# ISC Maths MCQ Functions Class-12 for Semester-1

ISC Maths MCQ Functions Class-12 Semester-1 for 2021-22. These MCQ  / Objective Type Questions is based on latest reduced syllabus according 2021-22 session on bifurcated pattern. Main motto of MCQ Type Question is cracking the next upcoming exam of council. Visit official website CISCE for detail information about ISC Board Class-12 Physics.

## Semester-1 Exam of 2021-22 ISC Maths MCQ Relations for Class-12

 Board ISC Class 12th (XII) Subject Maths Chapter Functions Syllabus on bifurcated syllabus (after reduction) bifurcated pattern Semester-1 Session 2021-22 Topic MCQ / Objective Type Question

## Class-12 ISC Maths MCQ Relations for Semester-1 Exam

Question 1

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

Answer: (b) f(x) = x + 2

Question 2.
Let f: R → R be the function defined by f(x) = x³ + 5. Then f-1 (x) is
(a) (x + 5)1/3
(b) (x -5)1/3
(c) (5 – x)1/3
(d) 5 – x

Question 3
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
Answer: (c) Both (a) and (b)

Question 4
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

Question 5
For binary operation * defined on R – {1} such that a * b = 𝑎 / (𝑏+1) is
(a) not associative
(b) not commutative
(c) commutative
(d) both (a) and (b)
Answer: (d) both (a) and (b)

Question 6
The binary operation * defined 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

Question 7
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
Answer: (c) Both (a) and (b)
Question 8
Let * be a binary operation on set Q – {1} defined 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
Answer: (c) Both (a) and (b)
Question 9
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
Answer: (c) both commutative and associative
Question 10

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

Question 11
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

Question 12
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
Answer: (b) f(x) = x + 2

Question 13
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

Question 14
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

Question 15
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

Question 13
Let f(x) = x2 – x + 1, x ≥ 1/2, then the solution of the equation f(x) = f-1(x) is
(a) x = 1
(b) x = 2
(c) x = 1/2
(d) None of these

Question 14
Which one of the following function is not invertible?
(a) f : R → R, f(x) = 3x + 1
(b) f : R → [0, ∞), f(x) = x2
(c) f : R+ → R+, f(x) = 1/𝑥3
(d) None of these

Question 15
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

Question 16.
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

Question 17

Let * be the binary operation on N given by a * b = HCF (a, b) where, a, b ∈ N. Find the value of 22 * 4.
(a) 1
(b) 2
(c) 3
(d) 4

Question 18
Consider the binary operation * on Q defind by a * b = a + 12b + ab for a, b ∈ Q. Find 2 * 1/3
(a) 20/3
(b) 4
(c) 18
(d) 16/3

Question 19.
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

Question 20
Let f: A → B and g : B → C be the bijective functions. Then (g o f)-1 is,
(a) f-1 o g-1
(b) f o g
(c ) g-1 o f-1
(d) g o f

Question 21
A = {1, 2, 3} which of the following function f: A → A does not have an inverse function
(a) {(1, 1), (2, 2), (3, 3)}
(b) {(1, 2), (2, 1), (3, 1)}
(c) {(1, 3), (3, 2), (2, 1)}
(d) {(1, 2), (2, 3), (3, 1)

Answer: (b) {(1, 2), (2, 1), (3, 1)}

Question 22.
The function f : A → B defined by f(x) = 4x + 7, x ∈ R is
(a) one-one
(b) Many-one
(c) Odd
(d) Even

Question 23
If f(x1) = f (x2) ⇒ x1 = x2 ∀ x1 x2 ∈ A then the function f: A → B is
(a) one-one
(b) one-one onto
(c) onto
(d) many one

Question-24

Let  f : N→ R – {0} defined as f(x) = 1/x where x ∈ N is not an onto function. Which one of the following sets should be replaced by N such that the function f will become onto?​ (where R0 = R – {0})

(a) R0

(b) W

(c) Z

(d) None of these

Ans (a) R0

Question 25
The smallest integer function f(x) = [x] is
(a) One-one
(b) Many-one
(c) Both (a) & (b)
(d) None of these

Question: 26

#### If f: R→ R given by f(x) =(3 − x3)1/3, find f0f(x)

a) x

b) (3- x3)

c) x3

d) None of these

Question 27.

