GOVERNMENT OF KARNATAKA
DEPARTMENT OF SCHOOL EDUCATION
(PRE-UNIVERSITY)
REVISED QUESTION BANK (2024-25)
SUBJECT: MATHEMATICS (35)
CLASS: SECOND YEAR PUC
DSE(PU) Question Bank 1
,CO ORDINATOR:
1. Vasudeva K.H. Principal(in-charge), Govt. P.U.College,
Ripponpete, Hosanagara (Taluk), Shivamogga
Dist.(TT0035)
MEMBERS:
2. Satish Vaman Naik, Senior Lecturer, Govt Mohan K Shetty
PU College, Honnavar Uttara Kannada, (QQ0090)
3. Lawrence Sequeira ,Senior Lecturer, Pompei PU College,
Talipady, Aikala MULKI Taluk, DK Karnataka,(SS0054)
4. Vidyaranya K V , Senior Lecturer, Shri Marikamba Govt. P.
U. College, Sirsi ,Uttara Kannada (D) -581401(QQ0029)
5. Chalamalasetti Rama Krishna, Senior Lecturer,
Pragathi P.U. College Opp Whitefield Railway
Station , Kadugodi ,Bangalore -560067(As0737)
DISCLAIMER
The question bank is prepared for the benefit of
students and teachers. The committee that worked for the
preparation of question bank has made all efforts to make
the question bank comprehensive and foolproof.
However, if any mistakes or errors are found in the
question bank, please mail at
and . There is no guarantee that
only the questions from this question bank would appear in
the examination conducted by the department.
COPYRIGHTS
©
The copyrights of the question bank lies with the Director,
Department of School Education(Pre-university). The question
bank is prepared for academic purpose only. No part of the
question bank is allowed to be used for commercial gains.
DSE(PU) Question Bank 2
, CHAPTER -01
RELATIONS AND FUNCTIONS
MCQ /FB questions.
MCQ /FB questions.
1. A relation R in a set A, If each element of A is related to every element of A”, then R is called
(A) empty relation (B) universal relation
(C) Trivial relations (D) none of these.
2. Both the empty relation and the universal relation is
(A) empty relation (B) universal relation
(C) Trivial relations. (D) equivalence relations.
3. Let A be the set of all students of a boys school. Then the relation R in A given by
R = {(a, b) : a is sister of b} is
(A) empty relation (B) transitive relation
(C) symmetric relations. (D) reflexive relations.
4. A relation R in the set A is called a reflexive relations, if
(A) (a,a)∈R, for every a∈A,
(B) (a,a)∈R, at least one a ∈A
(C) if (a,b) ∈R implies that (b, a)∈R, for all a, b ∈A
(D) if (a,b)and (b, c) ∈R implies that (a, c)∈R, for all a, b,c ∈A
5. A relation R in the set {1, 2, 3} given by
R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (1,3)}. Then R is
(A) reflexive and symmetric (B) reflexive and transitive
(C) reflexive , symmetric and transitive. (D) reflexive but neither symmetric nor transitive
6. A relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is
(A) reflexive and symmetric (B) symmetric but not transitive
(C) symmetric and transitive (D)neither symmetric nor transitive.
7. A relation R in the set {1,2,3} given that 𝑅 = {(1,2), (2,1), (1,1)} is
(A) transitive but not symmetric (B) symmetric but not transitive
(C) symmetric and transitive (D)neither symmetric nor transitive.
8. Let R be the relation in the set {1, 2, 3, 4} given by
R = {(1, 2), (2, 2), (1, 1), (4,4),(1, 3), (3, 3), (3, 2)}.Choose the correct answer.
(A) R is reflexive and symmetric but not transitive.
(B) R is reflexive and transitive but not symmetric.
(C) R is symmetric and transitive but not reflexive.
(D) R is an equivalence relation.
9. Let R be the relation in the set N given by R = {(a, b) :a = b – 2, b > 6}. Choose the correct
answer.
(A) (2, 4) ∈R (B) (3, 8) ∈R (C) (6, 8) ∈R (D) (8, 6) ∈R.
10. Consider the non-empty set consisting of children in a family and a relation R defined as aRb
if a is brother of b. Then R is
(A) symmetric but not transitive (B) transitive but not symmetric
(C) neither symmetric nor transitive (D) both symmetric and transitive.
11. If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)},then R is
(A) reflexive (B) transitive (C) symmetric (D) none of these.
12. Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if and
only if l is perpendicular to m ∀l, m ∈L. Then R is
(A) reflexive (B) symmetric (C) transitive (D) none of these.
13. Let R be the relation in the set {1, 2, 3, 4} given by R = {(2, 2), (1, 1), (4, 4), (3, 3)}. Choose the
correct answer.
(A) R is reflexive and symmetric but not transitive
(B) R is reflexive and transitive but not symmetric.
(C) R is symmetric and transitive but not reflexive
(D) R is an equivalence relation.
14. Let W denote the words in the English dictionary. Define the relation R by
R = {(x, y) ∈ W × W ∶ the words x and y have at least one letter in common}. Then R is
(A) not reflexive, symmetric and transitive (B) reflexive, symmetric and not transitive
(C) reflexive, symmetric and transitive (D) reflexive, not symmetric and transitive.
DSE(PU) Question Bank 3
, 15. Let S = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is
(A) 1 (B) 2 (C) 3 (D) 4
16. The number of equivalence relation in the set {1, 2, 3} containing (1, 2) and (2, 1) is
(A) 5 (B) 2 (C) 4 (D) 3.
17. Let S = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and
symmetric but not transitive is
(A) 1 (B) 2 (C) 3 (D) 4.
18. If a relation R on the set {1, 2, 3} be defined by R = {(1, 1)},then R is
(A) symmetric but not transitive (B) transitive but not symmetric
(C) symmetric and transitive. (D) neither symmetric nor transitive.
19. Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is
(A) Reflexive and symmetric (B) Transitive and symmetric
(C) Equivalence (D) Reflexive, transitive but not symmetric
20. Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as
aRb if a is congruent to b a, b T . Then R is
(A) reflexive but not transitive (B) transitive but not symmetric
(C) equivalence (D) none of these
21. Let A = 2,3, 4,5 & B = 36, 45, 49,60,77 ,90 and let R be the relation ‘ is factor of’ from A to B
Then the range of R is the set
(A) 60 (B) { 36,45,60,90 } (C) 49, 77 (D) 49,60,77
22. The maximum number of equivalence relation on the set A = 1, 2,3 are
(A) 1 (B) 2 (C) 3 (D) 5
23. Let us define a relation R in R as aRb if a b . Then R is
(A) an equivalence relation (B) reflexive, transitive but not symmetric
(C) symmetric, transitive but not reflexive (D) neither transitive nor reflexive but symmetric .
24. A relation R in set A = {1,2,3} is defined as R = {(1, 1), (1, 2), (2, 2), (3, 3)}. Which of the
following ordered pair in R shall be removed to make it an equivalence relation in A?
(A) (1, 1) (B) (1, 2) (C) (2, 2) (D) (3, 3)
25. Let A = 1, 2,3 and consider the relation R = {(1, 1), (2, 2), (1, 2), (2, 3), (3, 3)}.
Then R is
(A) reflexive but not symmetric (B) reflexive but not transitive
(C) symmetric and transitive (D) neither symmetric, nor transitive.
26. If a relation R on the set {1, 2, 3} be defined by R = {(1, 1),(2, 2)},then R is
(A) symmetric but not transitive (B) transitive but not symmetric
(C) symmetric and transitive. (D) neither symmetric nor transitive.
27. Let f :R→ R be defined by f(x) = x 4 , x ∈R. Then
(A) f is one-one but not onto (B) f is one-one and onto
(C) f is many-one onto (D) f is neither one-one nor onto .
28. Let f :R→ R be defined by f(x) = 3x, x ∈R. Then
(A) f is one-one but not onto (B) f is one-one and onto
(C) f is many-one onto (D) f is neither one-one nor onto .
29. Let f :R→ R be defined by f(x) = x , x ∈R. Then
3
(A) f is one-one but not onto (B) f is one-one and onto
(C) f is many-one onto (D) f is neither one-one nor onto .
1
30. Let f :R→ R be defined by f(x) = , x ∈R. Then f is
x
(A) one-one (B) onto (C) bijective (D) f is not defined.
31. Let f: R → R defined by f(x) = 2x + 6 which is a bijective mapping then f −1 (x) is given by
x
(A) − 3 (B) 2x + 6 (C) x − 3 (D) 6x + 2.
2
32. If the set A contains 5 elements and the set B contains 6 elements, then the number of one-
one and onto mappings from A to B is
(A) 720 (B) 120 (C) 0 (D) none of these.
33. Let A = {1, 2, 3, ...n} and B = {a, b}. Then the number of surjections from A into B is
(A) nP2 (B) 2n − 2 (C) 2n − 1 (D) None of these.
