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NCERT Solutions for class 11 Maths | Chapter 2 - Relations and Functions

Questions
1 If f(x) is an odd differentiable function on R, then df(x)/dx is a/an
A Even function
B Odd function
C Either even or odd function
D Neither even nor odd function

Answer:Even function
2 If f(x) = log3 x and A = (3, 27) then f(A) =
A (1, 1)
B (3, 3)
C (1, 3)
D (2, 3)

Answer:(1, 3)
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3 If f(x) = (a – x)1/n, a > 0 and n ∈ N, then the value of f(f(x)) is
A 1/x
B x
C x²
D x1/2

Answer:x
4 A function f(x) is said to be an odd function if
A f(-x) = f(x)
B f(-x) = -f(x)
C f(-x) = k * f(x) where k is a constant
D None of these

Answer:f(-x) = -f(x)
5 If f(x) = ex and g(x) = loge x then the value of fog(1) is
A 0
B 1
C -1
D None of these

Answer:0
6 The function f(x) = sin (‎πx/2) + cos (πx/2) is periodic with period
A 4
B 6
C 12
D 24

Answer:4
7 Let R be the set of real numbers. If f(x) = x² and g(x) = 2x + 1, then fog(x) is equal to
A 2x + 1
B 2x² + 1
C (2x + 1)²
D None of these

Answer:2x² + 1
8 Let A = {-2, -1, 0} and f(x) = 2x – 3 then the range of f is
A {7, -5, -3}
B {-7, 5, -3}
C {-7, -5, 3}
D {-7, -5, -3}

Answer:{-7, -5, -3}
9 The period of the function f(x) = sin4 3x + cos4 3x is
A π/2
B π/3
C π/4
D π/6

Answer:π/6
10 If f is an even function and g is an odd function the fog is a/an
A Even function
B Odd function
C Either even or odd function
D Neither even nor odd function

Answer:Even function
11 Let f(x)=|x−1| +|x−3|+|x−4|, which one of the below is incorrect
A f(1) =4
B f(3.5)=3.5
C f(5)=7
D f(0)=7

Answer:f(0)=7
12 Range of the function defined as F(x)=x-2/3-x
A R –{2}
B R –{3}
C R –{1}
D R – {-1}

Answer:R – {-1}
13 if Set A = {1,2,3,4,5} and Set B is {1,4,5} and Relation R is defined as less than, the R can be written in ordered pair as
A {(1,4),(1,5), (2,4), (2,5),(3,4),(3,5) ,(4,5)}
B {(1,4), (2,4), (2,5),(3,4),(3,5) ,(4,5)}
C {(1,4),(5,1), (2,4), (2,5),(3,4),(3,5) ,(4,5)}
D {(1,4),(1,5), (2,4), (2,5),(3,4),(3,5) ,(4,5),(5,5)}

Answer:{(1,4),(1,5), (2,4), (2,5),(3,4),(3,5) ,(4,5)}
14 The range of the function defined as f(x)=|x-5|/x-5
A (-1, 1)
B [-1,1]
C {-1,1}
D {5, -5}

Answer:{-1,1}
15 Let A = {1, 2, 3,4, 5,6,7,8,9} and R is relation defined on Set A as R ={(1,2),(2,4),(3,6),(4,8)}. The which one is false
A Range of R is {2,4,6,8}
B Co domain of R is {1, 2, 3,4, 5,6,7,8,9}
C None of these
D Domain of R is {1,2,3,4}

Answer:None of these
16 if f is a function such that f(0) =2 ,f(1) =3 and f(x+2) = 2f(x) -f(x+1) for every real x, then f(5) is
A 6
B 5
C 13
D 1

Answer:13
17 if ƒ(x)=x3-1/x3 then f(x) + f(1/x) is
A 1
B 1/x3
C x3
D 0

Answer:0
18 The domain of the function F(x) =logx-4(x-11x+24)
A (-∞, 8)
B (8, ∞)
C (-1, ∞)
D [8, ∞)

Answer:(8, ∞)
19 If ƒ=[x]2+[x]+2, then which of them is incorrect

then which of them is incorrect

A f(0) =3
B f(-.50)=2
C f(1)=4
D f(.75)=2

Answer:f(0) =3
20 The domain of the real valued function

ƒ(x)=x-5/x-6

A R – {-5}
B R – {5}
C R – {-6}
D R –{6}

Answer:R –{6}

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