For Dhingra Classes, Nashik
Subject: Mathematics
Class: VIII
Maximum Marks: 80
Time Allowed: 3 Hours

🧭 General Instructions

• All questions are compulsory.

• Marks are indicated against each question.

• Answers should be written in a clear and stepwise manner.

• Use of calculator is not permitted.

📝 SECTION A: MCQ (20 × 1 = 20 Marks)

1. The value of (10⁶ ÷ 10⁴) × 10⁻³ is:
(a) 10⁻¹ (b) 10⁰ (c) 10¹ (d) 10²
Ans: (a) 10⁻¹

2. The Mayan numeral system was based on:
(a) Base 10 (b) Base 12 (c) Base 20 (d) Base 60
Ans: (c) Base 20

3. A parallelogram with all sides equal and all angles 90° is called:
(a) Rhombus (b) Rectangle (c) Square (d) Trapezium
Ans: (c) Square

4. The digital root of 2,457 is:
(a) 6 (b) 7 (c) 8 (d) 9
Ans: (a) 6

5. Using the distributive property, 56 × 103 equals:
(a) 5768 (b) 5700 (c) 5800 (d) 5750
Ans: (a) 5768

6. If 6 pipes fill a tank in 12 hours, how many pipes are needed to fill it in 8 hours?
(a) 8 (b) 9 (c) 10 (d) 12
Ans: (b) 9

7. In a right triangle, if the legs are 16 cm and 30 cm, the hypotenuse is:
(a) 32 cm (b) 34 cm (c) 36 cm (d) 38 cm
Ans: (b) 34 cm

8. The set {x : x is a prime number between 10 and 15} is:
(a) Empty set (b) Singleton set (c) Two-element set (d) Infinite set
Ans: (c) Two-element set

9. If A = {2, 4, 6} and B = {4, 6, 8}, then A ∪ B is:
(a) {2, 4, 6} (b) {4, 6, 8} (c) {2, 4, 6, 8} (d) {2, 8}
Ans: (c) {2, 4, 6, 8}

10. The value of (8⁻² × 8⁵) ÷ 8³ is:
(a) 8⁰ (b) 8¹ (c) 8² (d) 8⁻¹
Ans: (a) 8⁰

11. The Roman numeral for 1,989 is:
(a) MCMLXXXIX (b) MCMLXXXVIII (c) MCMXC (d) MCMLXXX
Ans: (a) MCMLXXXIX

12. If each exterior angle of a regular polygon is 24°, the number of sides is:
(a) 12 (b) 15 (c) 18 (d) 20
Ans: (b) 15

13. Which of the following is a Baudhāyana triple?
(a) (12, 35, 37) (b) (13, 84, 85) (c) (20, 99, 101) (d) All of these
Ans: (d) All of these

14. If 7 kg of wheat costs ₹210, then the cost of 11 kg wheat is:
(a) ₹300 (b) ₹330 (c) ₹360 (d) ₹390
Ans: (b) ₹330

15. The value of 5⁻³ × 5³ is:
(a) 0 (b) 1 (c) 5 (d) 125
Ans: (b) 1

16. In a rectangle, the diagonals:
(a) Are perpendicular (b) Are equal and bisect each other (c) Are parallel (d) None of these
Ans: (b) Are equal and bisect each other

17. The expansion of (x + 6)(x − 9) is:
(a) x² − 3x − 54 (b) x² + 3x − 54 (c) x² − 15x − 54 (d) x² − 3x + 54
Ans: (a) x² − 3x − 54

18. If 5 : 8 = 25 : x, then x is:
(a) 30 (b) 35 (c) 40 (d) 45
Ans: (c) 40

19. If n(A) = 4, n(B) = 6, and n(A ∩ B) = 2, then n(A ∪ B) is:
(a) 6 (b) 8 (c) 10 (d) 12
Ans: (b) 8

20. The Baudhāyana-Pythagoras Theorem is found in which ancient Indian text?
(a) Rigveda (b) Sulba Sutras (c) Upanishads (d) Arthashastra
Ans: (b) Sulba Sutras

✏️ SECTION B: Very Short Answers (5 × 2 = 10 Marks)

21. Evaluate: (4⁻³ × 4⁶) ÷ 4²
Ans:
4⁻³ × 4⁶ = 4³
4³ ÷ 4² = 4¹ = 4

22. Write the expanded form of 5,082 using powers of 10.
Ans:
5082 = 5 × 10³ + 0 × 10² + 8 × 10¹ + 2 × 10⁰

23. Find the value of x in the Baudhāyana triple (x, 72, 75).
Ans:
x² + 72² = 75²
x² + 5184 = 5625
x² = 441
x = 21

24. If 11 pens cost ₹275, find the cost of 15 pens.
Ans:
Cost of 1 pen = 275/11 = ₹25
Cost of 15 pens = 25 × 15 = ₹375

25. If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7}, find A − B and B − A.
Ans:
A − B = {1, 2, 3}
B − A = {6, 7}

📐 SECTION C: Short Answer Questions (6 × 3 = 18 Marks)

