Half Yearly Class 7 Mathematics Set 3 (Solutions) | Mathematics (Ganita Prakash) Class 7 - New NCERT PDF Download

Maximum Marks: 68
Time: 2.5 Hours
General Instructions:
(i) All questions are compulsory.
(ii) Marks for each question are indicated against it.
(iii) Section A consists of 12 MCQs carrying 1 mark each.
(iv) Section B consists of 12 questions carrying 2 marks each.
(v) Section C consists of 8 questions carrying 3 marks each.
(vi) Section D consists of 5 questions carrying 4 marks each.
(vii) Use of calculators is not allowed.

Section A

Q1. What is the predecessor of 10,00,000?  (1 mark)
(a) 9,99,999
(b) 10,00,001
(c) 9,99,998
(d) 10,00,100

Ans: (a)
Sol: Predecessor = 10,00,000 – 1 = 9,99,999.

Q2. What is the place value of 9 in 7,89,456?  (1 mark)
(a) 9,000
(b) 90,000
(c) 900
(d) 9,00,000

Ans: (b)
Sol: 9 is in the ten-thousands place: 9 × 10,000 = 90,000.

Q3. Simplify: 10 + 4 × 3.  (1 mark)
(a) 22
(b) 42
(c) 18
(d) 28

Ans: (a)
Sol: BODMAS: 4 × 3 = 12, then 10 + 12 = 22.

Q4. What is 4.8 ÷ 2?  (1 mark)
(a) 2.4
(b) 2.8
(c) 1.8
(d) 3.4

Ans: (a)
Sol: 4.8 ÷ 2 = 48/20 = 2.4.

Q5. If z = 4, what is the value of 3z – 5?  (1 mark)
(a) 7
(b) 9
(c) 12
(d) 10

Ans: (a)
Sol: 3 × 4 – 5 = 12 – 5 = 7.

Q6. Which number is equivalent to 5,00,00,000 + 3,000 + 20 + 8?  (1 mark)
(a) 5,00,03,028
(b) 5,03,028
(c) 5,30,028
(d) 50,03,028

Ans: (a)
Sol: 5 crore + 3 thousand + 20 + 8 = 5,00,03,028.

Q7. What is the decimal form of 9/25?  (1 mark)
(a) 0.36
(b) 0.9
(c) 0.25
(d) 0.09

Ans: (a)
Sol: 9 ÷ 25 = 0.36.

Q8. Simplify: (15 – 5) ÷ 2 + 6.  (1 mark)
(a) 11
(b) 9
(c) 13
(d) 15

Ans: (a)
Sol: Parentheses: 15 – 5 = 10. Divide: 10 ÷ 2 = 5. Add: 5 + 6 = 11.

Q9. If c = 3, what is the value of 2c²? (1 mark)
(a) 18
(b) 12
(c) 9
(d) 6

Ans: (a)
Sol: c² = 3² = 9, 2c² = 2 × 9 = 18.

Q10. Which number is 25,000 more than 34,56,789?  (1 mark)
(a) 34,81,789
(b) 34,56,814
(c) 34,31,789
(d) 35,81,789

Ans: (a)
Sol: 34,56,789 + 25,000 = 34,81,789.

Q11. What is 0.8 written as a fraction in its simplest form?  (1 mark)
(a) 4/5
(b) 8/10
(c) 2/5
(d) 1/8

Ans: (a)
Sol: 0.8 = 8/10 = 4/5.

Q12. What is the coefficient of m in the expression 7 + 4m?  (1 mark)
(a) 4
(b) 7
(c) m
(d) 0

Ans: (a)
Sol: Coefficient of m is 4.

Section B

Q13. Write 8,12,34,567 in words using the Indian number system.  (2 marks)

Ans: Eight crore twelve lakh thirty-four thousand five hundred sixty-seven.
Group digits: 8 crore + 12 lakh + 34 thousand + 567.

Q14. Simplify: 30 ÷ 5 + 4 × 2.  (2 marks)

Ans: BODMAS: 30 ÷ 5 = 6, 4 × 2 = 8, then 6 + 8 = 14.

Q15. Convert 1.25 into a fraction in its simplest form.  (2 marks)

Ans: 1.25 = 125/100 = 5/4.

Q16. If r = 6, find the value of 5r – 8.  (2 marks)

Ans: 5 × 6 – 8 = 30 – 8 = 22.

Q17. Arrange in descending order: 45,67,890; 45,67,789; 45,68,901.  (2 marks)

Ans: 45,68,901; 45,67,890; 45,67,789
Same up to lakh (45). Thousands: 68,901 > 67,890 > 67,789.

