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100 Math MCQs with answers and explanations for Army, Navy and PAF initial tests

100 Math MCQs with Answers and Explanations for Army, Navy and PAF Tests

By admin / October 14, 2026

About these Math MCQs

This set of 100 Math MCQs is made for candidates preparing for the Pak Army, Pak Navy and PAF initial tests. Every question has four options, the correct answer and a short working or reason, so you understand how each answer is reached and not just the result.

The mathematics section of an academic test checks school level skills: arithmetic, fractions, algebra, ratio, percentage, profit and loss, speed and time, geometry, number series and basic probability. The questions below cover all of these topics. Work through them in order, or jump straight to any topic from the list.

100MCQs
11Topics
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Topics covered in these 100 Math MCQs

Tip: attempt the question before you open the answer.

Basic Arithmetic MCQs Q1–10

1What is 15 + 25?

  1. 30
  2. 35
  3. 40
  4. 45
View answer

C) 40 because 15 + 25 = 40.

2What is 50 − 18?

  1. 28
  2. 32
  3. 38
  4. 42
View answer

B) 32 because 50 − 18 = 32.

3What is 12 × 8?

  1. 86
  2. 92
  3. 96
  4. 108
View answer

C) 96 because 12 × 8 = 96.

4What is 144 ÷ 12?

  1. 10
  2. 11
  3. 12
  4. 14
View answer

C) 12 because 144 ÷ 12 = 12.

5What is the square of 15?

  1. 125
  2. 200
  3. 225
  4. 250
View answer

C) 225 because 15 × 15 = 225.

6What is the square root of 169?

  1. 11
  2. 12
  3. 13
  4. 14
View answer

C) 13 because 13 × 13 = 169.

7What is the cube of 4?

  1. 16
  2. 32
  3. 64
  4. 128
View answer

C) 64 because 4 × 4 × 4 = 64.

8What is the cube root of 125?

  1. 3
  2. 4
  3. 5
  4. 6
View answer

C) 5 because 5 × 5 × 5 = 125.

9What is 25% of 200?

  1. 25
  2. 40
  3. 50
  4. 75
View answer

C) 50 because 25% × 200 = 50.

10What is 10% of 750?

  1. 50
  2. 65
  3. 75
  4. 85
View answer

C) 75 because 10% of 750 is 750 ÷ 10 = 75.

BODMAS, Fractions and Number Types MCQs Q11–20

11Simplify: 2 + 3 × 4.

  1. 20
  2. 14
  3. 24
  4. 18
View answer

B) 14 because multiplication comes before addition: 2 + 12 = 14.

12Simplify: (8 + 4) ÷ 3.

  1. 3
  2. 4
  3. 5
  4. 6
View answer

B) 4 because (8 + 4) ÷ 3 = 12 ÷ 3 = 4.

13What is ¾ of 100?

  1. 25
  2. 50
  3. 75
  4. 80
View answer

C) 75 because 100 × ¾ = 75.

14Convert 0.75 into a fraction in simplest form.

  1. ½
  2. ⅔
  3. ¾
  4. ⅘
View answer

C) ¾ because 0.75 = 75/100 = 3/4.

15Convert ⅖ into a percentage.

  1. 20%
  2. 25%
  3. 40%
  4. 50%
View answer

C) 40% because ⅖ × 100 = 40%.

16What is the LCM of 4 and 6?

  1. 8
  2. 10
  3. 12
  4. 24
View answer

C) 12 because 12 is the smallest number divisible by both 4 and 6.

17What is the HCF of 18 and 24?

  1. 3
  2. 6
  3. 9
  4. 12
View answer

B) 6 because 6 is the greatest number that divides both 18 and 24.

18Which of the following is a prime number?

  1. 9
  2. 15
  3. 17
  4. 21
View answer

C) 17 because it has exactly two positive factors: 1 and 17.

19Which of the following is an even number?

  1. 17
  2. 23
  3. 31
  4. 42
View answer

D) 42 because it is divisible by 2.

20What is the smallest prime number?

