Mathematics MCQs for Competitive Exams 2025 - Series 2: 50 Questions

Mathematics MCQs for Competitive Exams 2025|IAS ,PCS ,SSC, IPS BANK , RAILWAY AIRFORCE, AND, PCS Police Exam , CHSL

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Mathematics MCQs for Competitive Exams 2025 – Series 1: 50 Questions with Answers

Mathematics MCQs for Competitive Exams 2025 – Series 1: 50 Questions with Answers

Welcome to Series 1 of our Mathematics MCQs for Competitive Exams on The Art News. This post features 50 copyright-free, modern MCQs designed for exams like SSC CGL 2025, IBPS PO 2024, RRB NTPC 2025, UPSC, and more. Practice these quantitative aptitude questions to excel in your exam preparation. Each question includes detailed solutions for better understanding.

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These MCQs cover key topics like arithmetic, algebra, geometry, trigonometry, and data interpretation, aligned with the latest patterns of SSC CHSL 2024, IBPS Clerk 2025, CAT 2024, and other competitive exams. Test your skills and prepare effectively with this free resource.

Question 1

What is the value of (3/4) ÷ (2/5)?

  • A) 15/8
  • B) 6/20
  • C) 3/10
  • D) 8/15
Show Answer

Answer: A) 15/8

Explanation: To divide fractions, multiply by the reciprocal: (3/4) ÷ (2/5) = (3/4) × (5/2) = 15/8.

Question 2

If the ratio of two numbers is 5:3 and their sum is 40, what is the smaller number?

  • A) 15
  • B) 18
  • C) 20
  • D) 25
Show Answer

Answer: A) 15

Explanation: Let the numbers be 5x and 3x. Their sum is 5x + 3x = 8x = 40. Solving, x = 5. The smaller number is 3x = 3 × 5 = 15.

Question 3

A train travels 120 km in 2 hours. What is its speed in km/h?

  • A) 50
  • B) 60
  • C) 70
  • D) 80
Show Answer

Answer: B) 60

Explanation: Speed = Distance ÷ Time = 120 km ÷ 2 h = 60 km/h.

Question 4

A shop offers a 25% discount on a $200 item. What is the selling price?

  • A) $150
  • B) $160
  • C) $175
  • D) $180
Show Answer

Answer: A) $150

Explanation: Discount = 25% of $200 = $50. Selling price = $200 – $50 = $150.

Question 5

Solve: 2x + 7 = 15.

  • A) 3
  • B) 4
  • C) 5
  • D) 6
Show Answer

Answer: B) 4

Explanation: 2x + 7 = 15 → 2x = 8 → x = 4.

Question 6

The area of a square with side 8 cm is:

  • A) 48 cm²
  • B) 64 cm²
  • C) 72 cm²
  • D) 80 cm²
Show Answer

Answer: B) 64 cm²

Explanation: Area of a square = side² = 8 × 8 = 64 cm².

Question 7

If sin θ = 1/2 and θ is in the first quadrant, what is θ?

  • A) 30°
  • B) 45°
  • C) 60°
  • D) 90°
Show Answer

Answer: A) 30°

Explanation: sin θ = 1/2 corresponds to θ = 30° in the first quadrant.

Question 8

The average of 5 numbers is 20. If one number is 25, what is the average of the other four?

  • A) 18
  • B) 19
  • C) 20
  • D) 21
Show Answer

Answer: B) 19

Explanation: Total sum = 5 × 20 = 100. Sum of other four = 100 – 25 = 75. Average = 75 ÷ 4 = 18.75 ≈ 19.

Question 9

A man invests $5000 at 4% simple interest per annum. What is the interest after 2 years?

  • A) $300
  • B) $400
  • C) $500
  • D) $600
Show Answer

Answer: B) $400

Explanation: Simple Interest = (P × R × T) ÷ 100 = (5000 × 4 × 2) ÷ 100 = $400.

Question 10

The roots of x² – 7x + 12 = 0 are:

  • A) 3, 4
  • B) 2, 5
  • C) 1, 6
  • D) 4, 5
Show Answer

Answer: A) 3, 4

Explanation: Factorize: x² – 7x + 12 = (x – 3)(x – 4) = 0. Roots are x = 3, 4.

Question 11

What is the perimeter of a rectangle with length 10 cm and width 6 cm?

