Half Yearly Class 7 Mathematics Set 2 (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 successor of 9,99,999? (1 mark)
(a) 10,00,000
(b) 9,99,998
(c) 10,00,001
(d) 9,99,000

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

Q2. What is the place value of 3 in 8,34,672? (1 mark)
(a) 30,000
(b) 3,000
(c) 300
(d) 3,00,000

Ans: (a)
Sol: 3 is in the ten-thousands place: 3 × 10,000 = 30,000.

Q3. Simplify: 18 – 2 × 5. (1 mark)
(a) 8
(b) 10
(c) 16
(d) 28

Ans: (a)
Sol: BODMAS: 2 × 5 = 10, then 18 – 10 = 8.

Q4. What is 3.2 – 1.7? (1 mark)
(a) 1.5
(b) 2.5
(c) 1.8
(d) 2.0

Ans: (a)
Sol: 3.2 – 1.7 = 1.5.

Q5. If y = 2, what is the value of 4y + 3? (1 mark)
(a) 10
(b) 11
(c) 12
(d) 9

Ans: (b)
Sol: 4 × 2 + 3 = 8 + 3 = 11.

Q6. Which number is equivalent to 6,00,00,000 + 5,000 + 7? (1 mark)
(a) 6,00,05,007
(b) 6,50,007
(c) 6,05,007
(d) 60,00,507

Ans: (a)
Sol: 6 crore + 5 thousand + 7 = 6,00,05,007.

Q7. What is the fraction form of 0.4? (1 mark)
(a) 2/5
(b) 4/10
(c) 1/4
(d) 4/100

Ans: (a)
Sol: 0.4 = 4/10 = 2/5 (simplest form).

Q8. Simplify: (12 ÷ 3) × 2 + 5. (1 mark)
(a) 13
(b) 10
(c) 15
(d) 9

Ans: (a)
Sol: Parentheses: 12 ÷ 3 = 4. Multiply: 4 × 2 = 8. Add: 8 + 5 = 13.

Q9. If b = 5, what is the value of b² – 3? (1 mark)
(a) 22
(b) 25
(c) 28
(d) 20

Ans: (a)
Sol: b² = 5² = 25, then 25 – 3 = 22.

Q10. Which number is 50,000 less than 45,67,890? (1 mark)
(a) 45,17,890
(b) 45,67,840
(c) 44,67,890
(d) 45,17,840

Ans: (a)
Sol: 45,67,890 – 50,000 = 45,17,890.

Q11. What is 0.6 written as a fraction in its simplest form? (1 mark)
(a) 3/5
(b) 6/10
(c) 2/3
(d) 1/6

Ans: (a)
Sol: 0.6 = 6/10 = 3/5.

Q12. What is the constant term in the expression 5x + 9? (1 mark)
(a) 5
(b) 9
(c) x
(d) 0

Ans: (b)
Sol: The constant term is 9 (no variable).

Section B

Q13. Write 4,56,78,901 in words using the Indian number system.  (2 marks)

Ans: Four crore fifty-six lakh seventy-eight thousand nine hundred one.
Explanation: Group digits: 4 crore + 56 lakh + 78 thousand + 901.

Q14. Simplify: 25 – 5 × 3 + 2.  (2 marks)

Ans: 12
BODMAS: 5 × 3 = 15, then 25 – 15 = 10, then 10 + 2 = 12.

Q15. Convert 2.8 into a fraction in its simplest form.  (2 marks)

Ans: 2.8 = 28/10 = 14/5.

Q16. If q = 4, find the value of 2q + 9.  (2 marks)

Ans: 2 × 4 + 9 = 8 + 9 = 17.

Q17. Arrange in ascending order: 23,45,678; 23,45,789; 23,44,567.  (2 marks)

Ans: 23,44,567; 23,45,678; 23,45,789
Same digits up to lakh (23). Compare thousands: 44,567 < 45,678 < 45,789.

Q18. Evaluate: 3.6 ÷ 1.2.  (2 marks)

Ans: 3.6 ÷ 1.2 = 36/10 ÷ 12/10 = 36/12 = 3.

Q19. Form an algebraic expression: "Three times a number z decreased by 7."  (2 marks)

Ans: 3 × z – 7 = 3z – 7.

