NCERT Worksheet Class 8 Maths Chapter 6 Keeping Things in Proportion | 20 MCQs with Solutions | CBSE 2026-27

Class 8 Maths Chapter 6 Keeping Things in Proportion - NCERT 2026-27 Ganit Prakash - 20 MCQs Worksheet

Welcome to Galaxy Coaching Classes! This is the NEW NCERT Ganit Prakash 2026-27 worksheet for Class 8 Maths Chapter 6 Keeping Things in Proportion. This chapter covers Ratios, Proportions, Unitary Method, Direct & Inverse Proportion, Percentage, and Representation of Data. Perfect for CBSE students worldwide.

Board: CBSE | Class: 8 | Chapter: 6 Keeping Things in Proportion | Book: Ganit Prakash 2026-27 | Type: MCQ Worksheet with Solutions

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Learning Objectives (As per NCERT 2026-27):
✓ Understand Ratio and Proportion
✓ Unitary Method - Find value of one, then many
✓ Direct Proportion - Both increase together
✓ Inverse Proportion, Percentages, Tables & Graphs

Worksheet - Chapter 6 Keeping Things in Proportion - 20 MCQs with Answers

Q1. Ratio of 2 to 6 in simplest form is:
(a) 1:3 (b) 2:3 (c) 1:2 (d) 3:1

Q2. Which is equivalent ratio of 2:3?
(a) 4:5 (b) 6:9 (c) 2:6 (d) 3:2

Q3. If 2:3 = x:9, x =
(a) 4 (b) 6 (c) 9 (d) 3

Q4. If 5 pencils cost Rs 25, cost of 1 pencil is:
(a) Rs 5 (b) Rs 10 (c) Rs 25 (d) Rs 3

Q5. If 5 pencils cost Rs 25, cost of 3 pencils is:
(a) Rs 10 (b) Rs 15 (c) Rs 20 (d) Rs 12

Q6. Which is direct proportion?
(a) More workers, more time (b) More speed, less time (c) More workers, less time (d) None

Q7. Which is inverse proportion?
(a) More pens, more cost (b) More speed, less time (c) More distance, more time (d) More books, more pages

Q8. 50% of 200 is:
(a) 50 (b) 100 (c) 150 (d) 200

Q9. 25% of 80 is:
(a) 20 (b) 25 (c) 40 (d) 10

Q10. Ratio of 10 cm to 1 m is:
(a) 10:1 (b) 1:10 (c) 1:100 (d) 10:100

Q11. If a car covers 40 km in 1 hour, distance in 3 hours is:
(a) 80 km (b) 120 km (c) 40 km (d) 160 km

Q12. Map scale 1 cm = 100 km. If map distance is 3 cm, real distance is:
(a) 100 km (b) 200 km (c) 300 km (d) 30 km

Q13. Recipe for 4 people needs 2 cups flour. For 8 people needs:
(a) 2 cups (b) 4 cups (c) 6 cups (d) 8 cups

Q14. If x and y are in direct proportion, x=2, y=10, if x=5, y=
(a) 20 (b) 25 (c) 15 (d) 50

Q15. If 4 men finish work in 6 days, 8 men finish in:
(a) 12 days (b) 3 days (c) 6 days (d) 24 days

Q16. 2:4 = 1:2 is an example of:
(a) Ratio (b) Proportion (c) Percentage (d) Fraction

Q17. 3/5 as percentage is:
(a) 30% (b) 60% (c) 50% (d) 35%

Q18. Which shows part of whole in a circle?
(a) Bar chart (b) Pie chart (c) Line graph (d) Table

Q19. Ratio has:
(a) Unit (b) No unit (c) Always in cm (d) Always in Rs

Q20. If 12 kg of rice costs Rs 360, cost of 1 kg is:
(a) Rs 20 (b) Rs 30 (c) Rs 36 (d) Rs 12

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Answer Key - Chapter 6 Keeping Things in Proportion

1-a, 2-b, 3-b, 4-a, 5-b, 6-a, 7-b, 8-b, 9-a, 10-b, 11-b, 12-c, 13-b, 14-b, 15-b, 16-b, 17-b, 18-b, 19-b, 20-b

Detailed Solutions with Tricks

Q1, Q2. Ratio Trick: Divide both by HCF. 2:6 = 1:3. Equivalent ratio = multiply both by same number. 2:3 x 3 = 6:9.

Q3 & Q14. Proportion Trick: Cross multiply. 2:3 = x:9 => 3x = 18 => x=6. For direct proportion, y = 5 x (10/2) = 25.

Q4, Q5, Q20. Unitary Method: Find 1 first, then multiply. 25 ÷ 5 = 5 per pencil, 5 x 3 = 15. 360 ÷ 12 = 30 per kg.

