General & Pure Mathematics
1. What is the universal set in the context of a given problem?
a. Set of all real numbers
b. Set of all elements under consideration
c. Set of natural numbers
d. Set of prime numbers
2. If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∩ B?
a. {1, 2}
b. {3}
c. {1, 2, 3, 4, 5}
d. {4, 5}
3. How is the cardinality of a set defined?
a. The sum of all elements in the set
b. The product of all elements in the set
c. The count of elements in the set
d. The average of all elements in the set
4. If U is the universal set, what is the complement of the empty set (∅)?
a. U
b. ∅
c. Null set
d. The complement of the empty set is undefined
5. Which of the following is true for the Cartesian product A × B?
a. A × B = B × A
b. A × B is the set of all ordered pairs where the first element is from A and the second element is from B
c. A × B is always an empty set
d. A × B is the union of sets A and B
6. The square root of a negative number is a:
a) Real number
b) Complex number
c) Imaginary number
d) Rational number
7. The product of a complex number and its conjugate is always a:
a) Real number
b) Complex number
c) Imaginary number
d) Rational number
8. What is the intersection of sets A = {1, 2, 3} and B = {2, 3, 4}?
a) {1, 2, 3, 4}
b) {2, 3}
c) {1, 4}
d) {}
9. If set C = {a, b, c} and set D = {c, d, e}, what is the union of sets C and D?
a) {a, b, c, d, e}
b) {a, b, c}
c) {c}
d) {d, e}
10. What is the complement of set E = {apple, orange, banana} with respect to the universal set U = {apple, orange, banana, grape}?
a) {apple, orange, banana}
b) {grape}
c) {}
d) {grape}
11. If set F = {2, 4, 6, 8} and set G = {3, 6, 9}, what is the difference F - G?
a) {2, 4, 8}
b) {2, 4, 6, 8, 9}
c) {3, 9}
d) {2, 4}
12. If set P = {1, 2, 3, 4, 5} and set Q = {3, 4, 5, 6, 7}, what is the symmetric difference P Δ Q?
a) {1, 2, 6, 7}
b) {1, 2, 3, 4, 5, 6, 7}
c) {1, 2, 3, 4, 5}
d) {6, 7}
13. Which of the following numbers is irrational?
a) 0.25
b) √9
c) 0.333...
d) π
14. Choose the irrational number from the options:
a) 1/3
b) 0.5
c) √16
d) √7
15. Which of these numbers is rational?
a) √25
b) √13
c) 0.75
d) π
16. Select the rational number:
a) √2
b) 0.333...
c) 5.7
d) e
17. Which of the following numbers is irrational?
a) 0.75
b) √5
c) 2/3
d) -4
18. What type of number is 9.25?
a) Rational
b) Irrational
c) Integer
d) Whole number
19. The square root of a perfect square is always:
a) Rational
b) Irrational
c) Prime
d)Negative
20. Which of the following is an example of a non-repeating, non-terminating decimal?
a) 0.666...
b) 0.25
c) 0.121212...
