RELATIONS X CLASS TOPICS

NTSE Stage-1_Mathematics
Class-X
RELATIONS WORKSHEET-1
1. If (x + 1, 1) = (3, y – 2) thne x =_________
A) x = 2, y = 3 B) x = 3, y = 2 C) x = 1, y = 1 D) x = 0, y = 0
2. If A = {–1, 1} then n(A × A × A) =________
A) 8 B) 9 C) 10 D) 7
3. The cartesian product A × A has 9 elements among which are found (–1, 0) and (0,
1) then the set A=__________
A) {1, 0} B) {–1, 0, 1} C) {0, –1} D) {–1, 1}
4. If A × B = a,1,b,3,a,3,b,1,a,2,b,2 then A =_________
A) 1,2,3 B) a,b,c C) a,b D) b,c
5. Let A = { 1, 2, 3, ..., 45} and R be the relation ‘is square of’ in A. Which of the
following is false ?
A) R = { (1, 1), (4, 2), (9, 3), (16, 4), (25, 5), (36, 6) }
B) Domain of R = { 1, 4, 9, 16, 25, 36 }
C) Range of R = { 1, 2, 3, 4, 5, 6 }
D) At least one is false
6. If the relation R : A  B, where A = { 1, 2, 3 } and B = { 1, 3, 5 } is defined by
R = { (x, y) : x < y, x A, yB }, then
A) R = { (1, 3), (1, 5), (2, 3), (2, 5), (3, 5) }
B) R = { (1, 1), (1, 5), (2, 3), (3, 5) }
C) R–1 = { (3, 1), (5, 1), (3, 2), (5, 3) }
D) R–1 = { (1, 1), (5, 1), (3, 2), (5, 3) }
7. Let R be a relation in the set N of Natural numbers defined by the relation
nRm  n is a factor of m. The relation R is
A) reflexive and symmetric only B) symmetric and transitive only
C) reflexive and transitive only D) an equivalence relation
8. Let R be a relation in N defined by R = { { (x, y) : x + 2y = 8 }. The range of R is
A) { 2, 4, 6} B) { 1, 2, 3 } C) { 1, 2, 3, 4, 6 } D) none of these’
9. Let R be a relation defined by R = { (a, b) : a  b, a, bR}. Then R is
A) an equivalence relation in R B) reflexive , transitive but not symmetric
C) symmetric, transitive but not reflexive D) only reflexive
10. A relation R is defined in the set Z of integers as follows : (x, y)R iff x2 + y2 = 9.
Which of the following is false ?
A) R = { (0, 3), (0, –3), (3, 0), (–3, 0) } B) Domain of R = { –3, 0, 3 }
C) Range of R = { –3, 0, 3 } D) At least one is false
NTSE Stage-1_Mathematics
NARAYANA GROUP OF SCHOOLS 2 of 2
Class-X
11. The relation R defined on the set A = { 1, 2, 3, 4, 5 } by R = {(x, y) : |x2 – y2| < 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), (4, 3), (5, 4), (3, 4)} D) none of the these
12. If R = { (x, y) : x, yZ, x2 + y2  4 } is a relation in Z, then domain of R is
A) {0, 1, 2} B) {–2, –1, 0} C) {–2, –1, 0, 1, 2} D) none of these
13. Let a relation R be defined by R = {(4, 5), (1, 4), (4, 6), (7, 6), (3, 7)}. The relation
R–1oR is given by
A) {(1, 1), (4, 4), (7, 4), (4, 7), (7, 7) } B) { (1, 1), (4, 4), (4, 7), (7, 4), (7, 7), (3, 3)}
C) {(1, 5), (1, 6), (3, 6)} D) none of these
14. The relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on the set A = {1, 2, 3} is
A) reflexive but not symmetric B) reflexive but not transitive
C) symmetric and transitive D) neither symmetric nor transitive
15. The void relation in a set A is
A) reflexive B) symmetric and transitive
C) reflexive and transitive D) reflexive and symmetric
16. Let A = { 1, 2, 3, 4} and R = {(2, 2), (3, 3), (4, 4), (1, 2)} be a relation on A. Then A is
A) reflexive B) symmetric C) transitive D) none of these
17. Let R be the relation over the set N × N and is defined by (a, b) R (c, d)  a + d = b +
c. Then R is
A) reflexive only B) symmetric only
C) transitive only D) an equivalence relation.
18. R is a relation over the set of integers and it is given by (x, y)R  |x – y|  1.
Then R is
A) reflexive and symmetric B) reflexive and transitive
C) symmetric and transitive D) anti symmetric
19. Let L be the set of all straight lines in the Euclidean plane. Two lines l1 and l2 are
said to be related by the relation R iff l1  l2. Then the relation R is
A) reflexive B) symmetric C) transitive D) equivalence
20. Let R be the relation over the set of straight lines in a plane such that l R m l m.
Then R is
A) reflexive B) symmetric
C) Transitive D) an equivalence relation
NTSE Stage-1_Mathematics
NARAYANA GROUP OF SCHOOLS 3 of 3
Class-X
21. Let A = { 1, 2, 3, 4, 5, 6}. Define a relation R from A to A by
R = {(x, y) : y = x + 1}, then range of R is
A) { 1, 2, 3, 4, 5, 6} B) { 1, 2, 3, 4, 5}
C) { 2, 3, 4, 5, 6} D) { 2, 3, 4, 5}
22. Let A = {1, 2), B = {3, 4}, then number of relation from A to B is
A) 16 B) 8 C) 4 D) 32
RELATIONS WORKSHEET-1_KEY
1. A 2. A 3. B 4. C 5. D 6. A
7. C 8. B 9. B 10. D 11. D 12. C
13. D 14. A 15. B 16. D 17. D 18. A
19. D 20. B 21. C 22. A