.
CHAPTER 1 STD 12 Date : 16/12/25
Relation and functions Maths
//X Section A
• Write the answer of the following questions. [Each carries 3 Marks] [42]
1. Show that the relation R in the set R of real numbers, defined as R = {(a, b) : a £ b2} is neither reflexive
nor symmetric nor transitive.
2. Check whether the relation R in R defined by R = {(a, b) : a £ b3} is reflexive, symmetric or transitive.
3. Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2) : L1 is
parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line
y = 2x + 4.
Note : Accept that each line is parallel to itself.
æ x - 2ö
Let A = R – {3} and B = R – {1}. Consider the function f : A ® B defined by, f ( x ) = ç
è x - 3 ÷ø
4. Is f
one-one and onto ? Justify your answer.
x
5. Show that the function f : R ® {x Î R : –1 < x < 1} defined by f(x) = , x Î R is one and
1 + |x|
onto function.
6. Let f : N ® N be defined by
ìn + 1
ï , if n is odd
f (n ) = í 2 , for all n Î N.
n
ï , if n is even
î 2
State whether the function f is bijective. Justify your answer.
ì 1, if x > 0
ï
7. Show that the Signum Function f : R ® R, given by, f ( x ) = í 0, if x = 0 is neither one-one nor onto..
ï-
î 1, if x < 0
8. Prove that the Greatest Integer Function f : R ® R, given by f(x) = [x], is neither one-one not onto,
where [x] denotes the greatest integer less than or equal to x.
9. Show that the Modulus Function f : R ® R, given by f(x) = | x |, is neither one-one nor onto, where
| x | is x, if x is positive or 0 and | x | is – x, if x is negative.
10. Show that the relation R in R defined as R = {(a, b) : a £ b}, is reflexive and transitive but not symmetric.
11. ) In each of the following cases, state whether the function is one-one, onto or bijective. Justify your
answer. f : R ® R defined by f(x) = 3 – 4x
12. ) Show that each of the relation R in the set A = {x Î Z : 0 £ x £ 12}, given by
R = {(a, b) : |a – b| is a multiple of 4}
is an equivalence relation. Find the set of all elements related to 1 in each case.
13. Show that the relation R defined in the set A of all polygons as R = {(P1, P2) : P1 and P2 have same
number of sides}, is an equivalence relation. What is the set of all elements in A related to the right
angle triangle T with sides 3, 4 and 5 ?
14. Let f : N ® Y be a function defined as f(x) = 4x + 3, where, Y = {y Î N : y = 4x + 3 for some x Î N}. Show that
f is invertible. Find the inverse.
, .
CHAPTER 1 STD 12 Date : 16/12/25
Relation and functions Maths
Section [ A ] : 3 Marks Questions
No Ans Chap Sec Que Universal_QueId
1. - Chap 1 S1 2 QP25P11B1213_P1C1S1Q2
2. - Chap 1 S1 5 QP25P11B1213_P1C1S1Q5
3. - Chap 1 S1 14 QP25P11B1213_P1C1S1Q14
4. - Chap 1 S2 10 QP25P11B1213_P1C1S2Q10
5. - Chap 1 S3 1 QP25P11B1213_P1C1S3Q1
6. - Chap 1 S2 9 QP25P11B1213_P1C1S2Q9
7. - Chap 1 S2 5 QP25P11B1213_P1C1S2Q5
8. - Chap 1 S2 3 QP25P11B1213_P1C1S2Q3
9. - Chap 1 S2 4 QP25P11B1213_P1C1S2Q4
10. - Chap 1 S1 4 QP25P11B1213_P1C1S1Q4
11. - Chap 1 S2 7.1 QP25P11B1213_P1C1S2Q7.1
12. - Chap 1 S1 9.1 QP25P11B1213_P1C1S1Q9.1
13. - Chap 1 S1 13 QP25P11B1213_P1C1S1Q13
14. - Chap 1 S4 17 QP25P11B1213_P1C1S4Q17
Welcome To Future - Quantum Paper
CHAPTER 1 STD 12 Date : 16/12/25
Relation and functions Maths
//X Section A
• Write the answer of the following questions. [Each carries 3 Marks] [42]
1. Show that the relation R in the set R of real numbers, defined as R = {(a, b) : a £ b2} is neither reflexive
nor symmetric nor transitive.