  1. 0
  2. 1
  3. 2
  4. 3
View answer

C) 2 because it is the smallest integer with exactly two positive factors.

Algebra and Equations MCQs Q21–30

21Solve: x + 7 = 15.

  1. 6
  2. 7
  3. 8
  4. 9
View answer

C) 8 because x = 15 − 7 = 8.

22Solve: x − 9 = 11.

  1. 18
  2. 19
  3. 20
  4. 21
View answer

C) 20 because x = 11 + 9 = 20.

23Solve: 3x = 21.

  1. 5
  2. 6
  3. 7
  4. 8
View answer

C) 7 because x = 21 ÷ 3 = 7.

24Solve: 2x + 4 = 14.

  1. 4
  2. 5
  3. 6
  4. 7
View answer

B) 5 because 2x = 10, so x = 5.

25If x = 4, what is the value of 3x + 2?

  1. 10
  2. 12
  3. 14
  4. 16
View answer

C) 14 because 3 × 4 + 2 = 14.

26What is the value of 5² + 3²?

  1. 25
  2. 30
  3. 34
  4. 36
View answer

C) 34 because 25 + 9 = 34.

27Solve: 5x = 45.

  1. 7
  2. 8
  3. 9
  4. 10
View answer

C) 9 because 45 ÷ 5 = 9.

28Solve: 4x − 8 = 12.

  1. 4
  2. 5
  3. 6
  4. 7
View answer

B) 5 because 4x = 20, so x = 5.

29If x = 3 and y = 4, what is x + y?

  1. 5
  2. 6
  3. 7
  4. 12
View answer

C) 7 because 3 + 4 = 7.

30If a = 5, what is the value of a² − 1?

  1. 20
  2. 24
  3. 25
  4. 26
View answer

B) 24 because 5² − 1 = 25 − 1 = 24.

Ratio, Profit, Loss and Average MCQs Q31–40

31What is the ratio of 10 to 20 in simplest form?

  1. 1:2
  2. 2:1
  3. 1:3
  4. 3:2
View answer

A) 1:2 because both parts can be divided by 10.

32Divide 60 in the ratio 2:1. What is the larger share?

  1. 20
  2. 30
  3. 40
  4. 45
View answer

C) 40 because the total has 3 parts, and the larger share is 2/3 × 60 = 40.

33If 5 pens cost Rs. 100, what is the cost of one pen?

  1. Rs. 10
  2. Rs. 15
  3. Rs. 20
  4. Rs. 25
View answer

C) Rs. 20 because 100 ÷ 5 = 20.

34If 3 books cost Rs. 150, what is the cost of 7 books at the same rate?

  1. Rs. 250
  2. Rs. 300
  3. Rs. 350
  4. Rs. 400
View answer

C) Rs. 350 because one book costs Rs. 50, and 7 × 50 = Rs. 350.

35A number increases from 80 to 100. What is the percentage increase?

  1. 20%
  2. 25%
  3. 30%
  4. 40%
View answer

B) 25% because the increase is 20, and (20 ÷ 80) × 100 = 25%.

36A shirt costs Rs. 1,000 and has a 10% discount. What is the sale price?

  1. Rs. 800
  2. Rs. 850
  3. Rs. 900
  4. Rs. 950
View answer

C) Rs. 900 because the discount is Rs. 100, leaving Rs. 900.

37An item costs Rs. 500 and is sold for Rs. 600. What is the profit?

  1. Rs. 50
  2. Rs. 100
  3. Rs. 150
  4. Rs. 200
View answer

B) Rs. 100 because profit = selling price − cost price = 600 − 500.

38An item costs Rs. 800 and is sold for Rs. 720. What is the loss percentage?

  1. 5%
  2. 10%
  3. 15%
  4. 20%
View answer

B) 10% because the loss is Rs. 80, and (80 ÷ 800) × 100 = 10%.

39What is the average of 10, 20, and 30?

  1. 15
  2. 20
  3. 25
  4. 30
View answer

B) 20 because (10 + 20 + 30) ÷ 3 = 20.

