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

---

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

---

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 4 Quadrilaterals | 20 MCQs with Solutions | CBSE 2026-27

Class 8 Maths Chapter 4 Quadrilaterals - 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 4 Quadrilaterals. This chapter covers Types of Quadrilaterals, Properties of Parallelogram, Rectangle, Square, Rhombus, Trapezium, Kite, and Angle Sum Property. Perfect for CBSE students worldwide.

Board: CBSE | Class: 8 | Chapter: 4 Quadrilaterals | Book: Ganit Prakash 2026-27 | Type: MCQ Worksheet with Solutions

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Learning Objectives (As per NCERT 2026-27):
✓ Sum of interior angles of quadrilateral is 360°
✓ Properties of Parallelogram, Rectangle, Square, Rhombus
✓ Trapezium and Kite properties
✓ Classification based on sides, angles & diagonals

Worksheet - Chapter 4 Quadrilaterals - 20 MCQs with Answers

Q1. Sum of all interior angles of a quadrilateral is:
(a) 180° (b) 360° (c) 540° (d) 90°

Q2. A quadrilateral with all 4 sides equal and all angles 90° is:
(a) Rectangle (b) Square (c) Rhombus (d) Trapezium

Q3. Opposite sides are equal and parallel, all angles 90° is:
(a) Square (b) Rectangle (c) Kite (d) Rhombus

Q4. Diagonals bisect each other in:
(a) Parallelogram (b) Kite (c) Trapezium (d) None

Q5. A quadrilateral with only one pair of parallel sides is:
(a) Parallelogram (b) Trapezium (c) Rhombus (d) Square

Q6. All sides equal, opposite sides parallel, opposite angles equal is:
(a) Square (b) Rectangle (c) Rhombus (d) Kite

Q7. Diagonals are equal in:
(a) Parallelogram (b) Rectangle and Square (c) Rhombus (d) Kite

Q8. Diagonals intersect at 90° in:
(a) Rectangle (b) Rhombus and Square (c) Parallelogram (d) Trapezium

Q9. Two pairs of adjacent sides equal in:
(a) Parallelogram (b) Kite (c) Rectangle (d) Trapezium

Q10. If one angle of parallelogram is 70°, opposite angle is:
(a) 110° (b) 70° (c) 180° (d) 90°

Q11. Number of sides in a quadrilateral:
(a) 3 (b) 4 (c) 5 (d) 6

Q12. A square is also a:
(a) Rectangle (b) Rhombus (c) Parallelogram (d) All of these

Q13. In a rectangle, each angle is:
(a) 60° (b) 90° (c) 180° (d) 360°

Q14. If diagonals of a quadrilateral are equal and bisect at 90°, it is:
(a) Rectangle (b) Square (c) Parallelogram (d) Trapezium

Q15. Exterior angle + interior angle at same vertex =
(a) 90° (b) 180° (c) 360° (d) 270°

Q16. Which is NOT a parallelogram?
(a) Square (b) Rectangle (c) Trapezium (d) Rhombus

Q17. Kite has:
(a) One pair of equal opposite angles (b) All angles equal (c) All sides equal (d) Opposite sides parallel

Q18. In a parallelogram, adjacent angles are:
(a) Equal (b) Supplementary (180°) (c) Complementary (90°) (d) None

Q19. Minimum number of sides to form a polygon is 4. True/False?
(a) True (b) False, 3 sides triangle (c) False, 2 sides (d) None

Q20. If 3 angles of quadrilateral are 90°, 90°, 90°, fourth angle is:
(a) 90° (b) 180° (c) 270° (d) 360°

---

Answer Key - Chapter 4 Quadrilaterals

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

Detailed Solutions with Tricks

Q1 & Q20. Angle Sum Trick: Sum = 360°. So 90+90+90+x=360 => x=90°. Quadrilateral becomes rectangle/square.

Q10 & Q18. Parallelogram Tricks: Opposite angles equal, Adjacent angles supplementary (sum 180°). So if one is 70°, adjacent 110°, opposite 70°.

Q4, Q7, Q8. Diagonal Tricks: All parallelograms bisect each other. Rectangle/Square diagonals EQUAL. Rhombus/Square/Kite diagonals at 90°.

Q12. Important: Square is most special - it is rectangle (90°), rhombus (all sides equal), parallelogram (opposite parallel) - so ALL of these.

Q16. Classification: Square, Rectangle, Rhombus are all parallelograms. Only Trapezium has only ONE pair parallel, so NOT a parallelogram.

