12th Math Chapter 1 Objective in English

1. The function f : A → B defined by f(x) = 4x + 7, x ∈ R is

(a) one-one

(b) Many-one

(c) Odd

(d) Even

Ans (a)

2. The smallest integer function f(x) = [x] is

(a) One-one

(b) Many-one

(c) Both (a) & (b)

(d) None of these

Ans (b)

3. The function f : R → R defined by f(x) = 3 – 4x is

(a) Onto

(b) Not onto

(c) None one-one

(d) None of these

Ans (a)

4. The number of bijective functions from set A to itself when A contains 106 elements is

(a) 106

(b) (106)²

(c) 106!

(d) 2106

Ans (c)

5. If f : R → R, g : R → R and h : R → R is such that f(x) = x², g(x) = tanx and h(x) = logx, then the value of [ho(gof)](x), if x = √ π/2 will be

(a) 0

(b) 1

(c) -1

(d) 10

Ans (a)

6. If f : R → R and g : R → R defined by f(x) = 2x + 3 and g(x) = x²+ 7, then the value of x for which f(g(x)) = 25 is

(a) ±1

(b) ±2

(c) ±3

(d) ±4

Ans (b)

7. Let f : N → R : f(x) = (2x−1)/2 and g : Q → R : g(x) = x + 2 be two functions. Then, (gof) (3/2) is

(a) 3

(b) 1

(c) 7/2

(d) None of these

Ans (a)

8. If f : R → R, g : R → R and h : R → R are such that f(x) = x², g(x) = tan x and h(x) = log x, then the value of (go(foh)) (x), if x = 1 will be

(a) 0

(b) 1

(c) -1

(d) π

Ans (a)

9. The number of binary operations that can be defined on a set of 2 elements is

(a) 8

(b) 4

(c) 16

(d) 64

Ans (c)

10. Let * be a binary operation on Q, defined by a * b = 3ab/5 is

(a) Commutative

(b) Associative

(c) Both (a) and (b)

(d) None of these

Ans (c)

11. Let * be a binary operation on set Q of rational numbers defined as a * b = ab/5. Write the identity for *.

(a) 5

(b) 3

(c) 1

(d) 6

Ans (a)

12. For binary operation * defind on R – {1} such that a * b = a/b+1 is

(a) not associative

(b) not commutative

(c) commutative

(d) both (a) and (b)

Ans (d)

13. The binary operation * defind on set R, given by a * b = a+b/2 for all a,b ∈ R is

(a) commutative

(b) associative

(c) Both (a) and (b)

(d) None of these

Ans (a)

14. Let A = N × N and * be the binary operation on A defined by (a, b) * (c, d) = (a + c, b + d). Then * is

(a) commutative

(b) associative

(c) Both (a) and (b)

(d) None of these

Ans (c)

15. Find the identity element in the set I+ of all positive integers defined by a * b = a + b for all a, b ∈ I+.

(a) 1

(b) 2

(c) 3

(d) 0

Ans (d)

16. Let * be a binary operation on set Q – {1} defind by a * b = a + b – ab : a, b ∈ Q – {1}. Then * is

(a) Commutative

(b) Associative

(c) Both (a) and (b)

(d) None of these

Ans (c)

17. The binary operation * defined on N by a * b = a + b + ab for all a, b ∈ N is

(a) commutative only

(b) associative only

(c) both commutative and associative

(d) none of these

Ans (c)

18. The number of commutative binary operation that can be defined on a set of 2 elements is

(a) 8

(b) 6

(c) 4

(d) 2

Ans (d)

19. 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 ∈ Then R is

(a) reflexive but not transitive

(b) transitive but not symmetric

(c) equivalence

(d) None of these

Ans (c)

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

(a) 1

(b) 2

(c) 3

(d) 5

Ans (d)

21. 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

Ans (b)

22. 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

(a) reflexive but not symmetric

(b) reflexive but not transitive

(c) symmetric and transitive

(d) neither symmetric, nor transitive

Ans (a)

