1. $20$
2. $4^5$
3. $5^4-4^5$
4. $5^4$

Q. The number of possible many to one functions from $A=\{6,36\}$ to $B=\{1,2,3,4,5\}$ is

1. $32$
2. $25$
3. $5$
4. $20$

Q. A bag contains $9$ balls marked with digit $1,2,......9$. If two balls are drawn from the bag, then numbers of ways getting the sum of the digits on balls as $10$

1. $8$
2. $2^9$
3. ${}^9{C}_2$
4. ${}^9{P}_2$

Q. The number of functions $f$ from the set $A=\{0,1,2\}$ in to the set $B=\{0,1,2,3,4,5,6,7\}$ such that $f\left(i\right)<f\left(j\right)$ for $i<j$ and $i,j\in A$ is

1. ${}^8{C}_3$
2. ${}^8{C}_3+2{(}^8{C}_2)$
3. ${}^{10}{C}_3$
4. ${}^{10}{C}_4$

Q. Let $A=\{1,2,3,4,5,6\}$ and $B=\{a,b,c,d\}$, then the total number of possible functions from $A$ to $B$

1. without any restriction is $6^4$
2. such that every element in $B$ has atleast one pre-image is $1560$
3. such that all the elements in $B$ should not have pre-image is $2536$
4. without any restriction is $4^6$

Q. A square, non-singular matrix $A$ satifies $A^2-A+2I=0$, then $A^{-1}=$

1. $I-A$
2. $\frac{(I-A)}{2}$
3. $\frac{(I+A)}{2}$
4. $I+A$