26. Simplify: (7x² − 2x + 3) − (4x² + 5x − 8) + (2x² − 3x + 1)
Ans:
= 7x² − 2x + 3 − 4x² − 5x + 8 + 2x² − 3x + 1
= (7x² − 4x² + 2x²) + (−2x − 5x − 3x) + (3 + 8 + 1)
= 5x² − 10x + 12

27. The angles of a quadrilateral are in the ratio 2 : 3 : 4 : 6. Find all the angles.
Ans:
Let angles = 2x, 3x, 4x, 6x
2x + 3x + 4x + 6x = 360°
15x = 360° → x = 24°
Angles = 48°, 72°, 96°, 144°

28. A car travels 180 km in 2.5 hours. How far will it travel in 4 hours at the same speed?
Ans:
Speed = 180/2.5 = 72 km/h
Distance = 72 × 4 = 288 km

29. Verify whether (33, 56, 65) is a Baudhāyana triple.
Ans:
33² + 56² = 1089 + 3136 = 4225
65² = 4225
LHS = RHS, so (33, 56, 65) is a Baudhāyana triple

30. Using distributive property, find 73 × 97.
Ans:
73 × 97 = (85 − 12)(85 + 12)
= 85² − 12²
= 7225 − 144 = 7081

31. In a school, the ratio of students in classes 6, 7, and 8 is 5 : 4 : 3. If there are 720 students in total, find the number in each class.
Ans:
Total parts = 5 + 4 + 3 = 12
Class 6 = 720 × 5/12 = 300
Class 7 = 720 × 4/12 = 240
Class 8 = 720 × 3/12 = 180

📏 SECTION D: Long Answer Questions (4 × 5 = 20 Marks)

32. Simplify: 5p(3p² − 2p + 4) − 3p²(p − 2) + 2p(p² − 5)
Ans:
= 15p³ − 10p² + 20p − 3p³ + 6p² + 2p³ − 10p
= (15p³ − 3p³ + 2p³) + (−10p² + 6p²) + (20p − 10p)
= 14p³ − 4p² + 10p

33. A 26 m ladder reaches a window 24 m above the ground. Find the distance of the foot of the ladder from the wall.
Ans:
Let base = x
x² + 24² = 26²
x² + 576 = 676
x² = 100
x = 10 m

34. A sum of ₹3,600 is divided among P, Q, and R in the ratio 4 : 5 : 6. Find each share.
Ans:
Total parts = 4 + 5 + 6 = 15
Value of 1 part = 3600/15 = 240
P = 4 × 240 = ₹960
Q = 5 × 240 = ₹1200
R = 6 × 240 = ₹1440

35. Factorise: 12x² + 18x + 8xy + 12y
Ans:
= 6x(2x + 3) + 4y(2x + 3)
= (2x + 3)(6x + 4y)

📊 SECTION E: Case Study Questions (3 × 4 = 12 Marks)

Case Study 1

Read the passage and answer:

A confectionery shop sells chocolates, candies, and biscuits in the ratio 7 : 5 : 3. The total number of items is 900.

36. (a) Find the number of chocolates and candies.
Ans:
Total parts = 7 + 5 + 3 = 15
Chocolates = 900 × 7/15 = 420
Candies = 900 × 5/15 = 300

(b) Find the number of biscuits.
Ans:
Biscuits = 900 × 3/15 = 180

Case Study 2

Read the passage and answer:

In a right-angled triangle, the Baudhāyana-Pythagoras Theorem states that the square of the hypotenuse equals the sum of the squares of the other two sides.

37. (a) A right triangle has legs 14 cm and 48 cm. Find the hypotenuse.
Ans:
c² = 14² + 48²
= 196 + 2304 = 2500
c = √2500 = 50 cm

(b) If the hypotenuse is 41 cm and one leg is 9 cm, find the other leg.
Ans:
9² + b² = 41²
81 + b² = 1681
b² = 1600
b = 40 cm

Case Study 3

Read the passage and answer:

In a survey of 80 students, 45 like Tea, 35 like Coffee, and 20 like both Tea and Coffee.

38. (a) How many students like only Tea?
Ans:
Only Tea = 45 − 20 = 25

(b) How many students like neither Tea nor Coffee?
Ans:
n(T ∪ C) = 45 + 35 − 20 = 60
Neither = 80 − 60 = 20

🎯 Exam Tips for CBSE Class 8 Mathematics Students

🔢 Master exponent laws — they appear in every section

📐 Memorise angle properties of quadrilaterals and polygons

🧮 Use distributive property to simplify large calculations

📊 Read case studies twice before attempting

✅ Verify Baudhāyana triples by checking a² + b² = c²

🔗 Practise set operations like union, intersection, and difference

📞 Contact Dhingra Classes Today!

📍 Address: Plot No 3, XQ3G+H3M Deacon Homes, 301C, opp. Metro Zone, near Guru Govind Sing, Samarth Nagar, Dnyaneshwar Nagar, Pathardi Phata, Nashik, Maharashtra 422009

📱 Phone: 98230 62106

🌐 Website: https://www.dhingraclassesnashik.com/

📧 Email: dhingraclassesnsk@gmail.com