🧪 NCERT Class 12 MCQ Quiz Hub

1. If f(x1) = f (x2) ⇒ x1 = x2 ∀ x1 x2 ∈ A then the function f: A → B is
one-one
one-one onto
onto
many one

2. What type of a relation is R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} on the set A – {1, 2, 3, 4}
Reflexive
Transitive
Symmetric
None of the above

3. If F : R → R such that f(x) = 5x + 4 then which of the following is equal to f-1(x).
x−54
x−y5
x−45
x4 -5

4. If an operation is defined by a* b = a² + b², then (1 * 2) * 6 is
12
28
61
None of the above

5. Consider the binary operation * on a defined by x * y = 1 + 12x + xy, ∀ x, y ∈ Q, then 2 * 3 equals
31
40
43
None of the above

6. The range of the function f(x) = (x−1)(3−x)−−−−−−−−−−−√ is
[1, 3]
[0, 1]
[-2, 2]
None of the these

7. If f: R → R defined by f(x) = 2x + 3 then f-1(x) =
2x – 3
x−32
x+32
None of the these

8. The function f(x) = log (x² + x2+1−−−−−√ ) is
even function
odd function
Both of the above
None of the above

9. Let E = {1, 2, 3, 4} and F = {1, 2} Then, the number of onto functions from E to F is
14
16
12
8

10. If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C. then
A = B
A = C
B = C
A ∩ B = d

11. Let A = {1, 2}, how many binary operations can be defined on this set?
8
10
16
20

12. If A = (1, 2, 3}, B = {6, 7, 8} is a function such that f(x) = x + 5 then what type of a function is f?
Many-one onto
Constant function
one-one onto
into

13. Let function R → R is defined as f(x) = 2x³ – 1, then ‘f’ is
2x³ + 1
(2x)³ + 1
(1 – 2x)³
(1+x2)1/3

14. Let the functioin ‘f’ be defined by f (x) = 5x² + 2 ∀ x ∈ R, then ‘f’ is
onto function
one-one, onto function
one-one, into function
many-one into function

15. A relation R in human being defined as, R = {{a, b) : a, b ∈ human beings : a loves A} is-
reflexive
symmetric and transitive
equivalence
None of the above

16. If f(x) + 2f (1 – x) = x² + 2 ∀ x ∈ R, then f(x) =
x² – 2
1
13 (x – 2)²
None of the above

17. he period of sin² θ is
π²
π
2π
π2

18. The domain of sin-1 (log (x/3)] is. .
[1, 9]
[-1, 9]
[-9, 1]
[-9, -1]

19. f(x) = log2(x+3)x2+3x+2 is the domain of
R – {-1, -2}
(- 2, ∞) .
R- {- 1,-2, -3}
(-3, + ∞) – {-1, -2}

20. If the function f(x) = x³ + ex/2 and g (x) = fn(x), then the value of g'(1) is
1
2
3
4

21. What type of relation is ‘less than’ in the set of real numbers?
only symmetric
only transitive
only reflexive
equivalence

22. If A = [1, 2, 3}, B = {5, 6, 7} and f: A → B is a function such that f(x) = x + 4 then what type of function is f?
into
one-one onto
many-onto
constant function

23. f: A → B will be an into function if
range (f) ⊂ B
f(a) = B
B ⊂ f(a)
f(b) ⊂ A

24. If f : R → R such that f(x) = 3x then what type of a function is f?
one-one onto
many one onto
one-one into
many-one into

25. If f: R → R such that f(x) = 3x – 4 then which of the following is f-1(x)?
13 (x + 4)
13 (x – 4)
3x – 4
undefined

26. A = {1, 2, 3} which of the following function f: A → A does not have an inverse function
{(1, 1), (2, 2), (3, 3)}
{(1, 2), (2, 1), (3, 1)}
{(1, 3), (3, 2), (2, 1)}
{(1, 2), (2, 3), (3, 1)

27. 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 congruent to b ∀ a, b ∈ T. Then R is
eflexive but-not transitive
transitive but not symmetric
equivalence
None of the above

28. Consider the non-empty set consisting of children is a family and a relation R defined as aRb If a is brother of b. Then R is
symmetric but not transitive
transitive but not symmetric
neither symmetric nor transitive
both symmetric and transitive