d) √2
21. What is the value of x in the equation 2x + 5 = 11?
a) 2
b) 3
c) 4
d) 6
22. Solve for y: 3y - 7 = 14
a) 5
b) 7
c) 8
d) 9
23. If 2a + 4 = 10, what is the value of 'a'?
a) 2
b) 3
c) 4
d) 5
24. Which of the following is an algebraic expression?
a) √9
b) 2x + 5
c) Ï€r²
d) |3|
25. Simplify the expression: 3(2x - 4) + 7x.
a) 13x - 12
b) 6x + 12
c) 13x + 12
d) 6x - 12
26. Identify the coefficient in the expression 4y^2 - 2xy + 8.
a) 4
b) -2
c) 2
d) 8
27. Which of the following is NOT an algebraic expression?
a) 5x + 2y
b) √25
c) 3x² - 2x + 1
d) 4z³ + 7z
28. Question: What is the simplified form of 3x + 2y - 5x + 7y?
a) 8x + 9y
b) -2x + 9y
c) -2x + 2y
d) -2x + 7y
29. Evaluate the expression 4a^2 - 2a + 1 when a = 3.
a) 27
b) 34
c) 46
d) 64
30. Simplify the expression 2(x + 3) - 4 and write it in standard form.
a) 2x + 2
b) 2x - 2
c) 2x + 5
d) 2x - 8
31. Which of the following represents the distributive property?
a) a(b + c) = ab + ac
b) a + b = b + a
c) a - b = b - a
d) a/b = b/a
32. If 2x + 5 = 11, what is the value of x?
a) 3
b) 2
c) 6
d) 8
33. What is the value of (3 log2 8)?
a) 6
b) 9
c) 12
d) 24
34. What is the decimal equivalent of the binary number 1101?
a) 8
b) 10
c) 13
d) 14
35. Convert the binary number 101101 to its decimal equivalent.
a) 21
b) 45
c) 53
d) 77
36. Which of the following is a binary representation of the decimal number 25?
a) 11001
b) 10010
c) 11111
d) 10100
37. What is the binary representation of the decimal number 42?
a) 101010
b) 110110
c) 100101
d) 111000
38. Perform the binary addition: 1101 + 101.
a) 10110
b) 10101
c) 10010
d) 1110
39. Solve for x in the equation 2^x = 16.
a) 2
b) 3
c) 4
d) 5
40. If log3 (x+2) = 2, what is the value of x?
a) 1
b) 4
c) 5
d) 7
41. Which of the following is a pentagonal number?
a) 12
b) 16
c) 22
d) 30
42. What is the formula for the nth pentagonal number, P_n?
a) ( P_n = n(3n - 1)/2
b) ( P_n = n(2n - 1)
c) ( P_n = n(5n - 2)/2
d) ( P_n = n(4n - 1)/2
43. Identify the octagonal number in the given options:
a) 18
b) 28
c) 35
d) 42
44. What is the average of the numbers 12, 18, and 24?
a) 18
b) 20
c) 22
d) 24
45. If the average of five numbers is 15, and four of the numbers are 12, 18, 20, and 16, what is the fifth number?
a) 10
b) 15
c) 25
d) 30
46. The average of six numbers is 30. If one number is 40, what is the average of the remaining five numbers?
a) 25
b) 30
c) 35
d) 40
47. What is the measure of central tendency that represents the middle value in a data set?
a. Mean
b. Mode
c. Median
d. Both b and c
48. In a skewed distribution, which measure of central tendency is typically the most reliable?
a. Mean
b. Mode
c. Median
d. All are equally reliable
49. If a data set has an even number of observations, how is the median calculated?
a. Average of the two middle values
b. Sum of all values divided by the number of observations
c. Middle value of the ordered data set**
d. None of the above
50. The mode of a data set is:
a. The most frequently occurring value
b. The average of all values
c. The middle value
d. The value(s) that occur(s) most frequently
51. Which measure of central tendency is influenced by extreme values in a data set?
a. Mean
b. Mode
c. Median
d. All are equally influenced
52. In a symmetric distribution, which measure of central tendency is likely to be the same?
a. Mean
b. Mode
c. Median
d. None of the above
53. A group of students scored the following marks in a test: 25, 30, 35, 40, and 45. What is the mean of their scores?
a) 35
b) 38
c) 40
d) 45
54. In a set of data, if there are two modes, what does it indicate?
a) Data is symmetrical
b) Data is skewed
c) Data has two different averages
d) Data has repeating values
55. The median of a set of 7 distinct numbers is the fourth largest number. What is the median?
a) The smallest number
b) The fourth largest number
c) The fifth largest number
d) The largest number
56. If the mean of five numbers is 20, and four of the numbers are 15, 18, 22, and 25, what is the fifth number?
a) 20
b) 25
c) 30
d) 35
57. The ages of a group of friends are: 25, 27, 30, 32, 25, 28, 30, 29. What is the mode of their ages?
a) 25
b) 28
c) 30
d) 32
58. What is the average (mean) of the following set of numbers: 4, 7, 11, 14?
a) 9
b) 10
c) 11
d) 12
59. In a dataset, if the mode is 15 and the median is 18, what could be the mean?
a) 15
b) 18
c) 21
d) Cannot be determined
60. Sarah recorded the temperatures of the Larkana city for a week: 20, 22, 25, 21, 20, 24, 23. What is the median temperature?
a) 21
b) 22
c) 23
d) 24
6q. A set of test scores has a mean of 75. If one score of 95 is added to the set, what happens to the mean?
a) Increases
b) Decreases
c) Remains the same
d) Cannot be determined
61. The mode of a dataset is: 5, 8, 10, 12, 8, 15, 8, 20. What is the mode?
a) 8
b) 10
c) 15
d) 20
62. If the median of a set of numbers is 16, which of the following statements is true?
a) At least half the numbers are less than 16
b) At least half the numbers are greater than 16
c) All numbers are equal to 16
d) None of the above
63. Solve for x: 2x^2 - 5x + 3 = 0
a) x = 1, x = 3/2
b) x = 1, x = -3/2
c) x = -1, x = -3/2
d) x = -1, x = 3/2
64. A rectangular garden has a length that is 3 meters more than its width. If the area of the garden is 60 square meters, what are the dimensions of the garden?
a) Length = 8m, Width = 5m
b) Length = 10m, Width = 7m
c) Length = 9m, Width = 6m
d) Length = 12m, Width = 9m
65. What is the sum of the interior angles of a triangle?
a) 90 degrees
b) 180 degrees
c) 270 degrees
d) 360 degrees
66. Which of the following is true about a rectangle?
a) All sides are equal
b) Opposite sides are parallel
c) All angles are obtuse
d) Diagonals are of different lengths
67. In a right-angled triangle, what is the relationship between the lengths of the two legs?
a) They are equal
b) The sum of their squares is equal to the square of the hypotenuse
c) The product of their lengths is equal to the square of the hypotenuse
d) One leg is twice the length of the other
68. What is the formula for the area of a circle with radius 'r'?
a) πr
b) 2Ï€r
c) πr^2
d) 2Ï€r^2
69. If a polygon has n sides, what is the sum of its interior angles?
a) (n - 2) × 90 degrees
b) (n - 2) × 180 degrees
c) (n + 2) × 90 degrees
d) (n + 2) × 180 degrees
70. What is the tangent of a 45-degree angle?
a) 0
b) 1
c) √2/2
d) 2
71. In a right-angled triangle, if the length of one leg is 3 and the length of the hypotenuse is 5, what is the length of the other leg?
a) 4
b) 2
c) 3
d) 1
72. If sinθ = 0.8, what is cosθ?
a) 0.2
b) 0.4
c) 0.6
d) 0.8
73. What is the value of tan 60 degrees?
a) √3
b) 1/√3
c) √2
d) 1/√2
74. If cosα = 0.6, what is secα?
a) 1.2
b) 1.5
c) 1.67
d) 1.8
75. What is the formula for the area of a rectangle with length \(L\) and width \(W\)?
a) A = L + W
b) A = L×W
c) A = 1/2 L×W
d) A = 2 (L + W)
76. In a right-angled triangle, if one angle is 30 degrees, what is the value of the other acute angle?
a) 60 degrees
b) 90 degrees
c) 30 degrees
d) 45 degrees
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