23. The identity element for the binary operation * defined on Q – {0} as a * b = ab/2 ∀ a, b ∈ Q – {0) is

(a) 1

(b) 0

(c) 2

(d) None of these

Ans (c)

24. 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

Ans (b)

25. Let f : R → R be defind by f(x) = 1/x ∀ x ∈ Then f is

(a) one-one

(b) onto

(c) bijective

(d) f is not defined

Ans (d)

26. Which of the following functions from Z into Z are bijective?

(a) f(x) = x³

(b) f(x) = x + 2

(c) f(x) = 2x + 1

(d) f(x) = x² + 1

Ans (b)

27. Let f : R → R be given by f(x) = tan x. Then f^-1(1) is

(a) π/4

(b) {nπ + π/4; n ∈ Z}

(c) Does not exist

(d) None of these

Ans (b)

28. 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

(a) Reflexive and symmetric

(b) Transitive and symmetric

(c) Equivalence

(d) Reflexive, transitive but not symmetric

Ans (d)

29. Let S = {1, 2, 3, 4, 5} and let A = S × S. Define the relation R on A as follows:

(a, b) R (c, d) iff ad = cb. Then, R is

(a) reflexive only

(b) Symmetric only

(c) Transitive only

(d) Equivalence relation

Ans (d)

30. Let R be the relation “is congruent to” on the set of all triangles in a plane is

(a) reflexive

(b) symmetric

(c) symmetric and reflexive

(d) equivalence

Ans (d)

31. Total number of equivalence relations defined in the set S = {a, b, c} is

(a) 5

(b) 3!

(c) 23

(d) 33

Ans (a)

32. The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then, R^-1is given by

(a) {(2, 1), (4, 2), (6, 3),….}

(b) {(1, 2), (2, 4), (3, 6), ……..}

(c) R^-1 is not defiend

(d) None of these

Ans (b)

33. Let X = {-1, 0, 1}, Y = {0, 2} and a function f : X → Y defiend by y = 2x⁴, is

(a) one-one onto

(b) one-one into

(c) many-one onto

(d) many-one into

Ans (c)

34. Let g(x) = x²– 4x – 5, then

(a) g is one-one on R

(b) g is not one-one on R

(c) g is bijective on R

(d) None of these

Ans (b)

35. The mapping f : N → N is given by f(n) = 1 + n², n ∈ N when N is the set of natural numbers is

(a) one-one and onto

(b) onto but not one-one

(c) one-one but not onto

(d) neither one-one nor onto

Ans (c)

36. The function f : R → R given by f(x) = x³– 1 is

(a) a one-one function

(b) an onto function

(c) a bijection

(d) neither one-one nor onto

Ans (c)

37. Let f : [0, ∞) → [0, 2] be defined by f(x)=2x/1+x, then f is

(a) one-one but not onto

(b) onto but not one-one

(c) both one-one and onto

(d) neither one-one nor onto

Ans (a)

38. If N be the set of all-natural numbers, consider f : N → N such that f(x) = 2x, ∀ x ∈ N, then f is

(a) one-one onto

(b) one-one into

(c) many-one onto

(d) None of these

Ans (b)

39. Let A = {x : -1 ≤ x ≤ 1} and f : A → A is a function defined by f(x) = x |x| then f is

(a) a bijection

(b) injection but not surjection

(c) surjection but not injection

(d) neither injection nor surjection

Ans (a)

40. Let f : R → R be a function defined by f(x) = x³+ 4, then f is

(a) injective

(b) surjective

(c) bijective

(d) none of these

Ans (c)

41. Let * be a binary operation on set of integers I, defined by a * b = a + b – 3, then find the value of 3 * 4.

(a) 2

(b) 4

(c) 7

(d) 6

Ans (c)

42. If * is a binary operation on set of integers I defined by a * b = 3a + 4b – 2, then find the value of 4 * 5.

(a) 35

(b) 30

(c) 25

(d) 29

Ans (b)

43. Let * be the binary operation on N given by a * b = HCF (a, b) where, a, b ∈ Find the value of 22 * 4.

(a) 1

(b) 2

(c) 3

(d) 4

Ans (b)