Number of Elements in Cartesian Product

Q. If A = {a, b, p}, B = {2, 3}, C = {p, q, r, s} then
n [(A $\cup$ C) × B] is ____

1. 8
2. 20
3. 12
4. 16

Q.

If set A has 10 elements and set B has 4 elements, number of elements in set A $\times$ B is _____.

1. 40

2. 30

3. 4

4. 2.5

Q. If $(x+3,5)=(7,2x+y),$ then $x=$ and $y=$ .

1. -4
2. 4
3. -3
4. 3

Q.

What is the number of times 3 appears from 1 to 1000?

1. 300

2. 500

3. 400

4. 250

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

1. 7
2. 6
3. 9
4. 5

Q.

Sets A and B have 3 and 6 elements respectively. The minimum number of elements in $(A\cup B)$ is 6. State True/False.

1. 3

2. 6

Q.

If B $\times$ A = {(x, a), (x, b), (x, c), (y, a), (y, b), (y, c), (z, a), (z, b), (z, c)}. Find set A and set B.

1. A = {x, y, z}, B = {a, b, c}

2. A = {a, b, c}, B = {x, y, z}

3. A = {a, x, y}, B = {b, c, z}

4. A = {b, z, x}, B = {c, b, y}

Q. If $A$ and $B$ are two sets such that $n\left(A\right)=3$ and $n\left(B\right)=5,$ then $n(A\times B)=$ .

1. $8$
2. $15$
3. $10$
4. $3^5$

Q. For sets $A$ and $B,$ $n(A\times B)=n(B\times A).$

1. True
2. False

Q. If n(A) = 5 and n(B) = 6 then n(AXB) = ____

1. 11
2. 1
3. 30
4. 15

Q. Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set $A\times B$ each having at least three elements is:
(IIT JEE Main 2015)

1. 219
2. 256
3. 275
4. 510

Q.

If a set A has n elements, then the total number of subsets of A is

1. n²

2. 2ⁿ

3. 2n

4. n