  • A) 28 cm
  • B) 32 cm
  • C) 36 cm
  • D) 40 cm
Show Answer

Answer: B) 32 cm

Explanation: Perimeter = 2(length + width) = 2(10 + 6) = 32 cm.

Question 12

If tan θ = 1, what is θ?

  • A) 30°
  • B) 45°
  • C) 60°
  • D) 90°
Show Answer

Answer: B) 45°

Explanation: tan θ = 1 corresponds to θ = 45° in the first quadrant.

Question 13

A man completes a task in 12 days. How many days will it take for 3 men to complete the same task?

  • A) 3
  • B) 4
  • C) 6
  • D) 8
Show Answer

Answer: B) 4

Explanation: Work rate = 1/12 task per day. For 3 men, rate = 3 × (1/12) = 1/4. Time = 1 ÷ (1/4) = 4 days.

Question 14

The LCM of 12 and 18 is:

  • A) 24
  • B) 36
  • C) 48
  • D) 72
Show Answer

Answer: B) 36

Explanation: Prime factors: 12 = 2² × 3, 18 = 2 × 3². LCM = 2² × 3² = 36.

Question 15

A car travels 240 km in 4 hours. What is its speed in m/s?

  • A) 16.67 m/s
  • B) 20 m/s
  • C) 22.22 m/s
  • D) 25 m/s
Show Answer

Answer: A) 16.67 m/s

Explanation: Speed = 240 km ÷ 4 h = 60 km/h. Convert to m/s: 60 × (1000/3600) = 60 × (5/18) ≈ 16.67 m/s.

Question 16

If 20% of a number is 50, what is the number?

  • A) 200
  • B) 225
  • C) 250
  • D) 275
Show Answer

Answer: C) 250

Explanation: 0.2x = 50 → x = 50 ÷ 0.2 = 250.

Question 17

circumference of a circle with radius 7 cm?

  • A) 44 cm
  • B) 48 cm
  • C) 50 cm
  • D) 56 cm
Show Answer

Answer: A) 44 cm

Explanation: Circumference = 2πr = 2 × (22/7) × 7 = 44 cm.

Question 18

If a = 2 and b = 3, what is the value of a² + b²?

  • A) 13
  • B) 14
  • C) 15
  • D) 16
Show Answer

Answer: A) 13

Explanation: a² + b² = 2² + 3² = 4 + 9 = 13.

Question 19

A pipe fills a tank in 6 hours. How long will it take for 2 pipes to fill the tank?

  • A) 2 hours
  • B) 3 hours
  • C) 4 hours
  • D) 5 hours
Show Answer

Answer: B) 3 hours

Explanation: One pipe’s rate = 1/6 tank per hour. Two pipes’ rate = 2 × (1/6) = 1/3. Time = 1 ÷ (1/3) = 3 hours.

Question 20

The HCF of 24 and 36 is:

  • A) 6
  • B) 8
  • C) 12
  • D) 18
Show Answer

Answer: C) 12

Explanation: Prime factors: 24 = 2³ × 3, 36 = 2² × 3². HCF = 2² × 3 = 12.

Question 21

If a book costs $120 after a 20% discount, what was its original price?

  • A) $140
  • B) $150
  • C) $160
  • D) $180
Show Answer

Answer: B) $150

Explanation: Let original price = x. Then, 0.8x = 120 → x = 120 ÷ 0.8 = $150.

Question 22

The sum of three consecutive odd numbers is 57. What is the largest number?

  • A) 17
  • B) 19
  • C) 21
  • D) 23
Show Answer

Answer: C) 21

Explanation: Let numbers be n, n+2, n+4. Then, n + (n+2) + (n+4) = 3n + 6 = 57 → 3n = 51 → n = 17. Largest = 17 + 4 = 21.

Question 23

If cos θ = 1/√2, what is θ in the first quadrant?

  • A) 30°
  • B) 45°
  • C) 60°
  • D) 90°
Show Answer

Answer: B) 45°

Explanation: cos θ = 1/√2 corresponds to θ = 45° in the first quadrant.

Question 24

A boat travels 60 km downstream in 3 hours. What is the speed of the boat in still water if the stream speed is 5 km/h?

