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 (7⁻² × 7⁵) ÷ 7² is:
(a) 7 (b) 7² (c) 7⁻¹ (d) 7⁰
Ans: (a) 7

2. The Egyptian numeral system was based on:
(a) Base 2 (b) Base 5 (c) Base 10 (d) Base 60
Ans: (c) Base 10

3. In a quadrilateral, if all angles are equal, each angle measures:
(a) 60° (b) 90° (c) 120° (d) 45°
Ans: (b) 90°

4. The digit sum of 487 is:
(a) 18 (b) 19 (c) 20 (d) 21
Ans: (b) 19

5. Using the distributive property, 45 × 102 equals:
(a) 4590 (b) 4500 (c) 4650 (d) 4570
Ans: (a) 4590

6. If 8 workers complete a job in 6 days, how many days will 12 workers take?
(a) 3 days (b) 4 days (c) 5 days (d) 9 days
Ans: (b) 4 days

7. In a right triangle, if the legs are 7 cm and 24 cm, the hypotenuse is:
(a) 23 cm (b) 25 cm (c) 26 cm (d) 27 cm
Ans: (b) 25 cm

8. The set {x : x is a natural number less than 1} is:
(a) Singleton set (b) Empty set (c) Infinite set (d) Universal set
Ans: (b) Empty set

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

10. The value of (−3)³ × (−3)⁻¹ is:
(a) 9 (b) −9 (c) 27 (d) −27
Ans: (a) 9

11. The Mayan number system used which base?
(a) 10 (b) 20 (c) 60 (d) 12
Ans: (b) 20

12. The sum of exterior angles of any polygon is:
(a) 180° (b) 270° (c) 360° (d) 540°
Ans: (c) 360°

13. Which of the following is a Baudhāyana triple?
(a) (7, 24, 25) (b) (9, 40, 41) (c) (11, 60, 61) (d) All of these
Ans: (d) All of these

14. If 5 pens cost ₹60, then the cost of 8 pens is:
(a) ₹80 (b) ₹96 (c) ₹100 (d) ₹120
Ans: (b) ₹96

15. The value of 3⁻² + 3⁻¹ is:
(a) 4/9 (b) 2/9 (c) 1/3 (d) 2/3
Ans: (a) 4/9

16. In a rhombus, the diagonals:
(a) Are equal (b) Bisect each other at 90° (c) Are parallel (d) None of these
Ans: (b) Bisect each other at 90°

17. The product (x + 3)(x + 5) equals:
(a) x² + 8x + 15 (b) x² + 15x + 8 (c) x² + 8x + 8 (d) x² + 15
Ans: (a) x² + 8x + 15

18. If a : b = 5 : 7 and b : c = 3 : 4, then a : c is:
(a) 15 : 28 (b) 5 : 4 (c) 35 : 12 (d) 12 : 35
Ans: (a) 15 : 28

19. The number of elements in the power set of an empty set is:
(a) 0 (b) 1 (c) 2 (d) Infinite
Ans: (b) 1

20. The Baudhāyana-Pythagoras Theorem was discovered in:
(a) Greece only (b) India only (c) Both India and Greece (d) Egypt only
Ans: (c) Both India and Greece

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

21. Evaluate: (2⁻³ × 2⁵) ÷ 2²
Ans:
2⁻³ × 2⁵ = 2²
2² ÷ 2² = 2⁰ = 1

22. Write the Roman numeral for 846.
Ans:
846 = 800 + 40 + 6 = DCCC + XL + VI = DCCCXLVI

23. Find the value of x in the Baudhāyana triple (x, 20, 29).
Ans:
x² + 20² = 29²
x² + 400 = 841
x² = 441
x = 21

24. If 4 kg of rice costs ₹180, find the cost of 7 kg rice.
Ans:
Cost of 1 kg = 180/4 = ₹45
Cost of 7 kg = 45 × 7 = ₹315

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

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

26. Simplify: (3x² + 2x − 5) − (x² − 4x + 3)
Ans:
= 3x² + 2x − 5 − x² + 4x − 3
= (3x² − x²) + (2x + 4x) + (−5 − 3)
= 2x² + 6x − 8

27. In a quadrilateral ABCD, ∠A = 80°, ∠B = 95°, ∠C = 100°. Find ∠D.
Ans:
Sum of angles = 360°
∠D = 360° − (80° + 95° + 100°)
= 360° − 275° = 85°

28. A train covers 315 km in 3.5 hours. How far will it travel in 5 hours at the same speed?
Ans:
Speed = 315/3.5 = 90 km/h
Distance = 90 × 5 = 450 km

29. Check whether (20, 21, 29) is a Baudhāyana triple.
Ans:
20² + 21² = 400 + 441 = 841
29² = 841
LHS = RHS, so (20, 21, 29) is a Baudhāyana triple

30. Using distributive property, find 67 × 99.
Ans:
67 × 99 = 67 × (100 − 1)
= 6700 − 67
= 6633

31. In a class of 480 students, the ratio of boys to girls is 5 : 7. Find the number of boys and girls.
Ans:
Total parts = 5 + 7 = 12
Boys = 480 × 5/12 = 200
Girls = 480 × 7/12 = 280

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

32. Simplify: 4a(a² − 3a + 2) − 2a²(a − 1) + 5a(a − 4)
Ans:
= 4a³ − 12a² + 8a − 2a³ + 2a² + 5a² − 20a
= (4a³ − 2a³) + (−12a² + 2a² + 5a²) + (8a − 20a)
= 2a³ − 5a² − 12a

33. The hypotenuse of a right triangle is 26 cm and one leg is 10 cm. Find the other leg.
Ans:
10² + b² = 26²
100 + b² = 676
b² = 576
b = 24 cm

34. A sum of ₹1,350 is divided among three people in the ratio 2 : 3 : 4. Find each share.
Ans:
Total parts = 2 + 3 + 4 = 9
Value of 1 part = 1350/9 = 150
Share 1 = 2 × 150 = ₹300
Share 2 = 3 × 150 = ₹450
Share 3 = 4 × 150 = ₹600

35. Factorise: 6x² + 9x + 4xy + 6y
Ans:
= 3x(2x + 3) + 2y(2x + 3)
= (2x + 3)(3x + 2y)

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

Case Study 1

Read the passage and answer:

A school library has books on Mathematics, Science, and English. The ratio of these books is 3 : 4 : 5 respectively. The total number of books is 1,440.

36. (a) Find the number of Mathematics books.
Ans:
Total parts = 3 + 4 + 5 = 12
Math books = 1440 × 3/12 = 360

(b) Find the number of Science and English books.
Ans:
Science = 1440 × 4/12 = 480
English = 1440 × 5/12 = 600

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 ladder 25 m long 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 = 25²
x² + 576 = 625
x² = 49
x = 7 m

(b) A right triangle has legs 15 cm and 36 cm. Find the hypotenuse.
Ans:
c² = 15² + 36²
= 225 + 1296 = 1521
c = √1521 = 39 cm

Case Study 3

Read the passage and answer:

In a survey of 500 students, 280 like Cricket, 220 like Football, and 120 like both Cricket and Football.

38. (a) How many students like only Cricket?
Ans:
Only Cricket = 280 − 120 = 160

(b) How many students like only Football?
Ans:
Only Football = 220 − 120 = 100

🎯 Exam Tips for CBSE Class 8 Mathematics Students

🔢 Master exponent rules — 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

📞 Contact Dhingra Classes Today!

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