Q20. Find the difference: 89,12,345 – 12,34,567.  (2 marks)

Ans: 76,77,778

Q21. Simplify: (20 ÷ 5) × 3 – 6.  (2 marks)

Ans: Parentheses: 20 ÷ 5 = 4. Multiply: 4 × 3 = 12. Subtract: 12 – 6 = 6.

Q22. If n = 3, find the value of n² – 2n.  (2 marks)

Ans: n² = 3² = 9, 2n = 2 × 3 = 6, then 9 – 6 = 3.

Q23. Convert 3/5 into a decimal.  (2 marks)

Ans: 3 ÷ 5 = 0.6.

Q24. Compare: 5.43 and 5.34 (use <, >, or =).  (2 marks)

Ans: 5.43 > 5.34
Integer part same (5). Decimals: 0.43 vs 0.34, 4 > 3 in tenths place.

Section C

Q25. A library has 3,67,890 books. If 2,12,345 more books are added, how many books will there be in total?  (3 marks)

Ans: 5,80,235

Q26. Simplify: 15 × (4 ÷ 2) + 8 – 3.  (3 marks)

Ans: Parentheses: 4 ÷ 2 = 2. Multiply: 15 × 2 = 30. Add: 30 + 8 = 38. Subtract: 38 – 3 = 35.

Q27. Multiply: 2.3 × 1.4.  (3 marks)

Ans: 2.3 × 1.4 = 23/10 × 14/10 = 322/100 = 3.22.

Q28. If p = 2 and q = 5, find the value of 3p² + 2q.  (3 marks)

Ans: p² = 2² = 4, 3p² = 3 × 4 = 12, 2q = 2 × 5 = 10. Then, 12 + 10 = 22.

Q29. Write 6,78,90,123 in expanded form using powers of 10.  (3 marks)

Ans: 6 × 10⁷ + 7 × 10⁶ + 8 × 10⁵ + 9 × 10⁴ + 0 × 10³ + 1 × 10² + 2 × 10¹ + 3 × 10⁰

Q30. Add 67,89,123 and 23,45,678 and verify by subtraction.  (3 marks)

Ans: 91,34,801

Q31. Form an algebraic expression for: "A number m multiplied by 4, then increased by three times the same number." Simplify it.  (3 marks)

Ans: 4m + 3m = 7m.

Q32. Convert 0.125 into a fraction and verify by converting it back to a decimal.  (3 marks)

Ans: 0.125 = 125/1000 = 1/8. Verification: 1 ÷ 8 = 0.125.

Section D

Q33. The population of a town is 9,87,65,432. If 3,45,678 people move in and 1,23,456 move out, what is the new population? Show all steps.  (4 marks)

Ans: 9,89,87,654
Step 1: Add 3,45,678:

Step 2: Subtract 1,23,456:

Q34. Simplify the expression: 4 × (10 ÷ 5 + 3) – 2 × (8 ÷ 4). Show step-by-step working.  (4 marks)

Ans: 20

Parentheses: 10 ÷ 5 = 2, 2 + 3 = 5; 8 ÷ 4 = 2.

Expression: 4 × 5 – 2 × 2 = 20 – 4 = 16.

(Note: Recalculated; correct answer is 16, not 20, based on steps.)

Q35. A vendor buys a toy for ₹23.25 and sells it for ₹35.75. Find the profit and express it as a decimal and a fraction.  (4 marks)

Ans: Profit: ₹12.5, Fraction: 25/2
35.75 – 23.25 = 12.5. Fraction: 12.5 = 125/10 = 25/2.

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

Ans: 69
x² = 5² = 25, 3x² = 3 × 25 = 75; 2xy = 2 × 5 × 2 = 20; y² = 2² = 4. Then, 75 – 20 + 4 = 59 + 4 = 63.
(Note: Recalculated; correct answer is 63, not 69.)

Q37. Compare the numbers 56,78,901 and 56,87,901 using place value analysis and write the numbers in words.  (4 marks)

Ans: 56,78,901 < 56,87,901

• 56,78,901: Fifty-six lakh seventy-eight thousand nine hundred one.
• 56,87,901: Fifty-six lakh eighty-seven thousand nine hundred one.
• Same up to lakh (56). Thousands: 78 < 87.