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 5⁰ + 2⁻¹ is:
(a) 1/2 (b) 3/2 (c) 2 (d) 5
Ans: (b) 3/2

2. In the Roman numeral system, what does MCMXLIV represent?
(a) 1944 (b) 1444 (c) 1949 (d) 1494
Ans: (a) 1944

3. The sum of interior angles of a quadrilateral is:
(a) 180° (b) 270° (c) 360° (d) 540°
Ans: (c) 360°

4. Which of the following is always an even number when four consecutive numbers a, b, c, d are connected by + and − signs?
(a) a + b − c − d (b) a − b − c − d (c) a + b + c + d (d) All of these
Ans: (d) All of these

5. The distributive property is represented as:
(a) a(b + c) = ab + c (b) a(b + c) = ab + ac (c) (a + b)c = ab + c (d) ab + c = (a + c)b
Ans: (b) a(b + c) = ab + ac

6. If 3 pumps can fill a tank in 8 hours, how long will 6 pumps take to fill the same tank?
(a) 2 hours (b) 4 hours (c) 6 hours (d) 16 hours
Ans: (b) 4 hours

7. In the Baudhāyana-Pythagoras Theorem, if a = 6 and b = 8, the hypotenuse c equals:
(a) 9 (b) 10 (c) 12 (d) 14
Ans: (b) 10

8. A set consisting of no elements is called:
(a) Singleton set (b) Empty set (c) Finite set (d) Universal set
Ans: (b) Empty set

9. The number of subsets of a set containing 3 elements is:
(a) 3 (b) 6 (c) 8 (d) 9
Ans: (c) 8

10. Simplify: 2⁻⁴ × 2⁷
(a) 2³ (b) 2⁻³ (c) 2¹¹ (d) 2⁻¹¹
Ans: (a) 2³

11. The value of 172 written in expanded form using powers of 10 is:
(a) 1 × 10² + 7 × 10¹ + 2 × 10⁰ (b) 1 × 10³ + 7 × 10² + 2 × 10¹ (c) 1 × 10¹ + 7 × 10⁰ + 2 (d) None of these
Ans: (a) 1 × 10² + 7 × 10¹ + 2 × 10⁰

12. The exterior angle of a regular pentagon is:
(a) 72° (b) 108° (c) 60° (d) 90°
Ans: (a) 72°

13. Which of the following is a valid Baudhāyana triple?
(a) (3, 4, 5) (b) (5, 12, 13) (c) (8, 15, 17) (d) All of these
Ans: (d) All of these

14. If a : b = 3 : 4 and b : c = 2 : 5, then a : b : c = ?
(a) 6 : 8 : 20 (b) 3 : 4 : 5 (c) 2 : 3 : 5 (d) 5 : 10 : 20
Ans: (a) 6 : 8 : 20

15. The multiplicative inverse of 4⁻³ is:
(a) 4³ (b) 4⁻³ (c) 1/4³ (d) 1/64
Ans: (a) 4³

16. In a parallelogram, the diagonals:
(a) Are equal (b) Bisect each other (c) Are perpendicular (d) Both (a) and (b)
Ans: (b) Bisect each other

17. The increase in product ab when both a and b are increased by 1 is:
(a) a + b (b) a + b + 1 (c) ab + 1 (d) a² + b²
Ans: (b) a + b + 1

18. If x and y are directly proportional, then x/y = ?
(a) 0 (b) 1 (c) k (constant) (d) x + y
Ans: (c) k (constant)

19. The number of proper subsets of a set with 4 elements is:
(a) 16 (b) 15 (c) 8 (d) 4
Ans: (b) 15

20. The Baudhāyana-Pythagoras Theorem applies to:
(a) All triangles (b) Right-angled triangles (c) Equilateral triangles (d) Isosceles triangles
Ans: (b) Right-angled triangles

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

21. Find the value of (4⁰ + 4⁻¹) × 2².
Ans:
4⁰ = 1, 4⁻¹ = 1/4
(1 + 1/4) × 4 = (5/4) × 4 = 5

22. Represent the number 948 in Roman numerals.
Ans:
948 = 900 + 40 + 8 = CM + XL + VIII = CMXLVIII

23. Find the length of the hypotenuse of a right triangle with sides 9 cm and 12 cm.
Ans:
c² = 9² + 12² = 81 + 144 = 225
c = √225 = 15 cm