40The average of five numbers is 12. What is their total?

  1. 50
  2. 55
  3. 60
  4. 65
View answer

C) 60 because total = average × number of values = 12 × 5.

Speed, Time and Conversions MCQs Q41–50

41A car travels 120 km in 2 hours. What is its average speed?

  1. 40 km/h
  2. 50 km/h
  3. 60 km/h
  4. 80 km/h
View answer

C) 60 km/h because speed = distance ÷ time = 120 ÷ 2.

42How far will a vehicle travel in 3 hours at 50 km/h?

  1. 100 km
  2. 120 km
  3. 150 km
  4. 180 km
View answer

C) 150 km because distance = speed × time = 50 × 3.

43How long will it take to travel 180 km at 60 km/h?

  1. 2 hours
  2. 3 hours
  3. 4 hours
  4. 5 hours
View answer

B) 3 hours because time = distance ÷ speed = 180 ÷ 60.

44A person walks 5 km in 1 hour. What is the speed?

  1. 3 km/h
  2. 4 km/h
  3. 5 km/h
  4. 6 km/h
View answer

C) 5 km/h because speed = 5 ÷ 1 = 5 km/h.

45A train travels 240 km in 4 hours. What is its average speed?

  1. 40 km/h
  2. 50 km/h
  3. 60 km/h
  4. 80 km/h
View answer

C) 60 km/h because 240 ÷ 4 = 60 km/h.

46How many minutes are there in 3 hours?

  1. 120
  2. 150
  3. 180
  4. 240
View answer

C) 180 because 3 × 60 = 180 minutes.

47How many seconds are there in 5 minutes?

  1. 100
  2. 200
  3. 300
  4. 500
View answer

C) 300 because 5 × 60 = 300 seconds.

48How many metres are there in 2 kilometres?

  1. 200
  2. 500
  3. 1,000
  4. 2,000
View answer

D) 2,000 because 1 kilometre equals 1,000 metres.

49Convert 72 km/h into metres per second.

  1. 10 m/s
  2. 15 m/s
  3. 20 m/s
  4. 25 m/s
View answer

C) 20 m/s because 72 × 5/18 = 20 m/s.

50A person travels 60 km at 30 km/h and another 60 km at 60 km/h. What is the total travel time?

  1. 2 hours
  2. 3 hours
  3. 4 hours
  4. 5 hours
View answer

B) 3 hours because the first part takes 2 hours and the second takes 1 hour.

Perimeter, Area and Angles MCQs Q51–59

51What is the perimeter of a square with side 5 cm?

  1. 10 cm
  2. 15 cm
  3. 20 cm
  4. 25 cm
View answer

C) 20 cm because perimeter = 4 × side = 4 × 5.

52What is the area of a square with side 6 cm?

  1. 12 cm²
  2. 24 cm²
  3. 30 cm²
  4. 36 cm²
View answer

D) 36 cm² because area = side² = 6 × 6.

53What is the perimeter of a rectangle with length 8 cm and width 4 cm?

  1. 12 cm
  2. 24 cm
  3. 32 cm
  4. 36 cm
View answer

B) 24 cm because perimeter = 2 × (8 + 4) = 24 cm.

54What is the area of a rectangle with length 10 cm and width 5 cm?

  1. 15 cm²
  2. 30 cm²
  3. 50 cm²
  4. 100 cm²
View answer

C) 50 cm² because area = length × width = 10 × 5.

55What is the area of a triangle with base 10 cm and height 6 cm?

  1. 20 cm²
  2. 30 cm²
  3. 40 cm²
  4. 60 cm²
View answer

B) 30 cm² because area = ½ × base × height = ½ × 10 × 6.

56What is the sum of the interior angles of a triangle?

  1. 90°
  2. 180°
  3. 270°
  4. 360°
View answer

B) 180° because the interior angles of every triangle add up to 180° in Euclidean geometry.

57What is a right angle?

