12th Math chapter 1 Bihar board with NCERTDetails & Highlights
name of content  12th Math chapter 1 full solution 
content  Math objective type MCQ question with answer 
name of subjects  class 12 Math 
important for exam  Bihar board & other state board 
pattern & Level  NCERT & State level question 
12th Math chapter 1 all objective solutions – download PDF
1. The function f : A → B defined by f(x) = 4x + 7, x ∈ R is

 (a) oneone
 (b) Manyone
 (c) Odd
 (d) Even
Ans (a)
2. The smallest integer function f(x) = [x] is

 (a) Oneone
 (b) Manyone
 (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 oneone
 (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) = x^{2}, 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) = x^{2}+ 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) = x^{2}, 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)
Bihar Board most mcq solution 12th math chapter 1
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)
Important mcq notes 12th math chapter 1
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) ^{n}P_{2}
 (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) oneone
 (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) = x^{3}
 (b) f(x) = x + 2
 (c) f(x) = 2x + 1
 (d) f(x) = x^{2} + 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^{1}is 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)
BSEB 12th math chapter 1 most mcq solution
33. Let X = {1, 0, 1}, Y = {0, 2} and a function f : X → Y defiend by y = 2x^{4}, is

 (a) oneone onto
 (b) oneone into
 (c) manyone onto
 (d) manyone into
Ans (c)
34. Let g(x) = x^{2}– 4x – 5, then

 (a) g is oneone on R
 (b) g is not oneone 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 + n^{2}, n ∈ N when N is the set of natural numbers is

 (a) oneone and onto
 (b) onto but not oneone
 (c) oneone but not onto
 (d) neither oneone nor onto
Ans (c)
36. The function f : R → R given by f(x) = x^{3}– 1 is

 (a) a oneone function
 (b) an onto function
 (c) a bijection
 (d) neither oneone nor onto
Ans (c)
37. Let f : [0, ∞) → [0, 2] be defined by f(x)=2x/1+x, then f is

 (a) oneone but not onto
 (b) onto but not oneone
 (c) both oneone and onto
 (d) neither oneone nor onto
Ans (a)
38. If N be the set of allnatural numbers, consider f : N → N such that f(x) = 2x, ∀ x ∈ N, then f is

 (a) oneone onto
 (b) oneone into
 (c) manyone 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) = x^{3}+ 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)
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