Half Yearly Class 7 Mathematics Set 1 (Solutions) | Mathematics (Ganita Prakash) Class 7 - New NCERT PDF Download

Maximum Marks: 80
Time: 3 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. Which number is equivalent to 5,00,000 in the Indian number system? (1 mark)
(a) Five lakh
(b) Fifty thousand
(c) Five crore
(d) Five hundred

Ans: (a)
Sol: In the Indian number system, 5,00,000 is written as five lakh.

Q2. What is the place value of 7 in 4,72,891? (1 mark)
(a) 7,000
(b) 70,000
(c) 700
(d) 7,00,000

Ans: (b)
Sol: The digit 7 is in the ten-thousands place. Place value = 7 × 10,000 = 70,000.

Q3. Simplify: 15 + 3 × 4. (1 mark)
(a) 72
(b) 27
(c) 48
(d) 33

Ans: (b)
Sol: Using BODMAS, multiply first: 3 × 4 = 12. Then add: 15 + 12 = 27.

Q4. What is the value of 2.5 + 1.3?  (1 mark)
(a) 3.8
(b) 3.6
(c) 2.8
(d) 4.8

Ans: (a)
Sol: Align decimals: 2.5 + 1.3 = 3.8.

Q5. If x = 3, what is the value of 2x + 5? (1 mark)
(a) 10
(b) 11
(c) 12
(d) 9

Ans: (b)
Sol: Substitute x = 3: 2 × 3 + 5 = 6 + 5 = 11.

Q6. Which of the following is the standard form of 8000000 + 4000 + 50 + 6? (1 mark)
(a) 8,004,056
(b) 80,40,506
(c) 8,40,056
(d) 80,04,056

Ans: (a)
Sol: Write in standard form: 8,000,000 + 4,000 + 50 + 6 = 8,004,056.

Q7. What is the decimal form of 7/10? (1 mark)
(a) 0.7
(b) 7.0
(c) 0.07
(d) 70

Ans: (a)
Sol: Divide 7 by 10: 7 ÷ 10 = 0.7.

Q8. