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

Answer: (b) (x -5)^{1/3}

**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

Answer: (a) 5

**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

Answer: (a) commutative

**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

Answer: (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

Answer: (c) 2

**Question 12**

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

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

**Question 13**

The function f : R → R given by f(x) = x^{3} – 1 is

(a) a one-one function

(b) an onto function

(c) a bijection

(d) neither one-one nor onto

Answer: (c) a bijection

**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

Answer: (a) a bijection

**Question 15**

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

Answer: (c) bijective

**Question 13**

Let f(x) = x^{2} – 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

Answer: (a) x = 1

**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) = x^{2}

(c) f : R^{+} → R^{+}, f(x) = 1/𝑥3

(d) None of these

Answer: (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

Answer: (c) 7

**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

Answer: (b) 30

**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

Answer: (b) 2

**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

Answer: (a) 20/3

**Question 19.**

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) 2^{n} – 2

(c) 2^{n} – 1

(d) None of these

Answer: (b) 2^{n} – 2

**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

Answer: (a) f-1 o g-1

**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

Answer: (a) one-one

**Question 23**

If f(x_{1}) = f (x_{2}) ⇒ x_{1} = x_{2} ∀ x_{1} x_{2} ∈ A then the function f: A → B is

(a) one-one

(b) one-one onto

(c) onto

(d) many one

Answer: (a) one-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 R_{0} = R – {0})

(a) R_{0}

(b) W

(c) Z

(d) None of these

Ans (a) R_{0}

**Question 25**

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

(a) One-one

(b) Many-one

(c) Both (a) & (b)

(d) None of these

Answer: (b) Many-one

**Question: 26**

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

a) x

b) (3- x^{3})

c) x^{3}

d) None of these

Answer: a) x

**Question 27.**

If F : R → R such that f(x) = 5x + 4 then which of the following is equal to f^{-1}(x).

(a) (𝑥−5)/4

(b) (𝑥−𝑦)/5

(c) (𝑥−4)/5

(d) 𝑥/4 -5

Answer: (c) (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

Answer: (a) Onto

**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) 2

^{106}

Answer: (c) 106!

**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

Answer- (d) An onto function

**Question: 31**

#### Let f:R→R defined by f(x) = x^{4}. 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

Answer: (a) 31

**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) n^{2}

(b) n

(c) n!

(d) 2n

Answer- (c) n!

**Question 34**

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

Answer: (a) 0

Question 35

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

Answer: (b) ±2.

**Question 36.**

The range of the function f(x) = √(𝑥−1)(3−𝑥) is

(a) [1, 3]

(b) [0, 1]

(c) [-2, 2]

(d) None of these

Answer: (a) [1, 3]

**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/(4𝑥−5)

(c) g(x) = (𝑥−4)/5

(d) g(x) = 5x – 4

Answer: (c) g(x) = (𝑥−4)/5

**Question 38**

If f: R → R be given by f(x) = (3 – x³)^{1/3}, then fof (x) is

(a) x^{1/3}

(b) x³

(c) x

(d) 3 – x³.

Answer: (c) x

**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) = (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

Answer: (a) 3

**Question 42**

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

Answer: (a) 0

**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

Answer: (c) 16

**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

Answer: (a) 14

**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

Answer: (c) one-one onto

**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)

Answer: — (b) 0

**Question-50**

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

(a) tan^{-1}xtan(x)

(b) tan^{-1}xcot(x)

(c) x

(d) tan^{-1}xsin(x)

Answer: —** : –**(c) x

**Question 51.**

If the function f(x) = x³ + e^{x/2} and g (x) = f^{n}(x), then the value of g'(1) is

(a) 1

(b) 2

(c) 3

(d) 4

Answer: (b) 2

**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**

(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 :-

-: also visit :-

- ISC Class-12 Text book Solutions, Notes , Syllabus, Paper
- MCQ Type Questions ISC Class-12 Semester-1 Session 2021-22

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