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Next Chapter: Chapter 5 Finding The Unknown Worksheet | Previous: Chapter 3 A Story of Numbers Worksheet

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

NCERT Worksheet Class 8 Maths Chapter 3 A Story of Numbers | 20 MCQs with Solutions | CBSE 2026-27

Class 8 Maths Chapter 3 A Story of Numbers - 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 3 A Story of Numbers. This chapter covers History of Counting, Tally Marks, Roman Numerals, Egyptian, Mesopotamian, Mayan Systems, and Hindu Number System with Base, Place Value and Zero. Perfect for CBSE students worldwide.

Board: CBSE | Class: 8 | Chapter: 3 A Story of Numbers | Book: Ganit Prakash 2026-27 | Type: MCQ Worksheet with Solutions

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Learning Objectives (As per NCERT 2026-27):
✓ How humans learned to count - one-to-one mapping & tally marks
✓ Early systems: Roman, Egyptian, Mesopotamian (base-60), Mayan (base-20)
✓ Four Big Ideas: Grouping, Landmark Numbers, Base, Place Value with Zero
✓ Why Hindu (Indian) base-10 system is the most efficient

Worksheet - Chapter 3 A Story of Numbers - 20 MCQs with Answers

Q1. What is the earliest method of counting?
(a) Roman numerals (b) One-to-one mapping with sticks/stones (c) Place value (d) Base-10

Q2. In the Gumulgal system (Australia), how do they count beyond two?
(a) Use 0 (b) Grouping of twos - "two-two", "two-two-one" (c) Base-10 (d) Roman letters

Q3. Symbols used to write numbers are called:
(a) Numbers (b) Numerals (c) Digits (d) Landmarks

Q4. Landmark numbers in Egyptian system are:
(a) 1, 10, 100, 1000... (b) I, V, X (c) 0-9 (d) 60

Q5. Roman numeral IV stands for:
(a) 6 (b) 4 (c) 5 (d) 2

Q6. Which number system does NOT have place value?
(a) Hindu system (b) Roman system (c) Mayan system (d) Mesopotamian system

Q7. Base of Mesopotamian number system is:
(a) 10 (b) 20 (c) 60 (d) 5

Q8. Base of Mayan number system is:
(a) 10 (b) 20 (c) 60 (d) 2

Q9. The concept of ZERO was first developed in:
(a) Egypt (b) Rome (c) India (Hindu system) (d) Mesopotamia

Q10. In Hindu system, place value of 5 in 543 is:
(a) 5 (b) 50 (c) 500 (d) 5000

Q11. What is the base of our present Hindu number system?
(a) 5 (b) 10 (c) 20 (d) 60

Q12. Tally marks are grouped in:
(a) 2s (b) 5s (c) 10s (d) 60s

Q13. Which of these is NOT a feature of Hindu system?
(a) Base 10 (b) Place value (c) Zero (d) No place value, add symbols

Q14. Egyptian numeral for 100 is different from numeral for 10 because of:
(a) Place value (b) Landmark numbers - new symbol for each power of 10 (c) Base 60 (d) Zero

Q15. Value of Roman numeral XL is:
(a) 60 (b) 40 (c) 90 (d) 15

Q16. Four big ideas that led to modern number system are:
(a) Grouping, Landmark numbers, Base, Place value with Zero (b) Addition, Subtraction, Multiplication, Division (c) I, V, X, L (d) Tally, Roman, Egyptian, Hindu

Q17. Why is Roman system inefficient for large numbers?
(a) No zero and no place value, need many symbols (b) It has base 60 (c) It uses dots and bars (d) It is base-20

Q18. In a base-5 system, how many distinct numerals are needed?
(a) 5 (0,1,2,3,4) (b) 10 (c) 2 (d) 60

Q19. Chinese rod numerals used:
(a) Place value and base-10 (b) Only Roman letters (c) Base-60 (d) Tally grouping in 5s only

Q20. The modern numerals 0-9 that we use today are called:
(a) Roman numerals (b) Egyptian numerals (c) Hindu-Arabic numerals / Hindu numerals (d) Mayan numerals

---

Answer Key - Chapter 3 A Story of Numbers

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

Detailed Solutions with Tricks

Q1 & Q2. Trick: Earliest counting = one-to-one mapping. Gumulgal people had only words for 1, 2. For 3 they said "two-one", for 4 "two-two". So grouping idea starts early.

Q3. Numerals: Numbers are ideas, numerals are symbols to write them. Like 5 is a number, '5' is a numeral.

Q5 & Q15. Roman Trick: If smaller before larger, subtract. IV = 5-1=4, XL = 50-10=40. If smaller after, add. VI = 5+1=6.

