JEE Mathematics Relation and Functions MCQs Set D

Question: Let S be a finite set containing n elements. Then the total number of binary operations on S is:

• a)
• 
• b)

  

• c) nⁿ
• d) n²

Answer:  

Question: If a function f : [2, ∞) →B defined by f(x) = x² – 4x + 5 is a bijection, then B is equal to:

• a) [1, ∞)
• b) [5, ∞)
• c)  R
• d) [2, ∞)

Answer: [1, ∞)

Question:

• a) 2
• b) 0
• c) 1
• d) 1/2

Answer: 2

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Let Φ(x)= ax-b/x-a, the range being all real numbers except a, and b = a². Then its inverse is:

• a) (ax – b)/(x – a)
• b) (bx – a)/(x – a)
• c) (x – a)/(ax – b)
• d) (a – bx)/(1 – ax)

Answer: (ax – b)/(x – a)

Question:

• a) – 1
• b) 2
• c) 1
• d) 0

Answer: – 1

Question: The domain of f(x) = cos^–1 (3x – 1) is :

• a) f (x)= 1-x/1+x
• b) f (x) = 3^{log x}
• c) f (x) = 3^x(x+1)
• d) none of these

Answer: f (x)= 1-x/1+x

Question: Let A = R – {3}, B = R – {1}. Let f : A → B be defined by f(x) =x-2/x+3 Then :

• a) f is bijective
• b) f is one-one but not onto
• c) f is onto but not one-one
• d) none of these

Answer: f is bijective

Question: The function f : R → R defined by f (x) = (x – 1) (x – 2) (x – 3) is

• a) onto but not one-one
• b) neither one-one nor onto
• c) one-one but not onto
• d) both one-one and onto

Answer: onto but not one-one

Question:

• a) [1, 2)
• b) [0, 2]
• c) [0, 2)
• d) [1, 2]

Answer: [1, 2)

Question:

• a) None of these
• b) 1
• c) – 1
• d) – 2

Answer: None of these

Question: Given the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3}, the number of ordered pairs which when added to R make the R an equivalence relation is :

• a) 6
• b) None of these
• c) 5
• d) 7

Answer: 6

Question:

• a) – 1
• b) 2
• c) – 2
• d) 1

Answer: – 1

Question:

The function f : R → R defined by f (x) = sin x is :

• a) many one
• b) onto
• c) into
• d) one-one

Answer: many one

Question: If the number of elements in set A is m and number of element in set B is n then find number of relation defined from A to B

• a) 2^mn
• b) 2^m+n
• c) 2^m–n
• d) 2^m/n

Answer: 2^mn

Question:

• a) {(9, 1), (6, 2), (3, 3)}
• b) {(8, 1), (6, 2), (3, 3)}
• c) {(9, 1), (4, 2), (3, 3)}
• d) {(7, 1), (6, 2), (2, 2)}

Answer: {(9, 1), (6, 2), (3, 3)}

Question: In the above question, find Domain of R

• a) {9, 6, 3}
• b) {6, 4, 3}
• c) {9, 5, 3}
• d) {8, 1, 3}

Answer: {9, 6, 3}

Question: In the above question, find Range of R

• a) {1, 2, 3}
• b) {9, 5, 3}
• c) {9, 6, 3}
• d) {6, 4, 3}

Answer: {1, 2, 3}

Question: Which of the following is a function?

• a) { (1,2), (2,2), (3,2), (4,2)}
• b) { (1,2), (3,3), (2,3), (1,4)}
• c) {(1,4), (2,5), (1,6) , (3,9)}
• d) {(2,1), (2,2), (2,3), (2,4)}

Answer: { (1,2), (2,2), (3,2), (4,2)}

Question:

• a) 1 – x
• b) x – 1
• c) x
• d) x + 1

Answer: 1 – x

Question:

• a) R – {–1,0,1}
• b) R – {0,1}
• c) R
• d) None of these

Answer: R – {–1,0,1}

Question:

• a) [–1,1]
• b) {–1,1}
• c) {0,1}
• d) {–1,0,1}

Answer: [–1,1]

Question:

• a)

  

• b)

  

• c)

  

• d) x + 3

Answer:

Question: Function f (x) = x^–2 + x^–3 is-

• a) a rational function
• b) an inverse function
• c) None of these
• d) an irrational function

Answer: a rational function

Question: The period of | sin 2x | is-

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a) x
• b) –x
• c) 1/x
• d) –1/x

Answer: x

Question: If f(x) = 2|x – 2| – 3|x – 3|, then the value of f(x) when 2 < x < 3 is

• a) 5x – 13
• b) 5 – x
• c) x – 5
• d) None of these

Answer: 5x – 13

Question:

• a)

  

• b)

  

• c) R
• d) No value of x

Answer:

Question:

• a) [–2,2] – (–1,1)
• b) [1,2]
• c) [–1,2] – {0}
• d) [–2,2] – {0}

Answer: [–2,2] – (–1,1)

Question:

• a) –7
• b) 7
• c) –14
• d) 14

Answer: –7

Question: The relation R = { (1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is :

• a) reflexive only
• b) an equivalence relation
• c) transitive only
• d) symmetric only

Answer: reflexive only

Question:

• a) one-one and onto
• b) one-one but not onto
• c) onto but not one-one
• d) neither one-one nor onto

Answer: one-one and onto

Question:

• a) one-one but not onto
• b) onto but not one-one
• c) neither one-one nor onto
• d) one-one and onto

Answer: one-one but not onto

Question:

• a) one-one & onto
• b) neither one-one nor onto
• c) one-one but not onto
• d) onto but not one-one