2. Check whether the relation R in R defined by R = {(a, b) : a £ b3} is reflexive, symmetric or transitive.
3. Let L be the set of all lines in XY plane and R be the relation in L defined as R = {(L1, L2) : L1 is
parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line
y = 2x + 4.
Note : Accept that each line is parallel to itself.
æ x - 2ö
Let A = R – {3} and B = R – {1}. Consider the function f : A ® B defined by, f ( x ) = ç
è x - 3 ÷ø
4. Is f
one-one and onto ? Justify your answer.
x
5. Show that the function f : R ® {x Î R : –1 < x < 1} defined by f(x) = , x Î R is one and
1 + |x|
onto function.
6. Let f : N ® N be defined by
ìn + 1
ï , if n is odd
f (n ) = í 2 , for all n Î N.
n
ï , if n is even
î 2
State whether the function f is bijective. Justify your answer.
ì 1, if x > 0
ï
7. Show that the Signum Function f : R ® R, given by, f ( x ) = í 0, if x = 0 is neither one-one nor onto..
ï-
î 1, if x < 0
8. Prove that the Greatest Integer Function f : R ® R, given by f(x) = [x], is neither one-one not onto,
where [x] denotes the greatest integer less than or equal to x.
9. Show that the Modulus Function f : R ® R, given by f(x) = | x |, is neither one-one nor onto, where
| x | is x, if x is positive or 0 and | x | is – x, if x is negative.
10. Show that the relation R in R defined as R = {(a, b) : a £ b}, is reflexive and transitive but not symmetric.
11. ) In each of the following cases, state whether the function is one-one, onto or bijective. Justify your
answer. f : R ® R defined by f(x) = 3 – 4x
12. ) Show that each of the relation R in the set A = {x Î Z : 0 £ x £ 12}, given by
R = {(a, b) : |a – b| is a multiple of 4}
is an equivalence relation. Find the set of all elements related to 1 in each case.
13. Show that the relation R defined in the set A of all polygons as R = {(P1, P2) : P1 and P2 have same
number of sides}, is an equivalence relation. What is the set of all elements in A related to the right
angle triangle T with sides 3, 4 and 5 ?
14. Let f : N ® Y be a function defined as f(x) = 4x + 3, where, Y = {y Î N : y = 4x + 3 for some x Î N}. Show that
f is invertible. Find the inverse.
, .
CHAPTER 1 STD 12 Date : 16/12/25
Relation and functions Maths
Section [ A ] : 3 Marks Questions
No Ans Chap Sec Que Universal_QueId
1. - Chap 1 S1 2 QP25P11B1213_P1C1S1Q2
2. - Chap 1 S1 5 QP25P11B1213_P1C1S1Q5
3. - Chap 1 S1 14 QP25P11B1213_P1C1S1Q14
4. - Chap 1 S2 10 QP25P11B1213_P1C1S2Q10
5. - Chap 1 S3 1 QP25P11B1213_P1C1S3Q1
6. - Chap 1 S2 9 QP25P11B1213_P1C1S2Q9
7. - Chap 1 S2 5 QP25P11B1213_P1C1S2Q5
8. - Chap 1 S2 3 QP25P11B1213_P1C1S2Q3
9. - Chap 1 S2 4 QP25P11B1213_P1C1S2Q4
10. - Chap 1 S1 4 QP25P11B1213_P1C1S1Q4
11. - Chap 1 S2 7.1 QP25P11B1213_P1C1S2Q7.1
12. - Chap 1 S1 9.1 QP25P11B1213_P1C1S1Q9.1
13. - Chap 1 S1 13 QP25P11B1213_P1C1S1Q13
14. - Chap 1 S4 17 QP25P11B1213_P1C1S4Q17
Welcome To Future - Quantum Paper