  • A) 15 km/h
  • B) 20 km/h
  • C) 25 km/h
  • D) 30 km/h
Show Answer

Answer: A) 15 km/h

Explanation: Downstream speed = 60 ÷ 3 = 20 km/h. Boat speed = Downstream speed – Stream speed = 20 – 5 = 15 km/h.

Question 25

The area of a triangle with base 10 cm and height 8 cm is:

  • A) 40 cm²
  • B) 48 cm²
  • C) 56 cm²
  • D) 64 cm²
Show Answer

Answer: A) 40 cm²

Explanation: Area = (1/2) × base × height = (1/2) × 10 × 8 = 40 cm².

Question 26

If 3x – 5 = 10, what is x?

  • A) 3
  • B) 4
  • C) 5
  • D) 6
Show Answer

Answer: C) 5

Explanation: 3x – 5 = 10 → 3x = 15 → x = 5.

Question 27

The profit percentage on selling an item for $240 if its cost price is $200 is:

  • A) 10%
  • B) 15%
  • C) 20%
  • D) 25%
Show Answer

Answer: C) 20%

Explanation: Profit = 240 – 200 = 40. Profit % = (40 ÷ 200) × 100 = 20%.

Question 28

The sum of angles in a triangle is:

  • A) 180°
  • B) 360°
  • C) 90°
  • D) 270°
Show Answer

Answer: A) 180°

Explanation: The sum of angles in any triangle is always 180°.

Question 29

A man walks 5 km/h. How far will he walk in 3 hours?

  • A) 12 km
  • B) 15 km
  • C) 18 km
  • D) 20 km
Show Answer

Answer: B) 15 km

Explanation: Distance = Speed × Time = 5 × 3 = 15 km.

Question 30

If a² + b² = 25 and ab = 12, what is a + b?

  • A) 5
  • B) 6
  • C) 7
  • D) 8
Show Answer

Answer: C) 7

Explanation: (a + b)² = a² + b² + 2ab = 25 + 2 × 12 = 49 → a + b = √49 = 7.

Question 31

A pie chart shows a sector of 90°. What percentage does this represent?

  • A) 20%
  • B) 25%
  • C) 30%
  • D) 35%
Show Answer

Answer: B) 25%

Explanation: Total angle = 360°. Percentage = (90 ÷ 360) × 100 = 25%.

Question 32

The volume of a cube with edge 4 cm is:

  • A) 32 cm³
  • B) 48 cm³
  • C) 64 cm³
  • D) 80 cm³
Show Answer

Answer: C) 64 cm³

Explanation: Volume = edge³ = 4 × 4 × 4 = 64 cm³.

Question 33

If 5 workers complete a task in 10 days, how long will 10 workers take?

  • A) 4 days
  • B) 5 days
  • C) 6 days
  • D) 8 days
Show Answer

Answer: B) 5 days

Explanation: Total work = 5 × 10 = 50 worker-days. Time for 10 workers = 50 ÷ 10 = 5 days.

Question 34

The value of 2³ × 3² is:

  • A) 48
  • B) 54
  • C) 72
  • D) 81
Show Answer

Answer: C) 72

Explanation: 2³ = 8, 3² = 9. So, 8 × 9 = 72.

Question 35

A number increased by 25% gives 125. What is the original number?

  • A) 90
  • B) 100
  • C) 110
  • D) 120
Show Answer

Answer: B) 100

Explanation: Let number = x. Then, 1.25x = 125 → x = 125 ÷ 1.25 = 100.

Question 36

The angles of a triangle are in the ratio 1:2:3. What is the smallest angle?

  • A) 20°
  • B) 30°
  • C) 40°
  • D) 50°
Show Answer

Answer: B) 30°

Explanation: Let angles be x, 2x, 3x. Then, x + 2x + 3x = 180 → 6x = 180 → x = 30°. Smallest angle = 30°.

Question 37

If a = 4 and b = 5, what is the value of (a + b)²?

  • A) 81
  • B) 64
  • C) 49
  • D) 36
Show Answer

Answer: A) 81

Explanation: (a + b)² = (4 + 5)² = 9² = 81.

Question 38

A boat’s speed in still water is 10 km/h, and the stream speed is 2 km/h. What is its upstream speed?

  • A) 6 km/h
  • B) 8 km/h
  • C) 10 km/h
  • D) 12 km/h
Show Answer

Answer: B) 8 km/h

Explanation: Upstream speed = Boat speed – Stream speed = 10 – 2 = 8 km/h.