  1. 45°
  2. 60°
  3. 90°
  4. 180°
View answer

C) 90° because a right angle measures exactly 90 degrees.

58How many degrees are there in a straight angle?

  1. 90°
  2. 120°
  3. 180°
  4. 360°
View answer

C) 180° because a straight angle forms a straight line.

59How many degrees are there in a complete circle?

  1. 90°
  2. 180°
  3. 270°
  4. 360°
View answer

D) 360° because one complete revolution equals 360 degrees.

Circles and Volume MCQs Q60–65

60What is the circumference of a circle with radius 7 cm? Use π = 22/7.

  1. 22 cm
  2. 44 cm
  3. 49 cm
  4. 154 cm
View answer

B) 44 cm because circumference = 2πr = 2 × 22/7 × 7.

61What is the area of a circle with radius 7 cm? Use π = 22/7.

  1. 44 cm²
  2. 77 cm²
  3. 154 cm²
  4. 308 cm²
View answer

C) 154 cm² because area = πr² = 22/7 × 7 × 7.

62What is the diameter of a circle with radius 9 cm?

  1. 9 cm
  2. 18 cm
  3. 27 cm
  4. 36 cm
View answer

B) 18 cm because diameter = 2 × radius = 18 cm.

63What is the volume of a cube with side 3 cm?

  1. 9 cm³
  2. 18 cm³
  3. 27 cm³
  4. 36 cm³
View answer

C) 27 cm³ because volume = side³ = 3 × 3 × 3.

64What is the volume of a cuboid measuring 4 cm × 3 cm × 2 cm?

  1. 12 cm³
  2. 18 cm³
  3. 24 cm³
  4. 30 cm³
View answer

C) 24 cm³ because volume = length × width × height = 4 × 3 × 2.

65What is the value of π approximately?

  1. 2.14
  2. 3.14
  3. 4.13
  4. 3.41
View answer

B) 3.14 because π is approximately 3.14159.

Fractions and Decimals MCQs Q66–72

66What is ⅓ + ⅓?

  1. ⅓
  2. ⅔
  3. 1
  4. ⅙
View answer

B) ⅔ because the denominators are equal, so the numerators add to 2.

67What is ½ + ¼?

  1. ¼
  2. ½
  3. ¾
  4. 1
View answer

C) ¾ because ½ = 2/4, and 2/4 + 1/4 = 3/4.

68What is ⅘ − ⅖?

  1. ⅕
  2. ⅖
  3. ⅗
  4. ⅘
View answer

B) ⅖ because 4/5 − 2/5 = 2/5.

69What is ⅔ × ¾?

  1. ½
  2. ⅔
  3. ¾
  4. ⅚
View answer

A) ½ because (2 × 3)/(3 × 4) = 6/12 = 1/2.

70What is ½ ÷ ¼?

  1. ½
  2. 1
  3. 2
  4. 4
View answer

C) 2 because dividing 1/2 by 1/4 is equivalent to 1/2 × 4 = 2.

71What is 0.2 expressed as a fraction in simplest form?

  1. ⅕
  2. ⅖
  3. ⅗
  4. ⅘
View answer

A) ⅕ because 0.2 = 2/10 = 1/5.

72What is 0.125 expressed as a fraction in simplest form?

  1. ⅛
  2. ¼
  3. ⅓
  4. ⅕
View answer

A) ⅛ because 0.125 = 125/1000 = 1/8.

Percentage and Simple Interest MCQs Q73–80

73What is 35% of 400?

  1. 120
  2. 130
  3. 140
  4. 150
View answer

C) 140 because 0.35 × 400 = 140.

7460 is what percentage of 240?

  1. 20%
  2. 25%
  3. 30%
  4. 40%
View answer

B) 25% because (60 ÷ 240) × 100 = 25%.

75Increase 200 by 15%.

  1. 215
  2. 220
  3. 230
  4. 250
View answer

C) 230 because 15% of 200 is 30, and 200 + 30 = 230.

76What is the simple interest on Rs. 1,000 at 5% per year for 2 years?