If F : R → R such that f(x) = 5x + 4 then which of the following is equal to f-1(x).
(a) (𝑥5)/4
(b) (𝑥𝑦)/5
(c) (𝑥4)/5
(d) 𝑥/4 -5

Question 28.
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

Question 29
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

Question 30

If f: A→B and g:B→C are onto, then gof: A→C is:​

(a) A many-one and onto function

(b) A bijective function

(c) An into function

(d) An onto function

Question: 31

#### Let f:R→R defined by f(x) = x4. Choose the correct answer

a) f is neither one-one nor onto

b) f is one one but not onto

c) f is many one onto

d) None of these

Answer: f is neither one-one nor onto

Question 32
Consider the binary operation * on a defined by x * y = 1 + 12x + xy, ∀ x, y ∈ Q, then 2 * 3 equals
(a) 31
(b) 40
(c) 43
(d) None of these

Question 33

How many onto functions from set A to set A can be formed for the set A = {1, 2, 3, 4, 5, ……n}?​

(a) n2

(b) n

(c) n!

(d) 2n

Question 34
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

Question 35

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

Question 36.
The range of the function f(x) = √(𝑥1)(3𝑥) is
(a) [1, 3]
(b) [0, 1]
(c) [-2, 2]
(d) None of these

Question-37

Given a function lf as f(x) = 5x + 4, x ∈ R. If g : R → R is inverse of function ‘f then
(a) g(x) = 4x + 5
(b) g(x) = 5/(4𝑥5)
(c) g(x) = (𝑥4)/5
(d) g(x) = 5x – 4

Question 38
If f: R → R be given by f(x) = (3 – x³)1/3, then fof (x) is
(a) x1/3
(b) x³
(c) x
(d) 3 – x³.

Question 39.

Let f : R → R be defined as f(x) = 3x. Then
(a) f is one-one onto
(b) f is many-one onto
(c) f is one-one but not onto
(d) f is neither one-one nor onto.

Answer  (a) f is one-one onto

Question-40

. The range of the function f(x) = [sin x] is

(a) [1, 1].

(b) (–1, 1)

(c) {– 1, 0, 1}

(d) {–1, 1}

Answer- (c) {– 1, 0, 1}

Question 41.
Let f : N → R : f(x) = (2𝑥1)/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

Question 42
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

Question 43
The number of binary operations that can be defined on a set of 2 elements is
(a) 8
(b) 4
(c) 16
(d) 64

Question 44
Let E = {1, 2, 3, 4} and F = {1, 2} Then, the number of onto functions from E to F is
(a) 14
(b) 16
(c) 12
(d) 8

Question 45.
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?
(a) Many-one onto
(b) Constant function
(c) one-one onto
(d) into

Question-46

Let A = {a,b,c} and B = {1,2,3} and f: A→B is defined by f={(a,2), (b,1), (c,3)}. Find f-1​

(a) {(2,a),(1,b), (3, c)}

(b) Can not be inverted as it is not one-one

(c) Can not be inverted as it is not onto

(d) {(a,2), b,1), (c,3)}

Answer: – (a) {(2,a),(1,b), (3, c)}

Question-47

A function f: A x B → B x A defined by f (a, b) = (b, a) on two sets A and B. The function is:​

(a) Many-one

(b) One-one but not onto

(c) One-one and onto

(d) Neither one-one nor onto

Answer: -: – (c) One-one and onto

Question-48

If ƒ(x) = xsecx, then ƒ(0) =

(a) −1

(b) 0

(c) 1

(d) √(2)

Question-50

If ƒ(x) = tan-1 x and g(x) = tan(x), then (gof)(x) =

(a) tan-1xtan(x)

(b) tan-1xcot(x)

(c) x

(d) tan-1xsin(x)

Question 51.
If the function f(x) = x³ + ex/2 and g (x) = fn(x), then the value of g'(1) is
(a) 1
(b) 2
(c) 3
(d) 4

Question 52

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

Answer: (a) range (f) ⊂ B

Question 53
If f: R → R such that f(x) = 3x – 4 then which of the following is f-1(x)?
(a)    (x + 4)/3
(b)    (x – 4)/3
(c) 3x – 4
(d) undefined

Answer: (a)  (x + 4) /3

Question 54
Let f : R → R be defined by f(x) = 1/𝑥 ∀ x ∈ R. Then f is
(a) one-one
(b) onto
(c) bijective
(d) f is not defined
Answer: (d) f is not defined

-: End of ISC Maths MCQ Functions Class-12  :-

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