Question 39

The mean of 10, 20, 30, 40, 50 is:

  • A) 25
  • B) 30
  • C) 35
  • D) 40
Show Answer

Answer: B) 30

Explanation: Mean = (10 + 20 + 30 + 40 + 50) ÷ 5 = 150 ÷ 5 = 30.

Question 40

If 4x² – 16 = 0, what is x?

  • A) ±2
  • B) ±3
  • C) ±4
  • D) ±5
Show Answer

Answer: A) ±2

Explanation: 4x² = 16 → x² = 4 → x = ±2.

Question 41

The compound interest on $1000 at 5% per annum for 2 years is:

  • A) $100
  • B) $102.50
  • C) $105
  • D) $110.25
Show Answer

Answer: B) $102.50

Explanation: Amount = 1000 × (1 + 0.05)² = 1000 × 1.1025 = $1102.50. CI = 1102.50 – 1000 = $102.50.

Question 42

The diagonal of a square with side 6 cm is:

  • A) 6√2 cm
  • B) 8 cm
  • C) 8√2 cm
  • D) 9 cm
Show Answer

Answer: A) 6√2 cm

Explanation: Diagonal = side × √2 = 6 × √2 = 6√2 cm.

Question 43

If a number is divided by 7, the remainder is 3. What is the remainder when the number is divided by 14?

  • A) 1
  • B) 3
  • C) 5
  • D) 7
Show Answer

Answer: B) 3

Explanation: Let number = 7k + 3. When divided by 14, remainder = 7k + 3 – 14m. Since 7k is divisible by 7, remainder = 3.

Question 44

The sum of the first 10 natural numbers is:

  • A) 45
  • B) 50
  • C) 55
  • D) 60
Show Answer

Answer: C) 55

Explanation: Sum = n(n+1)/2 = 10 × 11 ÷ 2 = 55.

Question 45

A shopkeeper sells an item at a 10% loss but uses a 10% heavier weight. What is the net profit/loss percentage?

  • A) 0%
  • B) 1% profit
  • C) 1% loss
  • D) 2% profit
Show Answer

Answer: A) 0%

Explanation: Let CP = $100/kg. Actual weight = 1.1 kg, SP = 0.9 × 100 = $90 for 1 kg, but for 1.1 kg, SP = $90. Net = (90 – 100) ÷ 100 = 0%.

  • A) 30°
  • B) 45°
  • C) 60°
  • D) 90°
    • Show Answer

    Answer: A) 30°

    Explanation: sin θ = √3/2 corresponds to θ = 60° in the first quadrant.

    Question 47

    A man buys an item for $400 and sells it for $500. What is the profit percentage?

    • A) 20%
    • B) 25%
    • C) 30%
    • D) 35%

    Question 48

    The surface area of a sphere with radius 3 cm is:

    • A) 36π cm²
    • B) 48π cm²
    • C) 64π cm²
    • D) 81π cm²
    Show Answer

    Answer: A) 36π cm²

    Explanation: Surface area = 4πr² = 4 × π × 3² = 36π cm².

    Question 49

    If a number is increased by 20% and then decreased by 20%, what is the net percentage change?

    • A) 0%
    • B) 4% decrease
    • C) 4% increase
    • D) 2% decrease
    Show Answer

    Answer: B) 4% decrease

    Explanation: Let number = 100. After 20% increase, number = 120. After 20% decrease, number = 120 × 0.8 = 96. Net change = (96 – 100) ÷ 100 = -4%.

    Question 50

    In a triangle, the angles are in the ratio 2:3:4. What is the measure of the largest angle?

    • A) 60°
    • B) 80°
    • C) 100°
    • D) 120°
    Show Answer

    Answer: B) 80°

    Explanation: Let angles be 2x, 3x, 4x. Then, 2x + 3x + 4x = 180 → 9x = 180 → x = 20. Largest angle = 4x = 4 × 20 = 80°.

    Prepare for Your Competitive Exams

    These Mathematics MCQs for Competitive Exams 2025 are crafted to help you excel in exams like SSC CGL 2025, IBPS PO 2024, RRB NTPC 2025, CAT 2024, and more. Stay tuned for Series 2, coming soon! Practice regularly to master quantitative aptitude.

    Next: Series 2

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