Q6, Q7, Q15. Direct vs Inverse: Direct = both increase together. Inverse = one increases, other decreases. More men = less days => Inverse.

Q10. Unit Trick: Convert to same unit. 1 m = 100 cm, so 10 cm : 100 cm = 1:10.

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Next Chapter: Chapter 7 Knowing Our Numbers - Part 2 Worksheet | Previous: Chapter 5 Number Play Worksheet

NCERT Worksheet Class 8 Maths Chapter 5 Number Play | 20 MCQs with Solutions | CBSE 2026-27

Class 8 Maths Chapter 5 Number Play - NCERT 2026-27 Ganit Prakash - 20 MCQs Worksheet

Welcome to Galaxy Coaching Classes! This is the NEW NCERT Ganit Prakash 2026-27 worksheet for Class 8 Maths Chapter 5 Number Play. This chapter covers Patterns in Numbers, Parity, Multiples of 4, Divisibility by 3, 9, 11, Digital Roots, Factors, Multiples and Cryptarithms. Perfect for CBSE students worldwide.

Board: CBSE | Class: 8 | Chapter: 5 Number Play | Book: Ganit Prakash 2026-27 | Type: MCQ Worksheet with Solutions

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Learning Objectives (As per NCERT 2026-27):
✓ Sum of consecutive numbers & patterns
✓ Parity (Even/Odd), Multiples of 4
✓ Divisibility Rules for 3, 9, 11 & Digital Roots
✓ Proving claims for every number - Always/Sometimes/Never

Worksheet - Chapter 5 Number Play - 20 MCQs with Answers

Q1. Which is divisible by 3?
(a) 124 (b) 126 (c) 130 (d) 137

Q2. Which is divisible by 9?
(a) 123 (b) 729 (c) 456 (d) 112

Q3. Which is divisible by 11?
(a) 121 (b) 123 (c) 145 (d) 111

Q4. Digital root of 987 is:
(a) 6 (b) 8 (c) 9 (d) 24

Q5. Sum of first 5 consecutive numbers 1+2+3+4+5 =
(a) 10 (b) 15 (c) 20 (d) 25

Q6. Sum of 7+8+9 =
(a) 24 = 3 x 8 (b) 20 (c) 26 (d) 30

Q7. Prime factors of 36 are:
(a) 2x2x3x3 (b) 2x3x6 (c) 4x9 (d) 6x6

Q8. Prime factors of 60 are:
(a) 2x2x3x5 (b) 2x3x10 (c) 4x15 (d) 6x10

Q9. Which is divisible by 4?
(a) 1316 (b) 1315 (c) 1317 (d) 1319

Q10. Which is divisible by 5?
(a) 75 (b) 72 (c) 73 (d) 74

Q11. 123 + 321 =
(a) 444 (b) 443 (c) 445 (d) 400

Q12. A 3-digit number + its reverse is always divisible by:
(a) 9 (b) 11 (c) 13 (d) 7

Q13. Even + Odd =
(a) Even (b) Odd (c) Both (d) None

Q14. Odd + Odd =
(a) Odd (b) Even (c) Zero (d) Prime

Q15. Digital root of 123 is:
(a) 5 (b) 6 (c) 7 (d) 9

Q16. Which number is divisible by 2, 3 and 9?
(a) 126 (b) 127 (c) 125 (d) 129

Q17. 101 - 010 = 91. Digital root of 91 is:
(a) 10 (b) 1 (c) 9 (d) 0

Q18. If sum of digits is divisible by 9, number is divisible by:
(a) 3 only (b) 9 and 3 (c) 11 (d) 4

Q19. Which is a multiple of 4?
(a) 14 (b) 22 (c) 28 (d) 30

Q20. 1+2+3+...+10 =
(a) 45 (b) 50 (c) 55 (d) 60

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Answer Key - Chapter 5 Number Play

1-b, 2-b, 3-a, 4-a, 5-b, 6-a, 7-a, 8-a, 9-a, 10-a, 11-a, 12-b, 13-b, 14-b, 15-b, 16-a, 17-b, 18-b, 19-c, 20-c

Detailed Solutions with Tricks

Q1, Q2, Q16. Divisibility Trick: Sum of digits divisible by 3 => divisible by 3. Sum divisible by 9 => divisible by 9 and 3. 126 => 1+2+6=9, so divisible by 3 and 9.

Q3 & Q12. Divisibility by 11 Trick: (Sum of alternate digits difference) = 0 or 11. 121 => (1+1)-2=0. Any 3-digit + reverse always gives multiple of 11.

