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**Qusetion 1.** If
1 2 5 1
3 3 33
, find the values of x and y.

**Question 2.** If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of
elements in (A×B).

**Question 3.** If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.

**Question 4.** State whether each of the following statements are true or false. If the statement
is false, rewrite the given statement correctly.

(i) If P = {m, n} and Q = { n, m}, then P × Q = {(m, n),(n, m)}.

(ii) If A and B are non-empty sets, then A × B is a non-empty set of ordered
pairs (x, y) such that x ∈ A and y ∈ B.

(iii) If A = {1, 2}, B = {3, 4}, then A × (B ∩ φ) = φ.

**Question 5.** If A = {–1, 1}, find A × A × A.
6. If A × B = {(a, x),(a , y), (b, x), (b, y)}. Find A and B.

**Question 6.** Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that
(i) A × (B ∩ C) = (A × B) ∩ (A × C). (ii) A × C is a subset of B × D.

**Question 7.** Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have?
List them.

**Question 8.** Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1)
are in A × B, find A and B, where x, y and z are distinct elements.

10. The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0,1). Find the set A and the remaining elements of A × A

**Qusetion 1.** Let A = {1, 2, 3,...,14}. Define a relation R from A to A by
R = {(x, y) : 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain and
range.

**Question 2.** Define a relation R on the set N of natural numbers by R = {(x, y) : y = x + 5,
x is a natural number less than 4; x, y ∈N}. Depict this relationship using roster
form. Write down the domain and the range.

**Question 3.** A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by
R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in
roster form.

**Question 4.** The Fi 2.7 shows a relationship
between the sets P and Q. Write this
relation
(i) in set-builder form (ii) roster form.
What is its domain and range?

**Question 5.** Let A = {1, 2, 3, 4, 6}. Let R be the
relation on A defined by
{(a, b): a , b ∈A, b is exactly divisible by a}.

(i) Write R in roster form

(ii) Find the domain of R

(iii) Find the range of R.

**Question 6.** Determine the domain and range of the relation R defined by
R = {(x, x + 5) : x ∈ {0, 1, 2, 3, 4, 5}}.

**Question 7.** Write the relation R = {(x, x3) : x is a prime number less than 10} in roster form.

**Question 8.** Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.

**Question 9.** Let R be the relation on Z defined by R = {(a,b): a, b ∈ Z, a – b is an integer}.
Find the domain and range of R.

**Qusetion 1.** Which of the following relations are functions? Give reasons. If it is a function,
determine its domain and range.

(i) {(2,1), (5,1), (8,1), (11,1), (14,1), (17,1)}

(ii) {(2,1), (4,2), (6,3), (8,4), (10,5), (12,6), (14,7)}

(iii) {(1,3), (1,5), (2,5)}.

**Question 2.** Find the domain and range of the following real functions:
(i) f(x) = – x (ii) f(x) = 9 − x 2.

**Question 3.** A function f is defined by f(x) = 2x –5. Write down the values of
(i) f (0), (ii) f (7), (iii) f (–3).

**Question 4.** The function ‘t’ which maps temperature in degree Celsius into temperature in
degree Fahrenheit is defined by t(C) =
9C
5 + 3 2.Find

(i) t(0)

(ii) t(28)

(iii) t(–10)

(iv) The value of C, when t(C) = 212.

**Question 5.** Find the range of each of the following functions.

(i) f (x) = 2 – 3x, x ∈ R, x > 0.

(ii) f (x) = x2 + 2, x is a real number.

(iii) f (x) = x, x is a real number

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उपर दिखायी दे रही पीडीऍफ़ को डाउनलोड करने का लिंक

- Chapter 10 Straight lines
**[Ques wise Ans]** - Chapter 11 Conic Section
**[Ques wise Ans]** - Chapter 12 Introduction to 3D Geometry
**[Ques wise Ans]** - Chapter 13 Limit and Derivatives
**[Ques wise Ans]** - Chapter 1 Sets
- Chapter 2 Relations and Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 6 Linear Inequalities
- Chapter 7 Permutations and Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences and Series
- Chapter 10 Straight Lines
- Chapter 11 Conic Sections
- Chapter 12 Introduction to Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 14 Mathematical Reasoning
- Chapter 15 Statistics
- Chapter 16 Probability

- NCERT Solutions for Class 9
- NCERT Solutions for Class 10
- NCERT Solutions for Class 11
- NCERT Solutions for Class 12

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