Chapter 1 important || English medium || unit test

Kalaimagal Academy

Unit Test - I (Mathematics)

Time: 45 Mins	Max. Marks: 25
Class: 10th Standard	Portion: Chapter 1 - Relations and Functions
Student Name: _______________________	Roll No: ____________
Date: ____________

I. CHOOSE THE CORRECT ANSWER 5 × 1 = 5 Marks

1. 1. If \( n(A \times B) = 6 \) and \( A = \{1, 3\} \), then \( n(B) \) is:
   (a) 1

   (b) 2

   (c) 3

   (d) 6
2. 2. If \( A = \{a, b, p\} \), \( B = \{2, 3\} \), and \( C = \{p, q, r, s\} \), then \( n[(A \cup C) \times B] \) is:
   (a) 8

   (b) 20

   (c) 12

   (d) 16
3. 3. If there are 1024 relations from a set \( A = \{1, 2, 3, 4, 5\} \) to a set \( B \), then the number of elements in \( B \) is:
   (a) 3

   (b) 2

   (c) 4

   (d) 8
4. 4. The range of the relation \( R = \{(x, x^2) \mid x \text{ is a prime number less than } 13\} \) is:
   (a) {2, 3, 5, 7}

   (b) {2, 3, 5, 7, 11}

   (c) {4, 9, 25, 49, 121}

   (d) {1, 4, 9, 25, 49, 121}
5. 5. If \( f: A \rightarrow B \) is a bijective function and \( n(A) = 5 \), then \( n(B) \) is equal to:
   (a) 10

   (b) 4

   (c) 5

   (d) 25

II. ANSWER THE FOLLOWING QUESTIONS 5 × 2 = 10 Marks

6. 6. If \( A \times B = \{(3, 2), (3, 4), (5, 2), (5, 4)\} \), then find \( A \) and \( B \).
7. 7. A relation \( f \) is defined by \( f(x) = x^2 - 2 \), where \( x \in \{-2, -1, 0, 3\} \). List the elements of \( f \) and state if it is a function.
8. 8. Let \( A = \{1, 2, 3\} \) and \( B = \{x \mid x \text{ is a prime number less than } 10\} \). Find \( A \times B \).
9. 9. Find \( k \), if \( f(k) = 2k - 1 \) and \( f \circ f(k) = 5 \).
10. 10. If \( f(x) = 3x - 2 \) and \( g(x) = 2x + k \), find the value of \( k \) if \( f \circ g = g \circ f \).

III. ANSWER THE FOLLOWING QUESTIONS 2 × 5 = 10 Marks

11. 11. Let \( A = \{x \in W \mid x < 2\} \), \( B = \{x \in N \mid 1 < x \le 4\} \), and \( C = \{3, 5\} \). Verify that:
    

    \( A \times (B \cup C) = (A \times B) \cup (A \times C) \)
12. 12. Let \( A = \{1, 2, 3, 4\} \) and \( B = \{2, 5, 8, 11, 14\} \) be two sets. Let \( f: A \rightarrow B \) be a function given by \( f(x) = 3x - 1 \). Represent this function:

    1. By arrow diagram
    2. In a table form
    3. As a set of ordered pairs
    4. In a graphical form

*** ALL THE BEST ***