Relations And Functions CBSE Questions & Answers

Relations And Functions

This is Mathematics Class 11 Relations and Functions CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
If \(f(x) = {x \over {x - 1}},then{{f(a)} \over {f(a + 1)}} = \)
  • A
    \(f\left( { - {a \over {a - 1}}} \right)\)
  • B
    \(f({a^2})\)
    Correct
  • C
    \(f\left( {{1 \over a}} \right)\)
  • D
    f ( - a)
2
Let function f : R \( \to \) R be defined by f (x )= 2x + sin x for x \( \in \) R. Then f is
  • A
    one-to-one and onto
    Correct
  • B
    neither one-to-one nor onto
  • C
    one-to-one but NOT onto
  • D
    onto but NOT one-to-one
3
Coefficient of \({x^3}\) in the expansion of tan x is
  • A
    \({2 \over {15}}\)
  • B
    \({1 \over 2}\)
  • C
    \({1 \over 3}\)
    Correct
  • D
    \({1 \over 4}\)
4
If f(x) =\({{2x + 1} \over {3x - 2}},\) then (fof) (2) is equal to
  • A
    3
  • B
    1
  • C
    2
    Correct
  • D
    4
5
If \(f(x) = \log \left( {{{1 + x} \over {1 - x}}} \right),\) then f (x) is
  • A
    \({{f({x_1})} \over {f({x_2})}} = f({x_1} - {x_2})\)
  • B
    even
  • C
    odd
    Correct
  • D
    \(f({x_1})f({x_2}) = f({x_1} + {x_2})\)
6
Let the function f be defined by f (x) \( = {{2x + 1} \over {1 - 3x}},\) then \({f^{ - 1}}\) (x) is
  • A
    \({{2x + 1} \over {1 - 3x}}\)
  • B
    \({{x - 1} \over {3x + 2}}\)
    Correct
  • C
    \({{x + 1} \over {3x - 2}}\)
  • D
    \({{3x + 2} \over {x - 1}}\)
7
If A = \(\left\{ {x:{x^2} - 5x + 6 = 0} \right\}\) , B = {2, 4}, C = {4, 5} then \(A \times (B \cap C)\) is
  • A
    {(2,4), (3, 4)}
    Correct
  • B
    {(4, 2), (4, 3)}
  • C
    {(2, 2), (3, 3), (4, 4), (5, 5)}
  • D
    {(2, 4), (3, 4), (4, 4)}
8
In a city 20 percent of the population travels by car, 50 percent travels by bus and 10 percent travels by both car and bus. Then persons travelling by a car or bus is
  • A
    80 percent
  • B
    60 percent
    Correct
  • C
    70 percent
  • D
    40 percent
9
If g(x) = \({x^2} + x - 2\;and\) \({1 \over 2}(gof)(x) = 2{x^2} - 5x + 2,\) then f (x) is equal to
  • A
    \(2{x^2} - 3x - 1\)
  • B
    2 x + 3
  • C
    \(2{x^2} + 3x + 1\)
  • D
    2 x – 3
    Correct
10
The minimum value of sin x + cos x is
  • A
    0
  • B
    \( - 2\sqrt 2 \)
  • C
    \( - \sqrt 2 \)
    Correct
  • D
    \(\sqrt 2 \)
11
The range of the function f (x) = cos (x/3) is
  • A
    none of these
  • B
    [ - 1, 1]
    Correct
  • C
    [-3, 3]
  • D
    \(\left[ { - {1 \over 3},{1 \over 3}} \right]\)
12
If n (A) = 10, n (B) = 6 and n (C) = 5 for three disjoint sets A, B and C, then \(n(A \cup B \cup C) = \)
  • A
    11
  • B
    21
    Correct
  • C
    1
  • D
    9
13
If B is the set of numbers obtained by adding 1 to each of the even numbers, then its set builder notation is
  • A
    B = {x ; x is odd and x \( \in \) Z}
    Correct
  • B
    B = {x : x is an integer}
  • C
    B = {x : x is even }
  • D
    B = {x : x is odd and x \(> \)1}
14
On the power set P of a non-empty set A , we define an operation \(\Delta \) by \(X\Delta Y = (X \cap \overline Y ) \cup (\overline X \cap Y)\). Then which one of the following statements is true about \(\left( {P,\Delta } \right)\)
  • A
    commutative and associative without identity
  • B
    commutative and associative with an identity
    Correct
  • C
    associative but not commutative without an identity
  • D
    commutative but not associative with an identity
15
The relation R = {1, 1), (2, 2), (3, 3)} on the set {1, 2, 3) is
  • A
    reflexive only
  • B
    an equivalence relation
    Correct
  • C
    transitive only
  • D
    symmetric only