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Relations and Functions MATHS - Relations and Functions

Rajasthan Board (RBSE) - STD 11 Science - MATHS (Rajasthan - English Medium). 265 questions in this chapter.

Question types

Relations and Functions question types

265 questions across 6 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

265
Questions
6
Question groups
5
Question types
Sample Questions

Relations and Functions questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 2M.C.Q (1 Marks)1 Mark
R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x - 3. Then, R-1 is:
  • A
    {(8, 11), (10, 13)}
  • B
    {(11, 8), (13, 10)}
  • C
    {(10, 13), (8, 11), (12, 10)}
  • D
    none of these.
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Q 4M.C.Q (1 Marks)1 Mark
Let $\text{f(x)}=\sqrt{\text{x}^2+1}$ Then which of the following is correct?
  • A
    $\text{f(xy)}=\text{f(x)}\text{f(y)}$
  • B
    $\text{f(xy)}\geq\text{f(x)}\text{f(y)}$
  • C
    $\text{f(xy)}\leq\text{f(x)}\text{f(y)}$
  • D
    None os these.
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Q 5M.C.Q (1 Marks)1 Mark
The domain of the function $ \text {f} (\text{x}) = \frac{1}{(2 -\cos 3\text{x})}$ is:
  • A
    $ \Big (\frac{1}{3}, 1\Big)$
  • B
    $ \Big (\frac{1}{3}, 1\Big)$
  • C
    $ \Big (\frac{1}{3}, 1\Big)$
  • D
    $ \text{R}$
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Q 61 Marks Question1 Mark
Let R be a relation from N to N defined by R = {(a, b) : a, b $\in$ N and a = b2}. Check whether, (a, b) $\in$ R, (b, c) $\in$ R implies $(a, c) \in R$ ? Justify your answer.
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Q 71 Marks Question1 Mark
Let R be a relation from N to N defined by R = {(a, b) : a, b $\in$ N and a = b2}. Is the given statement true? (a, b) $\in$ R, implies $(b,a) \in R$ ? Justify your answer.
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Q 81 Marks Question1 Mark
Let R be a relation from N to N defined by R = {(a, b) : a, b $\in$ N and a = b2}. Check whether  $(a,a) \in R$ for all $a \in N$ ? Justify your answer.
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Q 101 Marks Question1 Mark
Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2,11)}. Is the given statement true? f is a function from A to B? Justify your answer.
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Q 122 Marks Questions2 Marks
Let $f= \left\{ \left(x , \frac { x ^ { 2 } } { 1 + x ^ { 2 } } \right) : x \in R \right\}$ be a function from R into R. Determine the range of f.
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Q 173 Marks Question3 Marks
The relation f is defined by $f ( x ) = \left\{ \begin{array} { l } { x ^ { 2 } , 0 \leq x \leq 3 } \\ { 3 x , 3 \leq x \leq 10 } \end{array} \right.$and the relation g is defined by $g ( x ) = \left\{ \begin{array} { l } { x ^ { 2 } , 0 \leq x \leq 2 } \\ { 3 x , 2 \leq x \leq 10 } \end{array} \right..$ Show that f is a function and g is not a function.
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Q 183 Marks Question3 Marks
Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by {(a, b): a, b $ \in $A, b is exactly divisible by a}.
  1. Write R in roster form
  2. Find the domain of R
  3. Find the range of R.
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Q 193 Marks Question3 Marks
The function f is defined by $\begin{equation} f(x)=\left\{\begin{array}{ll} {1-x,} & {x<0} \\ {1} & {, x=0} \\ {x+1,} & {x>0} \end{array}\right. \end{equation}$ 
Draw the graph of f(x).
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Q 21Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: The range of the function f(x) = 2 -3x, $\text{x}\in\text{R},$ x > 0 is R.
Reason: The range of the function f(x) = x2 + 2 is $(2,\infty).$
  1. A is true, R is true; R is a correct explanation of A.
  2. A is true, R is true; R is not a correct explanation of A.
  3. A is true; R is false.
  4. A is false; R is true.
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Q 22Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: If (x, 1), (y, 2) and (z, 1) are in A - Band n(A) = 3, n(B) = 2, then A = {x, y, z} and B = {1, 2}.
Reason: If n(A) = 3 and n(B) = 2, then n(A . B) = 6.
  1. A is true, R is true; R is a correct explanation of A.
  2. A is true, R is true; R is not a correct explanation of A.
  3. A is true; R is false.
  4. A is false; R is true.
