Tag: Chapter 5

Short Description:
These MCQs are based on the latest Curriculum of Mathematics for SSC-II (Class 10) provided by the Federal Board of Intermediate and Secondary Education (FBISE). This set of 45 multiple-choice questions covers the concepts of sets, types of sets, set operations, relations, functions, domain, codomain, range, and function composition. Ideal for exam revision and self-assessment before Class 10 exams.

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MCQs – Sets and Functions

1. The set $\{x : x \text{ is a prime number less than 10}\}${x:x is a prime number less than 10} is:
   A. $\{2,3,5,7\}${2,3,5,7}
   B. $\{1,2,3,5\}${1,2,3,5}
   C. $\{2,3,5,7,9\}${2,3,5,7,9}
   D. $\{1,3,5,7\}${1,3,5,7}
2. If $A = \{1,2,3\}$A={1,2,3} and $B = \{3,4,5\}$B={3,4,5}, then $A \cup B$A∪B is:
   A. $\{1,2,3,4,5\}${1,2,3,4,5}
   B. $\{3\}${3}
   C. $\{1,2,4,5\}${1,2,4,5}
   D. $\{1,2,3\}${1,2,3}
3. For the same sets, $A \cap B$A∩B is:
   A. $\{1,2,3,4,5\}${1,2,3,4,5}
   B. $\{3\}${3}
   C. $\{1,2,4,5\}${1,2,4,5}
   D. $\{1,2\}${1,2}
4. If $U = \{1,2,3,4,5,6\}$U={1,2,3,4,5,6} and $A = \{2,4,6\}$A={2,4,6}, then $A’$A′ (complement of A) is:
   A. $\{1,3,5\}${1,3,5}
   B. $\{2,4,6\}${2,4,6}
   C. $\{1,2,3,4\}${1,2,3,4}
   D. $\{3,4,5\}${3,4,5}
5. Which of the following is a finite set?
   A. $\{1,2,3,4,5\}${1,2,3,4,5}
   B. $\mathbb{N}$N
   C. $\mathbb{Z}$Z
   D. $\mathbb{R}$R
6. Which of the following is an infinite set?
   A. $\{2,4,6,8,10\}${2,4,6,8,10}
   B. $\mathbb{N}$N
   C. $\{1,3,5,7\}${1,3,5,7}
   D. $\{a,b,c\}${a,b,c}
7. If $A = \{1,2\}$A={1,2} and $B = \{a,b\}$B={a,b}, the Cartesian product $A \times B$A×B is:
   A. $\{(1,a),(1,b),(2,a),(2,b)\}${(1,a),(1,b),(2,a),(2,b)}
   B. $\{(a,1),(b,1),(a,2),(b,2)\}${(a,1),(b,1),(a,2),(b,2)}
   C. $\{(1,2),(a,b)\}${(1,2),(a,b)}
   D. $\{(1,a),(2,b)\}${(1,a),(2,b)}
8. A function is defined as:
   A. A relation where each element of the domain has exactly one image in the codomain
   B. A relation where each element of the domain may have multiple images
   C. A set of ordered pairs with repeated first elements
   D. None of these
9. If $f(x) = 2x+3$f(x)=2x+3, then $f(2)$f(2) is:
   A. 4
   B. 5
   C. 7
   D. 8
10. For $f(x) = x^2-1$f(x)=x2−1, the domain is:
    A. All real numbers
    B. Positive real numbers
    C. Integers only
    D. Natural numbers only
11. The range of $f(x) = x^2$f(x)=x2 is:
    A. All real numbers
    B. Non-negative real numbers
    C. Negative real numbers
    D. Integers
12. Which of the following is a one-to-one function?
    A. $f(x) = 2x+1$f(x)=2x+1
    B. $f(x) = x^2$f(x)=x2
    C. $f(x) = |x|$f(x)=∣x∣
    D. $f(x) = x^2-4$f(x)=x2−4
13. The function $f(x) = x^3$f(x)=x3 is:
    A. One-to-one
    B. Not one-to-one
    C. Constant
    D. None of these
14. The function $f: \mathbb{R} \to \mathbb{R}$f:R→R, $f(x) = x^2$f(x)=x2, is:
    A. Many-to-one
    B. One-to-one
    C. Onto
    D. Constant
15. The composition of $f(x) = 2x$f(x)=2x and $g(x) = x+3$g(x)=x+3 is:
    A. $f(g(x)) = 2x+3$f(g(x))=2x+3
    B. $f(g(x)) = 2x+6$f(g(x))=2x+6
    C. $g(f(x)) = 2x+3$g(f(x))=2x+3
    D. $g(f(x)) = 2x+6$g(f(x))=2x+6
16. The set of even natural numbers is:
    A. Infinite and countable
    B. Infinite and uncountable
    C. Finite
    D. Empty
17. The empty set is denoted by:
    A. $\{\}${}
    B. $\varnothing$∅
    C. Both A and B
    D. None
18. If $A = \{1,2,3\}$A={1,2,3}, $B = \{2,3,4\}$B={2,3,4}, then $A – B$A−B is:
    A. $\{1\}${1}
    B. $\{4\}${4}
    C. $\{2,3\}${2,3}
    D. $\{1,4\}${1,4}
19. The union of disjoint sets $A$A and $B$B contains:
    A. All elements of A and B without repetition
    B. Only elements of A
    C. Only elements of B
    D. Only common elements
20. The intersection of disjoint sets $A$A and $B$B is:
    A. Empty set
    B. All elements of A
    C. All elements of B
    D. None
21. A bijective function is:
    A. One-to-one and onto
    B. One-to-one only
    C. Onto only
    D. Many-to-one
22. If $f(x) = 3x-2$f(x)=3x−2, then $f^{-1}(x)$f−1(x) is:
    A. $\frac{x+2}{3}$3x+2​
    B. $3x+2$3x+2
    C. $\frac{x-2}{3}$3x−2​
    D. $x^3-2$x3−2
23. Which of the following is a constant function?
    A. $f(x) = 5$f(x)=5
    B. $f(x) = x+1$f(x)=x+1
    C. $f(x) = 2x$f(x)=2x
    D. $f(x) = x^2$f(x)=x2
24. The domain of $f(x) = \frac{1}{x-2}$f(x)=x−21​ is:
    A. All real numbers except 2
    B. All real numbers
    C. All positive numbers
    D. All integers
25. If $f(x) = x+1$f(x)=x+1 and $g(x) = x^2$g(x)=x2, then $f(g(x))$f(g(x)) is:
    A. $x^2+1$x2+1
    B. $(x+1)^2$(x+1)2
    C. $x^2-1$x2−1
    D. $x^2+2$x2+2
26. If $A = \{1,2,3,4\}$A={1,2,3,4}, then the number of subsets of A is:
    A. 16
    B. 8
    C. 4
    D. 2
27. For set $A = \{a,b\}$A={a,b}, Cartesian product $A \times A$A×A has:
    A. 4 elements
    B. 2 elements
    C. 3 elements
    D. 1 element
28. A function $f(x) = |x|$f(x)=∣x∣ is:
    A. Many-to-one
    B. One-to-one
    C. Constant
    D. None
29. The set of integers divisible by 5 is:
    A. Infinite and countable
    B. Infinite and uncountable
    C. Finite
    D. Empty
30. If $A = \{1,2,3\}$A={1,2,3}, $B = \{4,5\}$B={4,5}, then $A \times B$A×B has:
    A. 6 elements
    B. 5 elements
    C. 3 elements
    D. 2 elements
31. A function with domain $\mathbb{R}$R and codomain $\mathbb{R}$R defined by $f(x) = x^2+1$f(x)=x2+1 has range:
    A. $y \ge 1$y≥1
    B. $y \ge 0$y≥0
    C. $y \le 0$y≤0
    D. All real numbers
32. $f(x) = x^3$f(x)=x3 is:
    A. One-to-one and onto
    B. Many-to-one
    C. Constant
    D. None
33. $f(x) = \sin x$f(x)=sinx for $x \in [0, \pi]$x∈[0,π] is:
    A. One-to-one
    B. Many-to-one
    C. Constant
    D. None
34. The union of A = {1,2} and B = {2,3} is:
    A. {1,2,3}
    B. {2}
    C. {1,3}
    D. {1,2}
35. Intersection of A = {1,2} and B = {2,3} is:
    A. {2}
    B. {1}
    C. {3}
    D. {1,3}
36. A function which is both one-to-one and onto is called:
    A. Bijective
    B. Injective only
    C. Surjective only
    D. None
37. If $f(x) = 2x+3$f(x)=2x+3 and $g(x) = x-1$g(x)=x−1, then $g(f(x))$g(f(x)) is:
    A. $2x+2$2x+2
    B. $2x+4$2x+4
    C. $2x+3$2x+3
    D. $2x+1$2x+1
38. If $A = \{1,2,3\}$A={1,2,3}, number of proper subsets of A is:
    A. 7
    B. 8
    C. 6
    D. 3
39. The set of natural numbers is:
    A. Infinite
    B. Finite
    C. Empty
    D. None
40. Domain of $f(x) = \frac{1}{x^2-4}$f(x)=x2−41​ is:
    A. All real numbers except ±2
    B. All real numbers
    C. x > 0
    D. x < 0
41. The range of $f(x) = x^2$f(x)=x2 is:
    A. y ≥ 0
    B. y ≤ 0
    C. All real numbers
    D. None
42. The function $f(x) = x^2+2x+1$f(x)=x2+2x+1 is:
    A. Many-to-one
    B. One-to-one
    C. Constant
    D. None
43. The inverse of $f(x) = 3x+4$f(x)=3x+4 is:
    A. $f^{-1}(x) = \frac{x-4}{3}$f−1(x)=3x−4​
    B. $f^{-1}(x) = 3x-4$f−1(x)=3x−4
    C. $f^{-1}(x) = \frac{x+4}{3}$f−1(x)=3x+4​
    D. $f^{-1}(x) = x-4$f−1(x)=x−4
44. If $A = {a,b}$A=a,b, the Cartesian product $A \times A \times A$A×A×A has:
    A. 8 elements
    B. 6 elements
    C. 4 elements
    D. 2 elements
45. Function $f(x) = x^2$f(x)=x2 restricted to x ≥ 0 is:
    A. One-to-one
    B. Many-to-one
    C. Constant
    D. None

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Answers – List Form

1. A
2. A
3. B
4. A
5. A
6. B
7. A
8. A
9. C
10. A
11. B
12. A
13. A
14. A
15. B
16. A
17. C
18. A
19. A
20. A
21. A
22. A
23. A
24. A
25. A
26. A
27. A
28. A
29. A
30. A
31. A
32. A
33. A
34. A
35. A
36. A
37. A
38. A
39. A
40. A
41. A
42. A
43. A
44. A
45. A