Q6, Q13 & Q17. Main Difference: Roman has NO place value and NO zero. You have to add values of all symbols (XXX = 10+10+10). Hindu has place value + zero, so very short and efficient.

Q7 & Q8. Must Remember Base: Mesopotamian = Base 60 (60 seconds, 60 minutes came from there!), Mayan = Base 20 (dots and bars, counted with fingers + toes), Egyptian & Hindu = Base 10

Q9 & Q11. Most Important: Zero and place value invented in India 2000 years ago. Our system = Base 10, 10 numerals 0-9.

Q12. Tally Trick: Tally marks grouped in 5s (four vertical lines + one cross line) for fast counting.

Q14. Egyptian Trick: They had different pictures for 1, 10, 100, 1000. These are called Landmark numbers - powers of base.

Q18. Base Rule: Base-n needs n numerals. Base-5 needs 0,1,2,3,4 = 5 numerals. Base-10 needs 10 numerals (0-9).

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Trusted by CBSE Students | Class 6-10 | All Subjects

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Next Chapter: Chapter 4 Mathematics and Beyond Worksheet | Previous: Chapter 2 Power Play 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

---

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

NCERT Worksheet for Class 8 Maths Chapter 3 Rational Numbers - 20 MCQs with Solutions (2026-27)

Welcome to Galaxy Coaching Classes! This free worksheet is for CBSE Class 8 Maths Chapter 3 Rational Numbers as per the latest NCERT syllabus 2026-27. Perfect for practice before exams. All questions are MCQ type with detailed solutions at the end.

Class: 8 | Chapter: 3 Rational Numbers | Type: MCQ Worksheet | Total Questions: 20 | Board: CBSE Worldwide

Instructions:
- Each question has 4 options, only one is correct.
- Try to solve without seeing solutions first.
- Solutions with tricks are given at the end of this post.

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Worksheet - Chapter 3 Rational Numbers - 20 MCQs

1. Which of the following is a rational number?
(a) √3   (b) π   (c) 0/1   (d) None of these

2. The additive identity for rational numbers is:
(a) 1   (b) -1   (c) 0   (d) None

3. The multiplicative identity for rational numbers is:
(a) 0   (b) 1   (c) -1   (d) 2

4. The reciprocal of -3/7 is:
(a) 3/7   (b) 7/3   (c) -7/3   (d) 7/-3 is not allowed

5. Which of the following lies between 0 and -1?
(a) -2/3   (b) 2/3   (c) -3/2   (d) 3/2

6. The rational number that is equal to its own negative is:
(a) 1   (b) -1   (c) 0   (d) 2

7. Value of -2/3 + 4/3 = ?
(a) 2/3   (b) -2/3   (c) 6/3   (d) -6/3

8. Product of a rational number and its reciprocal is:
(a) 0   (b) 1   (c) -1   (d) Number itself

9. Which is greater? -3/4 or -2/3
(a) -3/4   (b) -2/3   (c) Both equal   (d) Cannot compare

10. 0 ÷ (-4/5) = ?
(a) 0   (b) -4/5   (c) -5/4   (d) Undefined

11. If x + 2/3 = 0, then x = ?
(a) 2/3   (b) -2/3   (c) 3/2   (d) -3/2

12. Rational number between 1/2 and 3/4 is:
(a) 5/8   (b) 1/4   (c) 1   (d) 4/5

13. -5/2 + ___ = -5/2. The blank is:
(a) 0   (b) 5/2   (c) -5/2   (d) 1

14. Associative property does NOT hold for which operation on rational numbers?
(a) Addition   (b) Multiplication   (c) Subtraction   (d) Both a and b

15. The standard form of -36/48 is:
(a) -3/4   (b) 3/4   (c) -9/12   (d) -6/8

16. How many rational numbers are there between any two rational numbers?
(a) 1   (b) 2   (c) Finite   (d) Infinite

17. (-3/5) × (5/-3) = ?
(a) 1   (b) -1   (c) 9/25   (d) -9/25

18. If a/b is a rational number, then b cannot be:
(a) 0   (b) 1   (c) -1   (d) 2

19. The additive inverse of 7/-9 is:
(a) 7/9   (b) -7/9   (c) 9/7   (d) -9/7

20. (1/2 + 1/3) + 1/4 = 1/2 + (1/3 + 1/4). This shows:
(a) Commutative property   (b) Associative property   (c) Distributive   (d) Closure

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Answer Key

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

Detailed Solutions

12. Average = (1/2+3/4)/2 = 5/8. 15. -36/48 ÷12 = -3/4. 16. Infinite rationals between any two. 19. 7/-9 = -7/9, inverse = 7/9.

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