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Q 23Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: (A) Let 4 = {1, 2, 3, 5}, B = {4, 6, 9} and R = {$(\text{x},\text{y}):\mid\text{x}-\text{y}\mid$ is odd, $\text{x}\in\text{A},\text{y}\in\text{B}$}. Then, domain of R is {1, 2, 3, 5}.
Reason: $\mid\text{x}\mid$ is always positive $\forall\ \text{x}\in\text{R}.$
  1. A is true, R is true; R is a correct explanation of A.
  2. A is true, R is true; R is not a correct explanation of A.
  3. A is true; R is false.
  4. A is false; R is true.
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Q 24Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Let R be a relation defined by $\text{R}={\{(\text{x},\text{x}+5):\text{x}\in\{0, 1, 2, 3, 4, 5\}}\}$ Then, consider the following
Assertion: The domain of R is {0, 1, 2, 3, 4, 5}.
Reason: The range of R is {0, 1, 2, 3, 4, 5}.
  1. A is true, R is true; R is a correct explanation of A.
  2. A is true, R is true; R is not a correct explanation of A.
  3. A is true; R is false.
  4. A is false; R is true.
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Q 25Assertion (A) & Reason (B) MCQ1 Mark
Directions: In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
Assertion: If f : R → R and g : R → R are defined by f(x) = 2x + 3 and g(x) = x2 + 7, then the values of x such that g{f(x)} = 8 are -1 and 2.
Reason: If f : R → R be given by $\text{f}(\text{x})=\frac{4^{\text{x}}}{4^{\text{x}}+2}$ for all $\text{x}\in\text{R},$ then f(x) + f(1 - x) = 1.
  1. A is true, R is true; R is a correct explanation of A.
  2. A is true, R is true; R is not a correct explanation of A.
  3. A is true; R is false.
  4. A is false; R is true.
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Q 26Case study (4 Marks)4 Marks
Method to Find the Sets When Cartesian Product is Given For finding these two sets, we write first element of each ordered pair in first set say A and corresponding second element in second set B (say). Number of Elements in Cartesian Product of Two Sets If there are p elements in set A and g elements in set B, then there will be pq elements in A . B i.e. if n(A) = p and n(B) = q, then n(A . B) = pq.
Based on the above two topic, answer the following questions.
  1. If A . B = {(a, 1), (b, 3), (a, 3), (b, 1), (a, 2), (b, 2)}. Then, A and B are:
  1. {1, 3, 2}, {a, b}
  2. {a, b}, {1, 3}
  3. {a, b}, {1, 3, 2}
  4. None of these
  1. If the set A has 3 elements and set B has 4 elements, then the number of elements in A . B is:
  1. 3
  2. 4
  3. 7
  4. 12
  1. A and B are two sets given in such a way that A . B contains 6 elements. If three elements of A . B are (1, 3), (2, 5) and (3, 3), then A, B are:
  1. {1, 2, 3}, {3, 5}
  2. {3, 5,}, {1, 2, 3}
  3. {1, 2}, {3, 5}
  4. {1, 2, 3}, {5}
  1. The remaining elements of A . B in (iii) is:
  1. (5, 1), (3, 2), (3, 5)
  2. (1, 5), (2, 3), (3, 5)
  3. (1, 5), (3, 2), (5, 3)
  4. None of the above
  1. The cartesian product P . P has 16 elements among which are found (a, 1) and (b, 2). Then, the set P is:
  1. {a, b}
  2. {1, 2}
  3. {a, b,1, 2}
  4. {0, b, 1, 2, 4}
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Q 27Case study (4 Marks)4 Marks
Ordered Pairs The ordered pair of two elements a and 3 is denoted by (a, b) : a is first element (or first component) and d is second element (or second component). Two ordered pairs are equal if their corresponding elements are equal. ie. (a, b) = (c, d)

⇒ a = c and b = d

Cartesian Product of Two Sets For two non-empty sets A and B, the cartesian product A . B is the set of all ordered pairs of elements from sets Aand B. In symbolic form, it can be written as 

$\text{A}\cdot\text{B}=\{(\text{a},\text{b}):\text{a}\in\text{A},\text{b}\in\text{B}\}$

Based on the above topics, answer the following questions.

If (a - 3, 6 + 7) = (3, 7), then the value of aand d are:

6, 0

3, 7

7, 0

3, -7

If (x + 6, y - 2) = (0, 6), then the value of x and y are:

6, 8

-6, -8

-6, 8

6, -8

If (x + 2, 4) = (5, 2x + y), then the value of x and y are:

-3, 2

3, 2

-3, -2

Let A and B be two sets such that A . B consists of 6 elements. If three elements of A . B are (1, 4), (2, 6) and (3, 6), then

(A . B) = (B . A)

$(\text{A}\cdot\text{B})\neq(\text{B}\cdot\text{A})$

A . B = {(1, 4), (1, 6), (2, 4)}

None of the above

If m(A . B) = 45, then n(A) cannot be

15

17

5

9

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