  1. Rs. 50
  2. Rs. 100
  3. Rs. 150
  4. Rs. 200
View answer

B) Rs. 100 because simple interest = PRT/100 = 1000 × 5 × 2/100.

77What is the simple interest formula?

  1. SI = PRT/100
  2. SI = P + R + T
  3. SI = PT/R
  4. SI = PRT
View answer

A) SI = PRT/100 because simple interest is calculated from principal, annual rate, and time.

78A sum of Rs. 500 is increased by 20%. What is the new amount?

  1. Rs. 550
  2. Rs. 580
  3. Rs. 600
  4. Rs. 650
View answer

C) Rs. 600 because 20% of 500 is 100, and 500 + 100 = 600.

79If the cost price is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

  1. 20%
  2. 25%
  3. 30%
  4. 40%
View answer

B) 25% because profit is Rs. 100, and (100 ÷ 400) × 100 = 25%.

80If an item is bought for Rs. 1,000 and sold for Rs. 850, what is the loss?

  1. Rs. 100
  2. Rs. 150
  3. Rs. 200
  4. Rs. 250
View answer

B) Rs. 150 because loss = cost price − selling price = 1,000 − 850.

Number Series MCQs Q81–90

81What is the next number in the series 2, 4, 6, 8, _____?

  1. 9
  2. 10
  3. 11
  4. 12
View answer

B) 10 because each term increases by 2.

82What is the next number in the series 5, 10, 15, 20, _____?

  1. 22
  2. 24
  3. 25
  4. 30
View answer

C) 25 because each term increases by 5.

83What is the next number in the series 3, 6, 12, 24, _____?

  1. 36
  2. 42
  3. 48
  4. 54
View answer

C) 48 because each term is multiplied by 2.

84What is the next number in the series 1, 4, 9, 16, _____?

  1. 20
  2. 24
  3. 25
  4. 36
View answer

C) 25 because the numbers are squares: 1², 2², 3², 4², and 5².

85What is the next number in the series 2, 5, 8, 11, _____?

  1. 12
  2. 13
  3. 14
  4. 15
View answer

C) 14 because each term increases by 3.

86What is the next number in the series 100, 90, 80, 70, _____?

  1. 50
  2. 55
  3. 60
  4. 65
View answer

C) 60 because each term decreases by 10.

87What is the next number in the series 1, 2, 4, 8, 16, _____?

  1. 20
  2. 24
  3. 30
  4. 32
View answer

D) 32 because each term is multiplied by 2.

88What is the next number in the series 7, 14, 21, 28, _____?

  1. 32
  2. 35
  3. 36
  4. 42
View answer

B) 35 because each term increases by 7.

89What is the next number in the series 50, 45, 40, 35, _____?

  1. 25
  2. 28
  3. 30
  4. 32
View answer

C) 30 because each term decreases by 5.

90What is the next number in the series 1, 3, 6, 10, 15, _____?

  1. 18
  2. 20
  3. 21
  4. 25
View answer

C) 21 because the increments are 2, 3, 4, 5, and then 6.

Probability, Polygons and Powers MCQs Q91–100

91What is the probability of getting a head when tossing a fair coin once?

  1. 0
  2. ¼
  3. ½
  4. 1
View answer

C) ½ because there are two equally likely outcomes, and one is a head.

92What is the probability of rolling a 6 on a fair six-sided die?

  1. ⅙
  2. ⅓
  3. ½
  4. ⅔
View answer

A) ⅙ because one of the six equally likely outcomes is 6.

93How many sides does a hexagon have?

  1. 5
  2. 6
  3. 7
  4. 8
View answer

B) 6 because a hexagon is a six-sided polygon.

94How many sides does an octagon have?

  1. 6
  2. 7
  3. 8
  4. 9
View answer

C) 8 because an octagon has eight sides.

95What is the sum of the interior angles of a quadrilateral?

  1. 180°
  2. 270°
  3. 360°
  4. 540°
View answer

C) 360° because a quadrilateral can be divided into two triangles, each with angle sum 180°.

