Number of Elements in a Cartesian Product

Q.

Suppose that the number of elements in set $A$ is $p$, the number of elements in set $B$ is $q$ and the number of elements in $A\times B$ is $7$. Then $p^2+q^2=$

1. $42$

2. $49$

3. $50$

4. $51$

Q.

A and B are two sets given in such a way that $(A\times B)$ contains 6 elements. If three elements of $(A\times B)$ be (1, 3), (2, 5) and (3, 3), find its remaining elements.

Q.

What does $r$ mean in ${}^{n}P_r$?

Q. Let $A=\{a,b,c,d\},$ $B=\{b,c,e,f\},$ then $n\left(\right(A-B)\times (B-A\left)\right)=$

1. $4$
2. $16$
3. $8$
4. $12$

Q.

If the Cartesian product A $\times$ A has 16 elements among which few elements are found to be (-1, 0), (0, 1), (1, 2). Find set A.

1. {-1, 0, 2, 3}

2. {-1, 0, 1}

3. {-1, 0, 1, 2}

4. {0, 1, 2, 3}

Q.

Let $A$be a set with $n$ elements. The number of onto functions from $A$to $A$ is?

1. $n^n$

2. $n^n-n!$

3. $\frac{n^n}{n!}$

4. $n!$

Q. If $A=\{3,5\}$ and $A\times B=B\times A$, then the correct option(s) can be

1. $B=\{x:x^2-8x+15=0\}$
2. $B=\{x:|x-4|=1\}$
3. $B=\{x:x\text{is prime factor of}15\}$
4. $B=\{x:x\in N,3\le x\le 5\}$

Q. If the set $A$ has $3$ elements and the set $B=\{3,4,5\}$ then find the number of elements in $(A\times B)$?

Q. If set A = {1, 2, 3} and set B = {2, 3, 5, 7} then the number of elements in A $\times$ B is .

1. 10
2. 11
3. 12
4. 13

Q. A set contains 5 elements. If the number of ways to construct 3 subsets of this set with replacement is N, then find N if i)subsets have exactly one element common ii)union of these subsets contain 3 elements iii)these subsets are pairwise disjoint iv)none of 3 subsets is empty

Q. A set contains (2n+1) elements. The number of subsets of this set containing more than n elements is equal to 1) 2^n-1 2)2^n 3)2^{n+1} 4)2^{2n

Q. If $R$ is relation from $A$ to $B$, where $R=\left\{\right(x,y):x,y\in Z,x^2+y^2\le 4\}$, then the least value of $n(A\times B)$ is

1. $25$
2. infinite
3. $16$
4. $9$

Q. If $A\times B$ has $6$ elements and $(-3,-2),(4,4),(2,-2)$ are the elements of $A\times B$, then the correct option(s) is/are

1. $A=\{-3,2\}$
2. $B=\{-2,4\}$
3. $A\times B=\left\{\right(-3,-2),(2,-2),(4,-2),(-3,4),(2,4),(4,4\left)\right\}$
4. $B\times A=\left\{\right(-2,-3),(-2,2),(4,-3),(4,2\left)\right\}$

Q.

If set A = {1, 2, 3} and set B = {2, 3, 5, 7}. Find the number of elements in A $\times$ B.

__

Q.

Suppose A1, A2, .....................A30 are thirty sets each having 5 elements and B1, B2, ................Bn are n sets each with 3 elements, let $\bigcup _{i=1}^{30}$$A_i$=$\bigcup _{j=1}^n$$B_j$ = S and each element of S belongs to exactly 10 of $A_i$'S and exactly 9 of the $B_j$'S. Then n is equal to

1. 15

2. 50

3. 3

4. 45

Q. If set A has p elements and set B has q elements, then the number of elements in set $A\times B$ is .

1. $\frac{P}{q}$
2. $p^q$
3. $p\times q$
4. $q^p$

Q.

If set A has p element and set B has q element number of element in set (A $\times$ B) is _____.

1. 

2. 

3. 

4. 

Q. 5. Two finite sets A And B have p and q elements respectively (p>q). The number of the subsets of the power set of A is 240 more than the total number of subsets of the power set of B. Then p+q is

Q. If $A=\{5,6,7\},B=\{1,2,3,4\}$, then number of elements in set $(A-B)\times B$ is

1. $24$
2. $36$
3. $12$
4. $16$

Q. Let $A=\{1,2,3\},B=\{4,5,6,7,8\},$ $C=\{4,6,8,10,12\},$ then $n\left[\right(A\times B)-(A\times C\left)\right]=$

1. $6$
2. $12$
3. $1$
4. $24$

Q. If $A=\{y:|y|=3x,x\le 2,x\in N\},$
$B=\{x:x\text{is a positive even number},x<14\}$ and $C=\{1,4,8\},$ then $n\left(\right(A\times B)\cap (A\times C\left)\right)$ is

1. $40$
2. $8$
3. $20$
4. $36$

Q. How many functions can be defined from a set $A$ containing $5$ elements to a set $B$ having $3$ elements$?$ How many of these are onto functions$?$

Q.

If set A = {1, 2, 3} and set B = {2, 3, 5, 7}. Find the number of elements in A $\times$ B.

__

Q.

If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in $(A\times B).$

Q.

The least value of expression $x^2+4y^2+9z^2$ - 2x + 8y + 27z + 15 is :

1. 15

2. 5

3. 0

4. None

Q.

If A and B are subsets of the universal set U, then show that:-

(i) AsubsetAUB

(ii) AsubsetBAUB=B

Q.

If set A has p element and set B has q elements, then the number of element in set (A $\times$ B) is _____.

1. 

2. 

3. 

4. 

Q.

A $\times$ A $\times$ A has 512 elements. Find the number of elements in A.

Q. Let $A=\{1,2,3,4\},$ $B=\{4,5,6,7\},$ $C=\{3,6,9,12\}$ and $D=\{4,8,12,16,20\},$ then $n\left[\right(A\times B)\cap (C\times D\left)\right]$ =

1. $1$
2. $2$
3. $4$
4. $8$

Q.

Given two finite sets A and B such that n(A) = 3, n(B) = 3. Then total number of relations from A to B is _____.

1. 8

2. 4

3. 512

4. 6