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
In Z, the set of all integers, inverse of – 7 w.r.t. ‘\(*\)’ defined by a\(*\)b = a + b + 7 for all a, b \( \in \) Z, is
  • A
    7
  • B
    - 7
    Correct
  • C
    - 14
  • D
    14
2
A class has 175 students. The following data shows the number of students opting one or more subject. Maths – 100, Physics – 70, Chemistry – 40, Maths and Physics – 30, Maths and Chemistry – 38, Physics and Chemistry – 23, Maths, Physics and Chemistry – 18. How many have opted for Mathematics alone ?
  • A
    30
  • B
    50
    Correct
  • C
    48
  • D
    35
3
Let \(f\left( {x + {1 \over x}} \right) = {x^2} + {1 \over {{x^2}}},x \ne 0,\) then f(x) =
  • A
    \({x^2} + 1\)
  • B
    \({x^2} - 1\)
  • C
    \({x^2}\)
  • D
    \({x^2} - 2\)
    Correct
4
Suppose f : [2, 2] \( \to \)R be defined by \(f(x) = \left\{ \begin{gathered} \; - 1\;\;for\;\;\;\;\;\;\; - 2 \leq x \leq 0 \\ x - 1\;for\;\;\;\;\;\;\;0 \leq x \leq 2\;\;\; \\ \end{gathered} \right.,\) Then { x \( \in \) [-2, 2]: x \( \le \) 0 and f (| x |) = x} =
  • A
    { - 1 }
  • B
    {0}
  • C
    \(\left\{ { - {1 \over 2}} \right\}\)
    Correct
  • D
    \(\phi \)
5
If f : \(R \to R\) and g: \(R \to R\) are given by f (x0 = \({\text{| x |}}\) and g (x) = [x] for each x \( \in \) R, then {x \( \in \) R} : g (f (x0) \( \in \)f (g (x))] =
  • A
    R
    Correct
  • B
    Z
  • C
    Z U (-\(\infty \), 0)
  • D
    \(\left( { - \infty ,0} \right)\)
6
If f : \(R \to R\)and g : \(R \to R\)are defined by f (x) = 2x + 3 and g(x) = \({x^2} + 7,\) then the values of x such that g (f (x)) = 8 are
  • A
    - 1, - 2
    Correct
  • B
    1, - 2
  • C
    - 1, 2
  • D
    1, 2
7
Consider the following relations: 1. A – B = A – \((A \cap B)\) 2. A = \((A \cap B)\) \(\mathop \cup \nolimits \)(A – B). 3. A – (B \(\mathop \cup \nolimits \) C) = (A – B) \(\mathop \cup \nolimits \) (A – C). Which of these is/are correct ?
  • A
    2 and 3
  • B
    2 only
  • C
    1 and 3
  • D
    1 and 2
    Correct
8
If A is the set of even natural numbers less than 8 and B is the set of prime numbers less than 7, then the number of relations from A to B is
  • A
    \({2^9}\)
    Correct
  • B
    \({3^2}\)
  • C
    \({2^9} - 1\)
  • D
    \({9^2}\)
9
Two finite sets have m and n elements. The number o elements in the power set of the first is 48 more than the total number of elements in the power set of the second. Then the values of m and n are
  • A
    6, 4
    Correct
  • B
    3, 7
  • C
    6, 3
  • D
    7, 6
10
Let S be the set of all real numbers. Then the relation \({\text{R }} = {\text{ }}\left\{ {\left( {{\text{a}},{\text{ b}}} \right){\text{ }}:{\text{ 1 }} + {\text{ ab }} > {\text{ }}0} \right\}\) on S is
  • A
    reflexive and symmetric but not transitive
    Correct
  • B
    reflexive symmetric and transitive
  • C
    symmetric and transitive but not reflexive
  • D
    reflexive and transitive but not symmetric
11
A function f : [0, \(\infty \)] \( \to \) [0, \(\infty \)) defined as \(f(x) = {x \over {1 + x}}\) is
  • A
    one-one and onto
  • B
    one-one but not onto
    Correct
  • C
    neither one-one nor onto
  • D
    onto but not one-one
12
If f : [1, \(\infty \infty \)) \( \to \) [2, \(\infty \infty \)) is given by \(f(x) = x + {1 \over x}then{f^{ - 1}}(x)\) equals]
  • A
    \({x \over {1 + {x^2}}}\)
  • B
    \({{x + \sqrt {{x^2} - 4} } \over 2}\)
    Correct
  • C
    \({{x\sqrt {{x^2} - 4} } \over 2}\)
  • D
    \(1 + \sqrt {{x^2} - 4} \)
13
A function f from the natural numbers to the set of integers defined by \(f(x) = \left\{ \begin{gathered} \frac{{n - 1}}{2},\;\;when\;n\;is\;odd \\ - \frac{n}{2},\;\;\;\;when\;n\;iseven \\ \end{gathered} \right.is\)
  • A
    one-one but not onto
  • B
    both one-one and onto
    Correct
  • C
    neither one-one nor onto
  • D
    onto but not one-one
14
Domain of definition of the function \(f(x) = {3 \over {4 - {x^2}}} + {\log _{10}}({x^3} - x)\) is
  • A
    (- 1, 0) \({\rm{U}}\) (1, 2) U ( 2, \(\infty \))
    Correct
  • B
    ( 1, 2)
  • C
    (1, 2) \(\mathop \cup \nolimits \) ( 2, \(\infty \))
  • D
    (- 1, 0) \({\rm{U}}\) ( 1, 2)
15
If f : \(R \to R\) satisfies f (x + y) = f (x ) + f (y) for all x, y \( \in \) R and f (1) = 7, then \(\sum\limits_{r = 1}^n {f(r)} \) is
  • A
    \({{7(n + 1)} \over 2}\)
  • B
    7 n(n +1)
  • C
    \({{7n} \over 2}\)
  • D
    \({{7n(n + 1)} \over 2}\)
    Correct