12th Math chapter 1 Bihar board with NCERT-Details & 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) 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)
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) 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)
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 = 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)
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Bihar board 12th Math chapter 1 complete objective
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Bihar board 12th science stream subjects wise solution
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| SL.N. | Subject name with solutions |
| 01 | Physics |
| 02 | Chemistry |
| 03 | Biology |
| 04 | Math |
| 05 | Hindi |
| 06 | English |