Multiple choice questions

Multiple choice questions

1. If  n(A× B) = 6 and A = {1, 3} then n(B) is

(1) 1

(2) 2

(3) 3

(4) 6

Solution

2. A = {a,b, p},  B = {2, 3}, C  = {p,q,r,s} then n[(A ∪ C )× B] is

(1) 8

(2) 20

(3) 12

(4) 16

Solution

3. If  A = {1, 2}, B = {1, 2, 3, 4}, C  = {5, 6} and D = {5, 6, 7, 8} then state which of the following statement is true.

(1) (A×C ) ⊂ (B × D)

(2) (B × D) ⊂ (A×C )

(3) (A× B) ⊂ (A× D)

(4) (D × A) ⊂ (B × A)

Solution

4. If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is

(1) 3

(2) 2

(3) 4

(4) 8

Solution

5. The range of the relation R = {(x, x2 ) | x is a prime number less than 13} is

(1) {2,3,5,7}

(2) {2,3,5,7,11}

(3) {4,9,25,49,121}

(4) {1,4,9,25,49,121}

Solution

6. If the ordered pairs (a + 2, 4) and (5, 2a + b) are equal then (a,b) is

(1) (2, –2)

(2) (5,1)

(3) (2,3)

(4) (3, –2)

Solution

7. Let n(A) = m  and n(B) = n then the total number of non-empty relations that can be defined from A to B is

(1) Mn

(2) Nm

(3) 2mn – 1

(4) 2mn

Solution

8. If {(a, 8),(6,b)} represents an identity function, then the value of a and b are respectively

(1) (8,6)

(2) (8,8)

(3) (6,8)

(3) (6,6)

9. Let A = {1, 2, 3, 4} and B = {4, 8, 9,10}. A function f: A → B given by f  = {(1, 4),(2, 8),(3, 9),(4,10)} is a

(1) Many-one function

(2) Identity function

(3) One-to-one function

(4) Into function

10. If f (x) = 2x2 and g(x) = 1/3x then f o g is       

Ans: (3)

Solution

11. If f: A → B is a bijective function and if n(B) = 7 , then n(A) is equal to

(1) 7

(2) 49

(3) 1

(4) 4

12. Let f and g be two functions given by

f  = {(0,1),(2, 0),(3,−4),(4, 2),(5, 7)}

g = {(0, 2),(1, 0),(2, 4),(−4, 2),(7, 0)}

then the range of f o g is

(1) {0,2,3,4,5}

(2) {–4,1,0,2,7}

(3) {1,2,3,4,5}

(4) {0,1,2}

Solution

13. Let f (x) =  then

(1) f (xy) = f (x).f (y)

(2) f (xy) ≥  f (x).f (y)

(3) f (xy) ≤ f (x).f (y)

(4) None of these

Solution

14. If  g = {(1,1),(2, 3),(3, 5),(4, 7)} is a function given by  g(x) = αx + β  then the values of a and b are

(1) (–1,2) )

(2) (2, –1)

(3) (–1, –2)

(4) (1,2)

Solution

15. f (x) = (x + 1)3 − (x − 1)3 represents a function which is

(1) linear

(2) cubic

(3) reciprocal

(4) quadratic

Solution

Answers: