Class 11 Mathematics Relations and Functions MCQs Set 02

Question: The relation Rdefined on set A = {x : lxl <3,x ∈I}by R = {(x, y) : y = lxl} is
a) {(- 2, 2), (- 1, 1), (0, 0), (1, 1), (2, 2)}
b) {(- 2, – 2), (- 2, 2), (- 1, 1), (0, 0), (1, – 2), (1, 2), (2, -1), (2, – 2)}
c) {(0, 0), (1, 1), (2, 2)}
d) None of the options
Answer: a

Question: If R is a relation from a set A to the set B and S is a relation from B to C, then the relation SoR
a) is from C to A
b) is from A to C
c) does not exist
d) None of the options
Answer: b

Question: Let R be a relation on N defined by x + 2y = 8. The domain of R is
a) {2, 4, 8}
b) {2, 4, 6, 8}
c) {2, 4, 6}
d) {1, 2, 3, 4}
Answer: c

Question: Let a relation R be defined by R = {(4, 5), (1, 4), (4, 6), (7, 6), (3, 7)}. The relation R-1oR is given by
a) {(1, 1), (4, 4), (7, 4), (4, 7), (7, 7)}
b) {(1, 1), (4, 4), (4, 7), (7, 4), (7, 7), (3, 3)}
c) {(1, 5), (1, 6), (3, 6)}
d) None of the options Functions
Answer: b

Question: Let f : N → Y be a function defined as f (x) = 4x + 3 where If f is invertible, then its inverse is
a) g (y)=y-3/4
b) g (y)=3y+4/3
c) g (y)=4+y+3/4
d) g (y)=y+3/4
Answer: a

Question: Let R be the relation from A = {2, 3, 4, 5} to B = {3, 6, 7,10} defined by ‘x divides y’,then R-1 is equal to
a) {(6, 2), (3, 3)}
b) {(6, 2), (10, 2), (3, 3), (6, 3), (10, 5)}
c) {(6, 2), (10, 2), (3, 3), (6, 3)}
d) None of the options
Answer: b

Question:The relation R defined on the set of natural numbers as {(a, b) : a differs from b by 3}, is given by
a) {(1, 4), (2, 5), (3, 6), . . . . }
b) {(4, 1), (5, 2), (6, 3), . . . . }
c) {(1, 3), (2, 6), (3, 9), . . . . }
d) None of the options
Answer: b

Question: The domain of the function f defined by f (x)=√4-x+1/√x²-1is equal to
a) (-∞ -1)∪(1, 4]
b) (-∞, -1]∪(1, 4]
c) (–∞, -1)∪[1, 4]
d) (–∞, -1)∪[1, 4)
Answer: a

Question: The domain of the function f given by f (x)=x²+2x+1/x²-x-6
a) R – {3, – 2}
b) R – {-3, 2}
c) R – [3, – 2]
d) R – (3, – 2)
Answer: a

Question: R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x – 3. The relation R-1 is
a) {(11, 8), (13, 10)}
b) {(8, 11), (10, 13)}
c) {(8, 11), (9, 12), (10, 13)}
d) None of the options
Answer: b

Question: The domain and range of the function f given by f (x) = 2 -|x – 5|is
a) Domain = R+ , Range = (-∞, 1]
b) Domain = R, Range = (-∞, 2]
c) Domain = R , Range = (–∞, 2)
d) Domain = R+ , Range = (–∞, 2]
Answer: b

Question: If f (x) = cos (log x), then f (x) f (y)-1/2[f(x/y)+f(xy)] has the value 2
a) -1
b)1/2
c) –2
d) 0
Answer: d

Question: Given, f (x)= log(1+x/1-x)and g (x)3x+x³/1+3x²‘ then fog(x) equals
a) -f(x)
b) 3f(x)
c) [f(x)]³
d) None of the options
Answer: b

Question: 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 (ho( gof ))(x), if x =√π/4 will be
a) 0
b) 1
c) –1
d) p
Answer: a

Question: If [x]²-5 [x] + 6 = 0, where [ · ] denote the greatest integer function, then
a) x ∈3, 4]
b) x ∈(2, 3]
c) x ∈[2, 3]
d) x ∈[2, 4)
Answer: d

Question: The domain and range of the real function f defined by f (x)=4-x/x-4 is given by
a) Domain = R, Range = {-1, 1}
b) Domain = R – {1}, Range = R
c) Domain R=- { }4 , Range ={-}1
d) Domain = R – {-4}, Range = {-1, 1}
Answer: c

Question: The domain for which the functions defined by f (x) = 3x² -1 and g(x) = 3 + x are equal to
a){-1,4/3}
b){-1,-4/3}
c){1,4/3}
d){1,-4/3}
Answer: a

Question: If f (x) = ax + b, where a and b are integers, f (-1) = – 5 and f (3) = 3, then a and b are equal to
a) a = – 3,b = -1
b) a = 2, b = – 3
c) a = 0 , b = 2
d) a = 2, b = 3
Answer: a

Question: Range of f (x)=1/1-2cos x is
a) [1/3,1]
b) [-1,1/3]
c) (-∞,-1)∪[1/3,∞)
d) [-1/3,1]
Answer: b

Question: If f : R → R satisfies f (x + y) = f (x) + f ( y), for all x y ∈ R , and f ( 1)= 7 = then ⁿ∑=f (r) is r=1
a) 7n/2
b) 7(n+1)/2
c) 7n(n + 1)
d) 7n (n+1/2
Answer: b

Question: Domain of √a² -x² (a > 0) is
a) (-a, a)
b) [-a, a]
c) [0, a]
d) (-a, 0]
Answer: b

Question: The inverse of the function y=10x-10-x/10x+10-xis
a) log₁₀ (2 – x)
b)1/2 log₁₀1+x/1-x
c) 1/2log₁₀ (2x – 1)
d) 1/4log(2x/2-x)
Answer: b

Question: Let f (x) = √1 + x² then
a) f(xy ) = f(x) × f( y )
b) f(xy ) ³ f(x) × f( y )
c) f(xy ) £ f(x) × f( y )
d) None of the options
Answer: c

Question: 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 the options
Answer: a

Question: A real valued function f (x) satisfies the functional equation
f (x – y) = f (x) f ( y) – f (a – x) f (a + y)
where a is a given constant and f (0) = 1, f (2a – x) is equal to
a) f(-x)
b) fa) + f(a – x)
c) f(x)
d) -f(x)
Answer: d

Question:

Answer: a

Question:

Answer: a

Question: Let f : R → R, g : R → R be two functions such that f (x ) = 2x -3, g(x ) = x³ + 5 .
The function ( fog)-1(x) is equal to

Answer: d

Question: If f : R → R is given by

Answer: b

Question:

Answer: a