Q4, Q15, Q17. Digital Root Trick: Keep adding digits till single digit. 987 => 9+8+7=24 => 2+4=6. 91 => 9+1=10 => 1+0=1.

Q5, Q6, Q20. Consecutive Sum Trick: Sum = Middle number x Count. 1+2+3+4+5 = 3 x 5 = 15. 1 to 10 = 55 (n(n+1)/2).

Q13 & Q14. Parity Trick: Even+Odd=Odd, Odd+Odd=Even, Even+Even=Even. Always check last digit.

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Next Chapter: Chapter 6 Keeping Things in Proportion Worksheet | Previous: Chapter 4 Quadrilaterals Worksheet

NCERT Worksheet Class 8 Maths Chapter 2 Power Play | 20 MCQs with Solutions | CBSE 2026-27

Class 8 Maths Chapter 2 Power Play - NCERT 2026-27 Ganit Prakash - 20 MCQs Worksheet

Welcome to Galaxy Coaching Classes! This is the NEW NCERT Ganit Prakash 2026-27 worksheet for Class 8 Maths Chapter 2 Power Play. This chapter covers Exponents, Powers with Negative Exponents, Laws of Exponents, and Scientific Notation. Perfect for CBSE students worldwide.

Board: CBSE | Class: 8 | Chapter: 2 Power Play | Book: Ganit Prakash 2026-27 | Type: MCQ Worksheet with Solutions

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Learning Objectives (As per NCERT 2026-27):
✓ Understand exponents and powers
✓ Laws: a^m × aⁿ = a^m+n, (a^m)ⁿ = a^mn, a⁰=1
✓ Negative exponents & Scientific Notation

Worksheet - Chapter 2 Power Play - 20 MCQs with Answers

Q1. 2³ = ?
(a) 6 (b) 8 (c) 9 (d) 16

Q2. 3² × 3³ = ?
(a) 3⁵ = 243 (b) 3⁶ (c) 9⁵ (d) 3

Q3. (2³)² = ?
(a) 2⁵ (b) 2⁶ = 64 (c) 2⁹ (d) 4⁶

Q4. Any non-zero number to power 0 is:
(a) 0 (b) 1 (c) Number itself (d) Undefined

Q5. 10⁻² = ?
(a) 100 (b) 0.01 (c) -20 (d) -100

Q6. 5⁻³ = ?
(a) 125 (b) 1/125 (c) -125 (d) -15

Q7. a^m ÷ aⁿ = ?
(a) a^m+n (b) a^m-n (c) a^mn (d) a^m/n

Q8. (3/4)⁻² = ?
(a) 9/16 (b) 16/9 (c) -9/16 (d) -16/9

Q9. Standard form of 0.000045 = ?
(a) 4.5×10⁴ (b) 4.5×10⁻⁵ (c) 45×10⁻⁵ (d) 4.5×10⁻⁶

Q10. 1.5 × 10³ = ?
(a) 1500 (b) 15 (c) 0.0015 (d) 150

Q11. (-2)³ = ?
(a) -8 (b) 8 (c) 6 (d) -6

Q12. (-2)⁴ = ?
(a) -16 (b) 16 (c) -8 (d) 8

Q13. 2⁰ + 3⁰ + 4⁰ = ?
(a) 0 (b) 1 (c) 3 (d) 9

Q14. If 2^x = 32, x = ?
(a) 4 (b) 5 (c) 6 (d) 3

Q15. (2×3)² = ?
(a) 2²×3² = 36 (b) 2×3² (c) 2²×3 (d) 5²

Q16. (1/2)³ = ?
(a) 3/2 (b) 1/8 (c) 1/6 (d) 8

Q17. 10⁶ ÷ 10⁴ = ?
(a) 10² = 100 (b) 10¹⁰ (c) 10²⁴ (d) 10

Q18. Which is larger: 2³ or 3²?
(a) 2³=8 (b) 3²=9 (c) Equal (d) None

Q19. a⁻ⁿ = ?
(a) -aⁿ (b) 1/aⁿ (c) aⁿ (d) 0

Q20. Scientific notation of 1500000 = ?
(a) 1.5×10⁶ (b) 15×10⁵ (c) 0.15×10⁷ (d) 1.5×10⁵

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Answer Key - Chapter 2 Power Play

1-b, 2-a, 3-b, 4-b, 5-b, 6-b, 7-b, 8-b, 9-b, 10-a, 11-a, 12-b, 13-c, 14-b, 15-a, 16-b, 17-a, 18-b, 19-b, 20-a

