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CBSE 11th Mathematics Relations and Functions Model Questions Papers Study Material - QB365 Set A

Published on: 21/10/2025

Question Set A

CBSE 11th Mathematics Relations and Functions Model Questions Papers Study Material - QB365

Download CBSE Class 11th Standard CBSE Mathematics question papers, sample papers, important questions, and previous year solved papers in PDF format. Get free study materials, NCERT solutions, and exam preparation resources for Class 11th Standard CBSE Mathematics

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Std: 11th Standard CBSE - Mathematics

chapter: Relations and Functions - Model Questions Papers

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Questions:

Generic 2

5 x 2 = 10

Identify the curve, which is a relation or function.

If P = {a, b, c} and Q = {r}, form the sets P × Q and Q × P. Are these two products equal?

If f(x) = x³ -\(1\over x^3\) ,Then find f(x) + f\(({1\over x})\) = 0

Find the domain and range of the following functions:
f(x) = x²- 3x +\({13\over4}\)

Find the values of a and b, if (2a-5,4)=(5,b+6)

Generic 3

5 x 3 = 15

Let f = \([(x,{x^2\over 1+x^2}):x\in R]\) be a function from R into R. Determine the range of f.

Draw the graph of each the following function f(x) = 5

Let A={1,2,3} and B={3,4} .Represent following graphically
\(B\times A\)

If A = {1,3,6} and B = {X,Y}, then represent the following catesian products by an arrow diagrams \(B\times B\)

10.

If \(f(x)=\log { \left( 1-x \right) } \) and , \(g(x)=[x]\) then determine each of the following functions. \(f.g\) Also, find: \((f.g)(0)\)

Generic 5

5 x 5 = 25

11.

Find the domain of the function f given by f(x)=\(1\over \sqrt{[x]^2-[x]-6}\)

12.

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

13.

Find the domain of the function \(f(x)=\frac { { x }^{ 2 }+2x+1 }{ { x }^{ 2 }-8x+12 } \)

14.

Find the domain and range of the following real functions. f(x) = - |2x|

15.

Let A = {-3, -2, -1, 4} and \(f:A\rightarrow Z\) given by f(x) = x²+x+2 Find pre-images of 6 and 4.

Multiple Choice Question

10 x 1 = 10

16.

The graph of the function, f(x) = 4 - 2x is ______.

(a)

(b)

(c)

(d)

17.

If A is a finite set having n elements, then the number of relations which can be defined in A is ______.

(a)

2ⁿ

(b)

n²

(c)

2ⁿ²

(d)

nⁿ

18.

Let R = \(\{x \mid x \in N, x \text { is a multiple of } 3 \text { and } x \leq 100\}\) S = \(\{x \mid x \in N, x \text { is a multiple of } 5 \text { and } x \leqq 100\}\). What is the number of elements in \((R \times S) \cap(S \times R) ?\)

(a)

(b)

(c)

(d)

19.

If a relation R is defined on the set Z of integers as follows \((a, b) \in R \Leftrightarrow a^{2}+b^{2}=25,\) then domain (R) is equal to ______.

(a)

{3, 4, 5}

(b)

{0 ,3, 4, 5}

(c)

{0 ,± 3, ± 4, ± 5}

(d)

None of these

20.

The relation R defined on the set of natural numbers as {(a, b): a differs from b by 3},is given by ______.

(a)

{(I, 4), (2, 5), (3, 6),... }

(b)

{(4, 1), (5,2), (6,3),.... }

(c)

{(I, 3), (2, 6), (3, 9),.... }

(d)

None of the above

21.

The relation on the set A = \(\{x:|x|<3, x \in Z\}\) is defined by R = \(\{(x, y): y=|x|, x \neq-1\}\). Then, the number of elements in the power set of R is ______.

(a)

(b)

(c)

(d)

22.

If A = {x : x² - 5x + 6 = 0); B = {2, 4}, C = {4, 5}, then \(A \times(B \cap C)\) is ______.

(a)

{(2, 4), (3, 4)}

(b)

{(4, 2), (4, 3)}

(c)

{(2, 4), (3,4), (4, 4)}

(d)

{(2, 2), (3,3), (4,4), (5, 5)}

23.

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

(a)

(A X B) = (B X A)

(b)

(A X B) *(B X A)

(c)

A X B = {(l, 4), (1,6), (2, 4)}

(d)

None of the above

24.

Let f(x) = Ix-1I then ______.

(a)

f(x²) = [f(x)]²

(b)

f(x +y) = f(x) f(y)

(c)

f(IxI) = I f(x) I

(d)

none of these

25.

Which one of the following is not a function

(a)

{(x, y) (:) x, y \(\in\) R, x² = y}

(b)

{(x, y) (:) x, y \(\in\) R, y² = x}

(c)

{(x, y) (:) x, y \(\in\) R, x = y³}

(d)

{(x, y) (:) x, y \(\in\) R, y = x³}

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Answers Key:

Generic 2

5 x 2 = 10

If we draw a vertical line, then it will intersect the curve at two points. It shows that given curve is a relation.

By the definition of the cartesian product,
P × Q = {(a, r), (b, r), (c, r)} and Q × P = {(r, a), (r, b), (r, c)}
Since, by the definition of equality of ordered pairs, the pair (a, r) is not equal to the pair (r, a), we conclude that P × Q \(\begin{equation} \neq \end{equation}\) Q × P.
However, the number of elements in each set will be the same.

Domain = R, Range = [1,\(\infty\))

We know that, two ordered pairs are equal, if their corresponding elements are equal.
(2a-5,4)=(5,b+6)\(\Rightarrow \)2a-5=5 and 4=b+6
[equating corresponding elements]
\(\Rightarrow \) 2a=5+5 and and 4-6=b
\(\Rightarrow \) 2a=10 and -2=b
\(\Rightarrow \) a=5 and b=-2

Generic 3

5 x 3 = 15

Here f(x) = \({x^2\over 1+x^2}\)
Put \(y={x^2\over 1+x^2}\)
\(\Rightarrow\) y + yx² = x²\(\Rightarrow\) x²(1- y) = y
\(\Rightarrow\) \(x^2={y\over 1-y}\)
\(\Rightarrow\) \(x=\pm\sqrt{y\over 1-y}\)
Now x will be real if
\({y\over 1-y}\ge 0\)
\(\Rightarrow\)\({y\over 1-y}\ge 0\)
\(\Rightarrow\) 0 \(\le\) y<1
\(\Rightarrow\) y\(\in\) [0,1)
\(\therefore \) Range of f(x) =[0,1)

Given, \(f\left( x \right) =5\forall \ x\in R\)
Clearly, domain of f is R.
Range of f is {5}.
Npw, we prepare a table for different value of x as shown below

x	-3	-2	-1	0	1	2	3
f(x)	5	5	5	5	5	5	5

Locate the points (-3,5), (-2,5), (-1,5), (0,5), (1,5), (2,5) and (3,5) on the graph paper and joint them, we obtained the required graph as shown below.

Clearly the graph of f(x) =5 represents a straight line parallel to X-axis and at a distance of 5 unit above the X-axis and symmetric with respect to Y-axis.