29. The maximum number of equivalence relations on the set A = {1, 2, 3} are
1
2
3
5

30. If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is
reflexive
transitive
symmetric
None of the above

31. Let us define a relation R in R as aRb if a ≥ b. Then R is
an equivalence relation
reflexive, transitive but not symmetric
neither transitive nor reflexive but symmetric
symmetric, transitive but not reflexive

32. Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is
reflexive but not symmetric
reflexive-but not transitive
symmetric and transitive
neither symmetric, nor transitive

33. The identity element for the binary operation * defined on Q ~ {0} as a * b = ab2 ∀ a, b ∈ Q ~ {0} is
1
0
2
None of the above

34. 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
720
120
0
None of the above

35. Let f : R → R be defined by f (x) = 1x ∀ x ∈ R. Then f is
one-one
onto
bijective
f is not defined

36. Which of the following functions from Z into Z are bijective?
f(x) = x³
f(x) = x + 2
f(x) = 2x + 1
f{x) = x² + 1

37. Let f: R → R be the function defined by f(x) = x³ + 5. Then f-1 (x) is
(x + 5)1/3
(x -5)1/3
(5 – x)1/3
5 – x

38. Let f: A → B and g : B → C be the bijective functions. Then (g o f)-1 is,
f-1 o g-1
f o g
g-1 o f-1
g o f

39. Let f: R – {35} → R be defined by f(x) = 3x+25x−3 then
f-1(x) = f(x)
f-1(x) = -f(x)
(f o f)x = -x
f-1(x) = 119 f(x)

40. Let f: [0, 1| → [0, 1| be defined by
Constant
1 + x
x
None of the above

41. Let f: |2, ∞) → R be the function defined by f(x) – x² – 4x + 5, then the range of f is
R
[1, ∞)
[4, ∞)
[5, ∞)

42. Let f: N → R be the function defined by f(x) = 2x−12 and g: Q → R be another function defined by g (x) = x + 2. Then (g 0 f) 32 is
1
0
7/2
None of the above

43. Let f : R → R be given by f (,v) = tan x. Then f-1(1) is
π/4
{nπ + π/4 : n ∈ Z}
does not exist
None of these

44. The relation R is defined on the set of natural numbers as {(a, b): a = 2b}. Then, R-1 is given by
{(2, 1), (4, 2), (6, 3),….}
{(1, 2), (2, 4), (3, 6),….}
R-1 is not defined
None of the above

45. The relation R is defined on the set of natural numbers as {(a, b): a = 2b}. Then, R-1 is given by
{(2, 1), (4, 2), (6, 3),….}
{(1, 2), (2, 4), (3, 6),….}
R-1 is not defined
None of the above

46. The relation R = {(1,1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is
Reflexive but not symmetric
Reflexive but not transitive
Symmetric and transitive
Neither symmetric nor transitive

47. The relation R = {(1,1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3} is
Reflexive but not symmetric
Reflexive but not transitive
Symmetric and transitive
Neither symmetric nor transitive

48. Let P = {(x, y) | x² + y² = 1, x, y ∈ R]. Then, P is
Reflexive
Symmetric
Transitive
Anti-symmetric

49. Let R be an equivalence relation on a finite set A having n elements. Then, the number of ordered pairs in R is
Less than n
Greater than or equal to n
Less than or equal to n
None of the above

50. For real numbers x and y, we write xRy ⇔ x – y + √2 is an irrational number. Then, the relational R is
Reflexive
Symmetric
Transitive
None of the above

51. Let R be a relation on the set N be defined by {(x, y) | x, y ∈ N, 2x + y = 41}. Then R is
Reflexive
Symmetric
Transitive
None of the above

52. Which one of the following relations on R is an equivalence relation?
aR1b ⇔ |a| = |b|
aR2b ⇔ a ≥ b
aR3b ⇔ a divides b
aR4b ⇔ a < b

53. Let R be a relation on the set N of natural numbers denoted by nRm ⇔ n is a factor of m (i.e. n | m). Then, R is
Reflexive and symmetric
Transitive and symmetric
Equivalence
Reflexive, transitive but not symmetric