Detailed Solutions with Tricks

Q2. Trick: a^m × aⁿ = a^m+n. So 3²×3³ = 3⁵ = 243

Q3. Trick: (a^m)ⁿ = a^mn. (2³)² = 2⁶ = 64

Q5 & Q6. Negative Power: a⁻ⁿ = 1/aⁿ. So 10⁻² = 1/100 = 0.01 and 5⁻³ = 1/125

Q8. Flip Rule: (a/b)⁻ⁿ = (b/a)ⁿ. So (3/4)⁻² = (4/3)² = 16/9

Q13. Any number power 0 = 1. So 1+1+1=3

Q19. Most Important Formula: a⁻ⁿ = 1/aⁿ

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Next Chapter: Chapter 3 A Story of Numbers Worksheet | Previous: Chapter 1 A Square and A Cube Worksheet

Class 8 Maths Chapter 1 A Square and A Cube Worksheet | 20 MCQs with Solutions | NCERT 2026-27 Ganit Prakash

NCERT Solutions & Worksheet Class 8 Maths Chapter 1 A Square and A Cube | 20 MCQs with Solutions | CBSE 2026-27 New Syllabus

Welcome to Galaxy Coaching Classes! As per the NEW NCERT book Ganit Prakash 2026-27, Class 8 Maths Chapter 1 is now A Square and A Cube (Old Rational Numbers is now Chapter 3). This worksheet has 20 MCQs with detailed solutions as per latest CBSE pattern.

Chapter: 1 A Square and A Cube | Class: 8 | Board: CBSE | Book: Ganit Prakash 2026-27 | Questions: 20 MCQs

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What you will learn: Squares, square roots, cubes, cube roots, patterns in squares/cubes, estimating roots - as per new NCERT.

Worksheet - 20 MCQs - Chapter 1 A Square and A Cube

1. What is the square of 12?
(a) 144 (b) 121 (c) 169 (d) 124

2. Which is a perfect square?
(a) 50 (b) 64 (c) 70 (d) 80

3. Square root of 169 is:
(a) 12 (b) 13 (c) 14 (d) 15

4. Square of an odd number is always:
(a) Even (b) Odd (c) Prime (d) None

5. How many natural numbers lie between 8² and 9²?
(a) 15 (b) 16 (c) 17 (d) 18

6. What is cube of 4?
(a) 16 (b) 32 (c) 64 (d) 48

7. Which is a perfect cube?
(a) 100 (b) 125 (c) 150 (d) 200

8. Cube root of 216 is:
(a) 6 (b) 7 (c) 8 (d) 9

9. What is 11²?
(a) 100 (b) 121 (c) 144 (d) 110

10. Smallest number by which 32 should be multiplied to make perfect square:
(a) 2 (b) 3 (c) 4 (d) 8

11. Square of 0.5 is:
(a) 0.25 (b) 0.5 (c) 2.5 (d) 0.05

12. Cube of -3 is:
(a) -9 (b) -27 (c) 27 (d) 9

13. Which number's square ends with 6?
(a) 12 (b) 14 (c) 18 (d) 24

14. √0.04 = ?
(a) 0.2 (b) 0.02 (c) 2 (d) 0.4

15. Smallest 3-digit perfect square is:
(a) 100 (b) 121 (c) 144 (d) 169

16. Cube root of 0.008 is:
(a) 0.2 (b) 0.02 (c) 2 (d) 0.8

17. If square ends with 5, cube ends with:
(a) 0 (b) 5 (c) 25 (d) 125

18. Estimate: √300 lies between:
(a) 17-18 (b) 15-16 (c) 10-11 (d) 20-21

19. 1³+2³+3³ = ?
(a) 36 (b) 27 (c) 35 (d) 30

20. Number of zeros at end of 100²?
(a) 2 (b) 3 (c) 4 (d) 1

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Answer Key

1-a, 2-b, 3-b, 4-b, 5-b, 6-c, 7-b, 8-a, 9-b, 10-a, 11-a, 12-b, 13-b, 14-a, 15-a, 16-a, 17-b, 18-a, 19-a, 20-c

Detailed Solutions with Tricks (New Syllabus)

5. Trick: Numbers between n² and (n+1)² = 2n. So between 8² and 9² = 2×8=16 numbers.

10. 32=2×2×2×2×2 = 2⁴×2. To make pairs, need one more 2. 32×2=64=8².

18. 17²=289, 18²=324, so √300 is between 17-18. Estimation is new in 2026-27 book.

19. Important Pattern for new book: Sum of cubes = (sum of numbers)². 1+8+27=36 and (1+2+3)²=36.

20. 100 has 2 zeros, square doubles zeros: 100²=10000 has 4 zeros.

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Next: Chapter 2 Power Play Worksheet | Also Read: Chapter 3 A Story of Numbers (Rational Numbers) Worksheet