DSE(PU) Question Bank 4
DEPARTMENT OF SCHOOL EDUCATION
(PRE-UNIVERSITY)
REVISED QUESTION BANK (2024-25)
SUBJECT: MATHEMATICS (35)
CLASS: SECOND YEAR PUC
DSE(PU) Question Bank 1
,CO ORDINATOR:
1. Vasudeva K.H. Principal(in-charge), Govt. P.U.College,
Ripponpete, Hosanagara (Taluk), Shivamogga
Dist.(TT0035)
MEMBERS:
2. Satish Vaman Naik, Senior Lecturer, Govt Mohan K Shetty
PU College, Honnavar Uttara Kannada, (QQ0090)
3. Lawrence Sequeira ,Senior Lecturer, Pompei PU College,
Talipady, Aikala MULKI Taluk, DK Karnataka,(SS0054)
4. Vidyaranya K V , Senior Lecturer, Shri Marikamba Govt. P.
U. College, Sirsi ,Uttara Kannada (D) -581401(QQ0029)
5. Chalamalasetti Rama Krishna, Senior Lecturer,
Pragathi P.U. College Opp Whitefield Railway
Station , Kadugodi ,Bangalore -560067(As0737)
DISCLAIMER
The question bank is prepared for the benefit of
students and teachers. The committee that worked for the
preparation of question bank has made all efforts to make
the question bank comprehensive and foolproof.
However, if any mistakes or errors are found in the
question bank, please mail at
and . There is no guarantee that
only the questions from this question bank would appear in
the examination conducted by the department.
COPYRIGHTS
©
The copyrights of the question bank lies with the Director,
Department of School Education(Pre-university). The question
bank is prepared for academic purpose only. No part of the
question bank is allowed to be used for commercial gains.
DSE(PU) Question Bank 2
, CHAPTER -01
RELATIONS AND FUNCTIONS
MCQ /FB questions.
MCQ /FB questions.
1. A relation R in a set A, If each element of A is related to every element of A”, then R is called
(A) empty relation (B) universal relation
(C) Trivial relations (D) none of these.
2. Both the empty relation and the universal relation is
(A) empty relation (B) universal relation
(C) Trivial relations. (D) equivalence relations.
3. Let A be the set of all students of a boys school. Then the relation R in A given by
R = {(a, b) : a is sister of b} is
(A) empty relation (B) transitive relation
(C) symmetric relations. (D) reflexive relations.
4. A relation R in the set A is called a reflexive relations, if
(A) (a,a)∈R, for every a∈A,
(B) (a,a)∈R, at least one a ∈A
(C) if (a,b) ∈R implies that (b, a)∈R, for all a, b ∈A
(D) if (a,b)and (b, c) ∈R implies that (a, c)∈R, for all a, b,c ∈A
5. A relation R in the set {1, 2, 3} given by
R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (1,3)}. Then R is
(A) reflexive and symmetric (B) reflexive and transitive
(C) reflexive , symmetric and transitive. (D) reflexive but neither symmetric nor transitive
6. A relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is
(A) reflexive and symmetric (B) symmetric but not transitive
(C) symmetric and transitive (D)neither symmetric nor transitive.
7. A relation R in the set {1,2,3} given that 𝑅 = {(1,2), (2,1), (1,1)} is
(A) transitive but not symmetric (B) symmetric but not transitive
(C) symmetric and transitive (D)neither symmetric nor transitive.
8. Let R be the relation in the set {1, 2, 3, 4} given by
R = {(1, 2), (2, 2), (1, 1), (4,4),(1, 3), (3, 3), (3, 2)}.Choose the correct answer.
(A) R is reflexive and symmetric but not transitive.
(B) R is reflexive and transitive but not symmetric.
(C) R is symmetric and transitive but not reflexive.
(D) R is an equivalence relation.
9. Let R be the relation in the set N given by R = {(a, b) :a = b – 2, b > 6}. Choose the correct
answer.
(A) (2, 4) ∈R (B) (3, 8) ∈R (C) (6, 8) ∈R (D) (8, 6) ∈R.
10. Consider the non-empty set consisting of children in a family and a relation R defined as aRb
if a is brother of b. Then R is
(A) symmetric but not transitive (B) transitive but not symmetric
(C) neither symmetric nor transitive (D) both symmetric and transitive.
11. If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)},then R is
(A) reflexive (B) transitive (C) symmetric (D) none of these.
12. Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if and
only if l is perpendicular to m ∀l, m ∈L. Then R is
(A) reflexive (B) symmetric (C) transitive (D) none of these.