96If two angles of a triangle are 50° and 60°, what is the third angle?

  1. 60°
  2. 70°
  3. 80°
  4. 90°
View answer

B) 70° because 180° − 50° − 60° = 70°.

97What is the complement of 35°?

  1. 45°
  2. 55°
  3. 65°
  4. 145°
View answer

B) 55° because complementary angles add up to 90°.

98What is the supplement of 120°?

  1. 30°
  2. 50°
  3. 60°
  4. 90°
View answer

C) 60° because supplementary angles add up to 180°.

99What is the value of 2⁵?

  1. 16
  2. 25
  3. 32
  4. 64
View answer

C) 32 because 2 × 2 × 2 × 2 × 2 = 32.

100What is the value of 10³?

  1. 100
  2. 500
  3. 1,000
  4. 10,000
View answer

C) 1,000 because 10 × 10 × 10 = 1,000.

How to solve each type of Math question

Arithmetic and BODMAS

Learn squares up to 20 and cubes up to 10, as they appear again and again. For mixed operations, follow BODMAS: brackets first, then orders, division and multiplication, then addition and subtraction. For example, in 2 + 3 × 4 you multiply before you add.

Algebra

Treat an equation like a balance. Whatever you do to one side, do to the other. Move the number away from x step by step, and then put your answer back into the equation to check it.

Ratio, percentage, profit and loss

Profit or loss is always worked out on the cost price: profit % = (profit ÷ cost price) × 100. For a ratio, add the parts first, then find the share of each part. For a percentage increase, divide the change by the original value.

Speed, distance and time

Keep three formulas ready: speed = distance ÷ time, distance = speed × time and time = distance ÷ speed. To change km/h into m/s, multiply by 5/18. When a journey has two parts, find each time separately and add them.

Geometry and number series

Write the formula before putting in numbers: area of a rectangle is length × width, a triangle is ½ × base × height and a circle is πr². For a number series, check the difference between terms first, then the ratio, then squares.

A simple practice plan

  1. Attempt 20 to 25 MCQs a day, starting with your weakest topic.
  2. Solve each question on paper first, and only then open the answer.
  3. Keep one small notebook for formulas, squares, cubes and conversions, and revise it daily.
  4. Combine this set with 100 Physics MCQs, 100 Chemistry MCQs, 100 English MCQs and 200 Verbal Intelligence MCQs, and finish the week with a timed Mathematics Test.

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Frequently asked questions

What are Math MCQs for Army, Navy and PAF initial tests?

They are multiple-choice questions on school-level mathematics, such as arithmetic, fractions, algebra, ratio, percentage, speed and time, geometry and number series. The academic section of an initial test checks how fast and accurately you solve these basics.

Are these Math MCQs useful for Pak Army, Pak Navy and PAF preparation?

Yes. Academic papers for the armed forces commonly include mathematics along with English, physics, chemistry and other subjects, so regular practice builds speed and accuracy. This is a practice set and not an official paper.

How many Math MCQs should I solve each day?

Solving 20 to 25 questions a day with careful review works better than rushing through all 100 in one sitting. At that pace, the full set takes about four to five days.

Does every question have an answer and explanation?

Yes. Tap View answer under any question to see the correct option and the working. The Show all answers button opens every answer at once.

How can I improve my Math for the initial test?

Memorise squares, cubes and basic formulas first, revise one topic at a time, and always write the working on paper. Note your mistakes before each session and take a timed test to build speed.

Official recruitment sources

For dates, eligibility and test details, always check the official portals: Join Pak Army, Pakistan Navy and Join PAF. This page is not affiliated with any of them.

Related practice

Open Mathematics MCQs for more untimed practice, try the Mathematics Test, or read 100 Chemistry MCQs. You can also browse the Academic Test page and find preparation pages for the Pak Army, Pak Navy and Pak Air Force.

Ready for a timed attempt?

Test your speed with 25 timed mathematics questions and get instant results.

Take Mathematics TestMore Math MCQs

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