Polytechnic Mathematics Question Paper 2026
Practice Set – 1
Diploma / Polytechnic Entrance Mathematics
Questions: 50
Marks: 200
Time: 150 Minutes
Type: MCQ
Exam Instructions
- Each question has four options.
- Select the most appropriate answer.
- Each question carries 4 marks in this practice pattern.
- Practice the questions without looking at the answers first.
- This is a practice paper and is not an official 2026 question paper.
Part A – Number System & Algebra
Q1. What is the HCF of 24 and 36?
Correct Answer: C) 12
Solution: Factors common to 24 and 36 include 1, 2, 3, 4, 6 and 12. Therefore, HCF = 12.
Q2. What is the LCM of 12 and 18?
Correct Answer: C) 36
Solution: Multiples of 12 are 12, 24, 36… and 18 are 18, 36… Therefore, LCM = 36.
Q3. If x + 7 = 15, then x is equal to:
Correct Answer: C) 8
Solution: x = 15 − 7 = 8.
Q4. What is the value of 5² + 3²?
Correct Answer: B) 34
Solution: 5² = 25 and 3² = 9. Therefore, 25 + 9 = 34.
Q5. If 3x = 27, what is x?
Correct Answer: D) 9
Solution: Divide both sides by 3. x = 27 ÷ 3 = 9.
Q6. The value of 2³ × 2² is:
Correct Answer: C) 32
Solution: For the same base, powers are added: 2³ × 2² = 2⁵ = 32.
Q7. The roots of x² − 5x + 6 = 0 are:
Correct Answer: B) 2 and 3
Solution: x² − 5x + 6 = (x − 2)(x − 3). Hence x = 2 or 3.
Q8. What is the value of 10% of 250?
Correct Answer: C) 25
Solution: 10% of 250 = 250 × 10 / 100 = 25.
Q9. If a = 4 and b = 3, then a² + b² is:
Correct Answer: C) 25
Solution: a² + b² = 4² + 3² = 16 + 9 = 25.
Q10. The value of √81 is:
Correct Answer: C) 9
Solution: 9 × 9 = 81, therefore √81 = 9.
Part B – Geometry & Mensuration
Q11. The sum of angles of a triangle is:
Correct Answer: B) 180°
Solution: The interior angles of every triangle add up to 180°.
Q12. The area of a rectangle of length 12 cm and breadth 5 cm is:
Correct Answer: C) 60 cm²
Solution: Area = length × breadth = 12 × 5 = 60 cm².
Q13. The perimeter of a square having side 8 cm is:
Correct Answer: C) 32 cm
Solution: Perimeter of square = 4 × side = 4 × 8 = 32 cm.
Q14. The area of a circle with radius 7 cm is approximately:
Correct Answer: B) 154 cm²
Solution: Area = πr² = 22/7 × 7 × 7 = 154 cm².
Q15. A right angle is equal to:
Correct Answer: C) 90°
Solution: A right angle always measures 90°.
Q16. The volume of a cube with side 4 cm is:
Correct Answer: C) 64 cm³
Solution: Volume = side³ = 4³ = 64 cm³.
Q17. The diagonal of a square is related to its side by:
Correct Answer: C) d = a√2
Solution: By Pythagoras theorem, diagonal² = a² + a² = 2a². Therefore d = a√2.
Q18. The circumference of a circle is given by:
Correct Answer: B) 2πr
Solution: Circumference of a circle = 2πr.
Q19. If the radius of a circle is doubled, its area becomes:
Correct Answer: C) 4 times
Solution: Area depends on the square of radius. Doubling the radius makes the area 4 times.
Q20. The hypotenuse of a right triangle with other sides 6 cm and 8 cm is:
Correct Answer: B) 10 cm
Solution: By Pythagoras theorem, hypotenuse² = 6² + 8² = 36 + 64 = 100. Therefore hypotenuse = 10 cm.
Part C – Trigonometry
Q21. The value of sin 30° is:
Correct Answer: B) 1/2
Solution: The standard trigonometric value of sin 30° is 1/2.
Q22. The value of cos 60° is:
Correct Answer: B) 1/2
Solution: cos 60° = 1/2.
Q23. The value of tan 45° is:
Correct Answer: B) 1
Solution: tan 45° = 1.
Q24. What is sin 90°?
Correct Answer: C) 1
Solution: sin 90° = 1.
Q25. What is cos 0°?