Q18. Evaluate: 1.8 × 2.5.  (2 marks)

Ans: 1.8 × 2.5 = 18/10 × 25/10 = 450/100 = 4.5.

Q19. Form an algebraic expression: "Twice a number p increased by 10."  (2 marks)

Ans: 2 × p + 10 = 2p + 10.

Q20. Find the sum: 78,90,123 + 34,56,789.  (2 marks)

Ans: 1,13,46,912

Q21. Simplify: (18 ÷ 3) + 5 × 2.  (2 marks)

Ans: Parentheses: 18 ÷ 3 = 6. Multiply: 5 × 2 = 10. Add: 6 + 10 = 16.

Q22. If k = 4, find the value of k² + 3k.  (2 marks)

Ans: k² = 4² = 16, 3k = 3 × 4 = 12, then 16 + 12 = 28.

Q23. Convert 7/20 into a decimal.  (2 marks)

Ans: 7 ÷ 20 = 0.35.

Q24. Compare: 6.78 and 6.87 (use <, >, or =).  (2 marks)

Ans: 6.78 < 6.87
Integer part same (6). Decimals: 0.78 vs 0.87, 7 < 8 in tenths place.

Section C

Q25. A factory produces 4,56,789 units. If 1,78,901 more units are produced, how many units are there in total?  (3 marks)

Ans: 6,35,690

Q26. Simplify: 20 ÷ (5 – 3) × 4 + 2.  (3 marks)

Ans: Parentheses: 5 – 3 = 2. Divide: 20 ÷ 2 = 10. Multiply: 10 × 4 = 40. Add: 40 + 2 = 42.

Q27. Subtract: 5.67 – 2.89.  (3 marks)

Ans: 2.78

Q28. If a = 3 and b = 4, find the value of 2a² + b².  (3 marks)

Ans: a² = 3² = 9, 2a² = 2 × 9 = 18; b² = 4² = 16. Then, 18 + 16 = 34.

Q29. Write 7,89,12,345 in expanded form using powers of 10.  (3 marks)

Ans: 7 × 10⁷ + 8 × 10⁶ + 9 × 10⁵ + 1 × 10⁴ + 2 × 10³ + 3 × 10² + 4 × 10¹ + 5 × 10⁰

Q30. Subtract 56,78,901 from 1,12,34,567 and verify by addition.  (3 marks)

Ans: 55,55,666

Q31. Form an algebraic expression for: "A number n multiplied by 5, then decreased by four times the same number." Simplify it.  (3 marks)

Ans: 5n – 4n = n.

Q32. Convert 0.625 into a fraction and verify by converting it back to a decimal.  (3 marks)

Ans: 5/8
0.625 = 625/1000 = 5/8. Verification: 5 ÷ 8 = 0.625.

Section D

Q33. The population of a state is 15,67,89,123. If 4,56,789 people move out and 2,34,567 move in, what is the new population? Show all steps.  (4 marks)

Ans: 15,65,66,901
Step 1: Subtract 4,56,789:

Step 2: Add 2,34,567:

Q34. Simplify the expression: 6 × (12 ÷ 4 + 2) – 4 × (10 ÷ 5). Show step-by-step working.  (4 marks)

Ans: 22
Parentheses: 12 ÷ 4 = 3, 3 + 2 = 5; 10 ÷ 5 = 2.
Expression: 6 × 5 – 4 × 2 = 30 – 8 = 22.

Q35. A trader buys an item for ₹56.45 and sells it for ₹78.95. Find the profit and express it as a decimal and a fraction.  (4 marks)

Ans: Profit: ₹22.5, Fraction: 45/2
78.95 – 56.45 = 22.5. Fraction: 22.5 = 225/10 = 45/2.

Q36. If x = 3 and y = 5, evaluate the expression x² + 2xy – y². Show all substitutions and calculations.  (4 marks)

Ans: x² = 3² = 9; 2xy = 2 × 3 × 5 = 30; y² = 5² = 25. Then, 9 + 30 – 25 = 39 – 25 = 14.

Q37. Compare the numbers 67,89,123 and 67,98,123 using place value analysis and write the numbers in words.  (4 marks)

Ans: 67,89,123 < 67,98,123

• 67,89,123: Sixty-seven lakh eighty-nine thousand one hundred twenty-three.
• 67,98,123: Sixty-seven lakh ninety-eight thousand one hundred twenty-three.
• Same up to lakh (67). Thousands: 89 < 98.