Answer: one-one & onto

Question: R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x – 3. Then R^–1 is

• a) {(8, 11), (10, 13)}
• b) {(10, 13), (8, 11)}
• c) {(11, 18), (13, 10)}
• d) None of these

Answer: {(8, 11), (10, 13)}

Question:

• a) 1 and 2 are correct
• b) 1 and 3 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 2 are correct

Question:

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question:

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: If f : [0, 2]→ [0, 2] is a bijective function defined by f (x) = ax² + bx + c, where a, b, c are non-zero real numbers then f (2) is equal to –

• a) 0
• b) 2
• c) cannot be determined
• d)

  

Answer: 0

Question: If f : [0, 2]→ [0, 2] is a bijective function defined by f (x) = ax² + bx + c, where a, b, c are non-zero real numbers then Which of the following is one of the roots f (x) = 0 ?

• a) 1/a
• b) 1/b
• c) 1/c
• d) None of these

Answer: 1/a

Question: If f : [0, 2]→ [0, 2] is a bijective function defined by f (x) = ax² + bx + c, where a, b, c are non-zero real numbers then

Which of the following is not a value of a ?

• a) 1
• b) 1/2
• c) –1/4
• d) – 1/2

Answer: 1

Question:

• a) Statement -1 is True, Statement-2 is False
• b) Statement -1 is False, Statement-2 is True.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a explanation for Statement-1.

Answer: Statement -1 is True, Statement-2 is False

Question: Let for real numbers x and y we define the relation R such that

Statement-1 : The relation R is an equivalence relation.
Statement-2 : A relation R is an equivalence relation if it is reflexive, transitive and symmetric.

• a) Statement -1 is False, Statement-2 is True.
• b) Statement -1 is True, Statement-2 is False.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement -1 is False, Statement-2 is True.

Question: Statement-1 : Every relation which is symmetric and transitive is also reflexive.

• a) Statement -1 is False, Statement-2 is True.
• b) Statement -1 is True, Statement-2 is False.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement -1 is False, Statement-2 is True.

Question:

• a) None of these
• b) R – {1}
• c) [0,1]
• d) Both

Answer: None of these

Question:

• a) 0
• b) 1/2
• c) –1
• d) –2

Answer: 0

Question:

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question:

• a) 2f(x)
• b) – f(x)
• c) f (x)
• d) f (–x)

Answer: 2f(x)

Question: Find the range of f (x) = x– [x]

• a) [0, 1)
• b) (0, 1)
• c) [0, 1]
• d) [–1, 0)

Answer: [0, 1)

Question: Range of f (x) = 3 + x – [x+2] will be

• a) [1, 2)
• b) [0, 2)
• c) [0, 1]
• d) [–1, 0)

Answer: [1, 2)

Question: If X = {x1, x2, x3}, Y = (x1, x2, x3,x4,x5} and R1, is a relation from X to Y, then which of the followings are reflexive relation? (1) R1 : {(x1, x1), (x2, x2), (x3, x3)} (2) R1 : {(x1, x1), (x2, x2)} (3) R1 : {(x1, x1), (x2, x2),(x3, x3),(x1, x3),(x2, x4)} (4) R1 : {(x1, x1), (x2, x2),(x3, x3),(x4, x4)}

• a) 1 and 3 are correct
• b) 1 and 2 are correct
• c) 1, 2 and 3 are correct
• d) 2 and 4 are correct

Answer: 1 and 3 are correct

Question: If X = {a, b, c} and Y = {a, b, c, d, e, f} then find which of the following relation are symmetric relation?

(1) R₁ : { } i.e. void relation
(2) R₃ : {(a, b), (b, a)(a, c)(c, a)(a, a)}
(3) Every null relation
(4) R₂ : {(a, b)}

• a) 1, 2 and 3 are correct
• b) 2 and 4 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

Question: If X = {a, b, c} and Y = {a, b, c, d, e} then which of thefollowing are transitive relation.

(1) R₁ = { }
(2) R₂ = {(a, a)}
(3) R₃ = {(a, a).(c, d)}
(4) R₄ = {(a, b), (b, c)(a, c)}

• a) 1, 2 and 3 are correct
• b) 2 and 4 are correct
• c) 1 and 2 are correct
• d) 1 and 3 are correct

Answer: 1, 2 and 3 are correct

Question:

Domains of R and R^–1 are –

• a) {2, 4, 6, 8}, {4, 3, 2, 1}
• b) {4, 3, 2, 1}, {2, 4, 6, 8},
• c) {4, 6, 8, 10}, {4, 3, 2, 1}
• d) None of these

Answer: {2, 4, 6, 8}, {4, 3, 2, 1}

Question:

Range of R is –

• a) {4, 3, 2, 1}
• b) None of these
• c) {2, 4, 6, 8}
• d) {4, 6, 8, 10}

Answer: {4, 3, 2, 1}

Question:

Range of R^–1 is –

• a) {2, 4, 6, 8}
• b) {4, 6, 8, 10}
• c) {4, 3, 2, 1}
• d) None of these

Answer: {2, 4, 6, 8}

Question:

• a) Statement -1 is True, Statement-2 is False
• b) Statement -1 is False, Statement-2 is True.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement -1 is True, Statement-2 is False

Question:

• a) Statement -1 is False, Statement-2 is True.
• b) Statement -1 is True, Statement-2 is False.
• c) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• d) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

Answer: Statement -1 is False, Statement-2 is True.

Question:

• a) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.
• b) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.
• c) Statement -1 is False, Statement-2 is True
• d) Statement -1 is True, Statement-2 is False.

Answer: Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.