BITSAT Mathematics Relations and Functions MCQs

Question: If x is real number, then  must lie between

• a)

  

• b)

  

• c)

  –11 and 1

• d)

  

Answer:

Question: The domain of the function  is

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

Answer: (0, 1)

Question: Let x and y be two natural numbers such that xy= 12(x + y) and   Then the total number of pairs (x, y) is

• a) 8
• b) 6
• c) 4
• d) 16

Answer: 8

Question: If f(x) is a function that is odd and even simultaneously, then f(C) – f(B) is equal to

• a) 1
• b) -1
• c) 0
• d) None of these

Answer: 0

Question: The range of the function  where  is

• a) (– ∞, 3]
• b) (–∞,∞)
• c) [3, ∞)
• d) 

  

Answer:

Question: The domain of the functions f (x) = log₂ log₃ log₄ x is

• a) [4, ∞ )
• b) (4, ∞)
• c) (– ∞ ,4)
• d) None of these

Answer: (4, ∞)

Question: The range of the function  is

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: The domain of the function is

• a) ( – ∞, 1)
• b)

  

• c)

  

• d) (2, ∞)

Answer:

Question: If f(x) is a function that is odd and even simultaneously, then f(C) – f(B) is equal to

• a) 1
• b) -1
• c) 0
• d) None of these

Answer: 0

Question: The domain of the functions f (x) = log₂ log₃ log₄ x is

• a) [4, ∞ )
• b) (4, ∞)
• c) (– ∞ ,4)
• d) None of these

Answer: (4, ∞)

Question: Let f and g be functions from R to R defined as

Then

• a) (fog) (–3) = 8
• b) (fog) (9) = 683
• c) (gof) (0) = – 8
• d) (gof) (6) = 427

Answer: (fog) (9) = 683

Question: Let  , then fof (x) = x, provided that :

• a) d = – a
• b) d = a
• c) a = b = 1
• d) a = b = c = d = 1

Answer: d = – a

Question: If ρ = {(x, y) |x² + y² = 1; x, y € R}. Then,ρ is

• a) Reflexive
• b) Symmetric
• c) Transitive
• d) Anti-symmetric

Answer: Symmetric

Question: Let f : R →R be a function defined bywhere m ≠ n , then

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

Answer: f is one-one into

Question: The relation ‘less than’ in the set of natural numbers is :

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

Answer: only transitive

Question: If f is an even function and g is an odd function, then the function fog is

• a) an even function
• b) an odd function
• c) Neither even nor odd
• d) A periodic function

Answer: an even function

Question: If

is given as

• a) 1
• b) x
• c) 1 + x
• d) None of these

Answer: x

Question: If the domain of f^–1 (x) is

• a) R
• b) R – {– 1}
• c) (– ∞, – 1)
• d) (–1, ∞)

Answer: R – {– 1}

Question: Let E = {1, 2, 3, 4} and F = {1, 2}. Then the number of onto functions from E to Fis

• a) 14
• b) 16
• c) 12
• d) 8

Answer: 14

Question: If then (fof of) (x) is

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: If the function f : (– ∞,∞) → B defined by f (x) = – x² + 6x – 8 is bijective, then B =

• a) [1,∞)
• b) (– ∞, 1]
• c) (– ∞, ∞)
• d) None of these

Answer: (– ∞, 1]

Question: x² = xy is a relation which is

• a) Symmetric
• b) Reflexive
• c) Transitive
• d) None of these

Answer: Reflexive

Question: Let R = {(1,3),(4,2),(2,4),(2,3),(3,1)} be a relation on the set A = {1,2,3,4}. . The relation R is

• a) Reflexive
• b) Transitive
• c) Not symmetric
• d) A function

Answer: Not symmetric

Question: If f : R → R, f (x) = 2 x + 3 then f ^–1 (x) =

• a)

  

• b)

  

• c)

  

• d)

  

Answer:

Question: Let P = {(x, y) :| x² + y² | = 1, x, y €R}. Then P is

• a) Reflexive
• b) Symmetric
• c) Transitive
• d) Anti-symmetric

Answer: Symmetric

Question: Let be a function defined as f (x) = √3sin x - cos x + 2. Then f ^–1(x) is given by

• a)

  

• b)

  

• c)

  

• d) None of these

Answer:

Question: The relation ‘less than’ in the set of natural numbers is :

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

Answer: only transitive

Question: If f is an even function and g is an odd function, then the function fog is

• a) an even function
• b) an odd function
• c) neither even nor odd
• d) a periodic function

Answer: an even function

Question: Let E = {1, 2, 3, 4} and F = {1, 2}. Then the number of onto functions from E to Fis

• a) 14
• b) 16
• c) 12
• d) 8

Answer: 14

Question:  x² = xy is a relation which is

• a) Symmetric
• b) Reflexive
• c) Transitive
• d) None of these

Answer: Reflexive