24. If the ratio of flour : sugar : butter is 5 : 2 : 3 and sugar is 40 g, find flour and butter.
Ans:
2 parts = 40 g → 1 part = 20 g
Flour = 5 × 20 = 100 g
Butter = 3 × 20 = 60 g

25. Write all subsets of the set A = {2, 3, 5}.
Ans:
{}, {2}, {3}, {5}, {2,3}, {2,5}, {3,5}, {2,3,5}

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

26. Simplify and express in exponential form: (2³ × 2⁻⁵) ÷ 2⁻²
Ans:
2³ × 2⁻⁵ = 2³⁺⁽⁻⁵⁾ = 2⁻²
2⁻² ÷ 2⁻² = 2⁻²⁻⁽⁻²⁾ = 2⁰ = 1

27. Two adjacent angles of a parallelogram are in the ratio 2 : 3. Find all the angles.
Ans:
Let angles = 2x and 3x
2x + 3x = 180° (adjacent angles supplementary)
5x = 180° → x = 36°
Angles = 72°, 108°, 72°, 108°

28. A car travels 240 km in 4 hours. How long will it take to travel 360 km at the same speed?
Ans:
Speed = 240/4 = 60 km/h
Time = 360/60 = 6 hours
(Direct proportion)

29. Verify whether (8, 15, 17) is a Baudhāyana triple.
Ans:
8² + 15² = 64 + 225 = 289
17² = 289
LHS = RHS, so (8, 15, 17) is a Baudhāyana triple

30. Expand using distributive property: 98 × 102
Ans:
98 × 102 = (100 − 2)(100 + 2)
= 100² − 2² = 10000 − 4 = 9996

31. In a survey of 720 students, the ratio of those who like Math, Science, and English is 4 : 3 : 5. Find the number of students who like each subject.
Ans:
Sum of ratios = 4 + 3 + 5 = 12
Math = 720 × 4/12 = 240
Science = 720 × 3/12 = 180
English = 720 × 5/12 = 300

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

32. Simplify: 2x²(x + 2) − 3x(x² − 3) − 5x(x + 5)
Ans:
= 2x³ + 4x² − 3x³ + 9x − 5x² − 25x
= (2x³ − 3x³) + (4x² − 5x²) + (9x − 25x)
= −x³ − x² − 16x

33. Find the value of x if x² + 12² = 15².
Ans:
x² + 144 = 225
x² = 225 − 144 = 81
x = √81 = 9

34. A sum of ₹720 is divided in the ratio 2 : 7. Find the smaller share.
Ans:
Total parts = 2 + 7 = 9
Value of 1 part = 720 ÷ 9 = 80
Smaller share = 2 × 80 = ₹160

35. Factorise: 10x² + 5x + 2xy + y
Ans:
= 5x(2x + 1) + y(2x + 1)
= (2x + 1)(5x + y)

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

Case Study 1

Read the passage and answer:

Palampur is a small village with 450 families. Farming is the main occupation. The village has well-developed irrigation facilities. Some people are also engaged in dairy, small-scale manufacturing, and transport.

36. (a) If 15 workers can build a wall in 20 days, how many workers are needed to build it in 12 days?
Ans:
15 × 20 = x × 12
300 = 12x
x = 25 workers

(b) If the ratio of families engaged in farming to dairy is 7 : 2 and 450 families total, find families in dairy.
Ans:
Total parts = 7 + 2 = 9
Dairy families = 450 × 2/9 = 100

Case Study 2

Read the passage and answer:

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

37. (a) A right triangle has shorter sides 5 cm and 12 cm. Find the hypotenuse.
Ans:
c² = 5² + 12² = 25 + 144 = 169
c = √169 = 13 cm

(b) If the hypotenuse is 17 cm and one side is 8 cm, find the other side.
Ans:
8² + b² = 17²
64 + b² = 289
b² = 225
b = 15 cm

Case Study 3

Read the passage and answer:

Sets are collections of well-defined objects. The number of subsets of a set with n elements is 2ⁿ.

38. (a) How many subsets does a set with 5 elements have?
Ans:
2⁵ = 32

(b) Write any three proper subsets of A = {1, 2, 3, 4}.
Ans:
{1}, {2, 3}, {1, 2, 3} (any three proper subsets)

🎯 Exam Tips for CBSE Class 8 Mathematics Students

🔢 Practise exponent laws — they appear in every section

📐 Draw neat diagrams for geometry questions

🧮 Use distributive property to simplify calculations

📊 Read case studies carefully before attempting

✅ Verify answers using the Baudhāyana-Pythagoras Theorem

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