Correct Answer: B) 1
Solution: cos 0° = 1.
Q26. Which identity is correct?
Correct Answer: A) sin²θ + cos²θ = 1
Solution: This is the fundamental Pythagorean trigonometric identity.
Q27. If tan θ = 1, then θ can be:
Correct Answer: B) 45°
Solution: tan 45° = 1.
Q28. The reciprocal of sin θ is:
Correct Answer: D) cosec θ
Solution: cosec θ = 1/sin θ.
Q29. The reciprocal of cos θ is:
Correct Answer: A) sec θ
Solution: sec θ = 1/cos θ.
Q30. If sin θ = 0, one possible value of θ is:
Correct Answer: A) 0°
Solution: sin 0° = 0.
Part D – Coordinate Geometry
Q31. The coordinates of the origin are:
Correct Answer: D) (0, 0)
Solution: The origin is the point where the x-axis and y-axis intersect, so its coordinates are (0, 0).
Q32. The distance between (0,0) and (3,4) is:
Correct Answer: C) 5
Solution: Distance = √(3² + 4²) = √25 = 5.
Q33. The slope of a horizontal line is:
Correct Answer: A) 0
Solution: A horizontal line has no vertical change, so its slope is 0.
Q34. The midpoint of (2,4) and (6,8) is:
Correct Answer: B) (4,6)
Solution: Midpoint = ((2+6)/2, (4+8)/2) = (4,6).
Q35. The equation of the x-axis is:
Correct Answer: B) y = 0
Solution: Every point on the x-axis has y-coordinate equal to zero.
Part E – Statistics & Probability
Q36. The average of 4, 6 and 8 is:
Correct Answer: B) 6
Solution: Average = (4 + 6 + 8) / 3 = 18 / 3 = 6.
Q37. The median of 3, 5, 7, 9 and 11 is:
Correct Answer: C) 7
Solution: The middle value of the ordered data is 7.
Q38. The mode of 2, 3, 3, 4, 5 is:
Correct Answer: B) 3
Solution: 3 occurs more frequently than any other value, so mode = 3.
Q39. The probability of getting a head when a fair coin is tossed is:
Correct Answer: C) 1/2
Solution: A fair coin has two equally likely outcomes: Head and Tail. Probability of Head = 1/2.
Q40. The probability of an impossible event is:
Correct Answer: A) 0
Solution: An impossible event cannot occur, so its probability is 0.
Part F – Arithmetic & Applied Mathematics
Q41. A shopkeeper buys an article for ₹500 and sells it for ₹600. His profit is:
Correct Answer: C) ₹100
Solution: Profit = Selling Price − Cost Price = 600 − 500 = ₹100.
Q42. A number is increased from 200 to 240. The percentage increase is:
Correct Answer: C) 20%
Solution: Increase = 40. Percentage increase = 40/200 × 100 = 20%.
Q43. A train travels 120 km in 2 hours. Its average speed is:
Correct Answer: C) 60 km/h
Solution: Speed = Distance / Time = 120 / 2 = 60 km/h.
Q44. If 5 workers complete a job in 12 days, then the total work is:
Correct Answer: B) 60 worker-days
Solution: Total work = Number of workers × Number of days = 5 × 12 = 60 worker-days.
Q45. The simple interest on ₹1000 at 10% per year for 2 years is:
Correct Answer: C) ₹200
Solution: SI = P × R × T / 100 = 1000 × 10 × 2 / 100 = ₹200.
Q46. If the ratio of two numbers is 2:3 and the first number is 20, the second number is:
Correct Answer: B) 30
Solution: 2 parts = 20, so 1 part = 10. Therefore 3 parts = 30.
Q47. If 25% of a number is 50, the number is:
Correct Answer: C) 200
Solution: 25% = 1/4. Therefore the number = 50 × 4 = 200.
Q48. A man walks at 5 km/h. How far will he travel in 4 hours?
Correct Answer: C) 20 km
Solution: Distance = Speed × Time = 5 × 4 = 20 km.
Q49. If 8 pens cost ₹80, the cost of one pen is:
Correct Answer: B) ₹10
Solution: Cost of one pen = ₹80 ÷ 8 = ₹10.
Q50. The average of 10, 20, 30 and 40 is:
Correct Answer: B) 25
Solution: Average = (10 + 20 + 30 + 40) / 4 = 100 / 4 = 25.