13. Let R be the relation in the set {1, 2, 3, 4} given by R = {(2, 2), (1, 1), (4, 4), (3, 3)}. Choose the
correct answer.
(A) R is reflexive and symmetric but not transitive
(B) R is reflexive and transitive but not symmetric.
(C) R is symmetric and transitive but not reflexive
(D) R is an equivalence relation.
14. Let W denote the words in the English dictionary. Define the relation R by
R = {(x, y) ∈ W × W ∶ the words x and y have at least one letter in common}. Then R is
(A) not reflexive, symmetric and transitive (B) reflexive, symmetric and not transitive
(C) reflexive, symmetric and transitive (D) reflexive, not symmetric and transitive.
DSE(PU) Question Bank 3
, 15. Let S = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is
(A) 1 (B) 2 (C) 3 (D) 4
16. The number of equivalence relation in the set {1, 2, 3} containing (1, 2) and (2, 1) is
(A) 5 (B) 2 (C) 4 (D) 3.
17. Let S = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and
symmetric but not transitive is
(A) 1 (B) 2 (C) 3 (D) 4.
18. If a relation R on the set {1, 2, 3} be defined by R = {(1, 1)},then R is
(A) symmetric but not transitive (B) transitive but not symmetric
(C) symmetric and transitive. (D) neither symmetric nor transitive.
19. Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then R is
(A) Reflexive and symmetric (B) Transitive and symmetric
(C) Equivalence (D) Reflexive, transitive but not symmetric
20. Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as
aRb if a is congruent to b a, b T . Then R is
(A) reflexive but not transitive (B) transitive but not symmetric
(C) equivalence (D) none of these
21. Let A = 2,3, 4,5 & B = 36, 45, 49,60,77 ,90 and let R be the relation ‘ is factor of’ from A to B
Then the range of R is the set
(A) 60 (B) { 36,45,60,90 } (C) 49, 77 (D) 49,60,77
22. The maximum number of equivalence relation on the set A = 1, 2,3 are
(A) 1 (B) 2 (C) 3 (D) 5
23. Let us define a relation R in R as aRb if a b . Then R is
(A) an equivalence relation (B) reflexive, transitive but not symmetric
(C) symmetric, transitive but not reflexive (D) neither transitive nor reflexive but symmetric .
24. A relation R in set A = {1,2,3} is defined as R = {(1, 1), (1, 2), (2, 2), (3, 3)}. Which of the
following ordered pair in R shall be removed to make it an equivalence relation in A?
(A) (1, 1) (B) (1, 2) (C) (2, 2) (D) (3, 3)
25. Let A = 1, 2,3 and consider the relation R = {(1, 1), (2, 2), (1, 2), (2, 3), (3, 3)}.
Then R is
(A) reflexive but not symmetric (B) reflexive but not transitive
(C) symmetric and transitive (D) neither symmetric, nor transitive.
26. If a relation R on the set {1, 2, 3} be defined by R = {(1, 1),(2, 2)},then R is
(A) symmetric but not transitive (B) transitive but not symmetric
(C) symmetric and transitive. (D) neither symmetric nor transitive.
27. Let f :R→ R be defined by f(x) = x 4 , x ∈R. Then
(A) f is one-one but not onto (B) f is one-one and onto
(C) f is many-one onto (D) f is neither one-one nor onto .
28. Let f :R→ R be defined by f(x) = 3x, x ∈R. Then
(A) f is one-one but not onto (B) f is one-one and onto
(C) f is many-one onto (D) f is neither one-one nor onto .
29. Let f :R→ R be defined by f(x) = x , x ∈R. Then
3
(A) f is one-one but not onto (B) f is one-one and onto
(C) f is many-one onto (D) f is neither one-one nor onto .
1
30. Let f :R→ R be defined by f(x) = , x ∈R. Then f is
x
(A) one-one (B) onto (C) bijective (D) f is not defined.
31. Let f: R → R defined by f(x) = 2x + 6 which is a bijective mapping then f −1 (x) is given by
x
(A) − 3 (B) 2x + 6 (C) x − 3 (D) 6x + 2.
2
32. If the set A contains 5 elements and the set B contains 6 elements, then the number of one-
one and onto mappings from A to B is
(A) 720 (B) 120 (C) 0 (D) none of these.
33. Let A = {1, 2, 3, ...n} and B = {a, b}. Then the number of surjections from A into B is
(A) nP2 (B) 2n − 2 (C) 2n − 1 (D) None of these.
DSE(PU) Question Bank 4
