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
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:
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