RELATIONS & FUNCTIONS
1. Let A = {1, 2, 3}. The total number of distinct relations that can be defined over A is
(A) 2 9 (B)6
(C)8 (D) None of these
2. Let X = {1, 2, 3, 4, 5} and Y = {1, 3, 5, 7, 9} . Which of the following is/are relations from X to Y
(A) R1 = {(x, y)| y = 2 + x, x X, y Y } (B) R2 = {(1,1), (2,1), (3, 3), (4, 3), (5, 5)}
(C) R3 = {(1,1), (1, 3)(3, 5), (3, 7), (5, 7)} (D) R4 = {(1, 3), (2, 5), (2, 4), (7, 9)}
3. The relation R defined on the set A = {1, 2, 3, 4, 5} by R = {(x, y): | x 2 − y 2 | 16 } is given by
(A){(1, 1), (2, 1), (3, 1), (4, 1), (2, 3)} (B) {(2, 2), (3, 2), (4, 2), (2, 4)}
(C){(3, 3), (3, 4), (5, 4), (4, 3), (3, 1)} (D) None of these
4. A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by xRy x is relatively prime to y. Then
domain of R is
(A){2, 3, 5} (B) {3, 5}
(C){2, 3, 4} (D) {2, 3, 4, 5}
5. Let R be a relation on N defined by x + 2 y = 8 . The domain of R is
(A){2, 4, 8} (B) {2, 4, 6, 8}
(C){2, 4, 6} (D) {1, 2, 3, 4}
6. If R = {( x , y )| x , y Z, x + y 4 } is a relation in Z, then domain of R is
2 2
(A){0, 1, 2} (B) {0, – 1, – 2}
(C){– 2, – 1, 0, 1, 2} (D) None of these
7. The value of b and c for which the identity f (x + 1) − f (x ) = 8 x + 3 is satisfied, where
f (x ) = bx 2 + cx + d , are
(A) b = 2, c = 1 (B) b = 4, c = −1
(C) b = −1, c = 4 (D) b = −1, c = 1
−x
a +a
x
8. Given the function f (x ) = , (a 2) . Then f (x + y) + f (x − y) =
2
(A) 2 f (x ). f (y) (B) f (x ). f (y)
f (x )
(C) (D) None of these
f (y )
x f (a)
9. If f (x ) = , then =
x −1 f (a + 1)
(A) f (−a) (B) f 1
a
−a
(C) f (a 2 ) (D) f
−1
a
1 1
10. If f (x ) = + for x 2 , then f (11 ) =
x + 2 2x − 4 x − 2 2x − 4
(A)7/6 (B) 5/6
(C)6/7 (D) 5/7
| x − 3|
11. Domain and range of f (x ) = are respectively
x −3
(A) R, [−1, 1] (B) R − {3}, 1, − 1
(C) R + , R (D) None of these
12. If in greatest integer function, the domain is a set of real numbers, then range will be set of
(A)Real numbers (B) Rational numbers
(C)Imaginary numbers (D) Integers
13. If the domain of function f (x ) = x 2 − 6 x + 7 is (−, ) , then the range of function is
(A) (−, ) (B) [−2, )
(C) (−2, 3) (D) (−, − 2)
1
14. The domain of the function 𝑦 = is
√|𝑥| −𝑥
(A) (−, 0) (B) (−, 0]
(C) (−, − 1) (D) (−, )
15. R = ({x, y): y = x + 5, x is a natural number less than 4; x, y ∈ N} then Roster form of
Relation R is
(A) {(1,6) (2, 5), (3, 8)} (B) {(1,6) (2, 5), (3, 7)}
(C) {(1,6) (2, 7), (3, 6)} (D) {(1,6) (2, 7), (3, 8)}
3 2
16. If 𝑓: 𝑅 → 𝑅, 𝑔: 𝑅 → 𝑅 are defined by f(x)=𝑥 , 𝑔(𝑥) = 𝑥 , then (2f+3g) (x) is equal to
(A) 𝑥 3 + 𝑥 2 (B) 𝑥 3 − 𝑥 2
(C) 2𝑥 3 + 3𝑥 2 (D) 3𝑥 3 − 2𝑥 2
17. If A = Φ , n(B) = 4 then n(A x B) is
(A)0 (B)5
(C)1 (D)4
18. If A = {-1, 1, 2}, then n(A x A x A) =
(A) 9 (B)16 (C)27 (D)3
19. If n(A) = 3, n(B) = 2 and if (x, 4), (y, 5), (z, 4) are three distinct elements of A x B, then
(A) A = {x, y, z} and B = {4, 5}
(B) A = {4, x, y} and B = {5, z}
(C) A ={y, z, 5} and B = {x, 4}
(D) A = {4, 5} and B = {x, y, z}
20. If n(A) = 3 and n(B) =4 then find the number of elements in the power set of A × B
(A) 64 (B)24 (C)4096 (D)8
1 2 3 4 5 6 7 8
A A, B, C D D C C B A
9 10 11 12 13 14 15 16
C C B D B A D C
17 18 19 20
A C A C
2 Mark Questions
1. Let A = {1, 2} and B = { 3, 4}. Find the number of relations from A to B.
2. Find the domain of the function:
(a). f(x) =
(b). f(x) =
3. Determine the domain and range of the relation R defined by
R = {(x, x + 5) : x ∈{0, 1, 2, 3, 4, 5}}.
4. Let f(x) = x2 and g(x) = 2x + 1 be two real functions.
(A) Find (f – g)(x) (B) f/g (x).
4 Marks Questions
1. Draw the graph of Signum function write its Domain and Range
2 . Draw graph of following functions:
1
(i) f(x) = (ii) f(x) = x – [x]
x
3 . Define Modulus function. Draw its graph. What is its domain & range?;
4. Define Signum function. Draw its graph & mapping. What is its domain & range?
6 Marks questions
1. Let f = {(1,1), (2,3), (0,–1), (–1, –3)} be a function from Z to Z defined by: f(x) = ax + b,
for some integers a, b. Determine a, b.
2. The function f is defined by : f(x) = Draw the graph of f(x).
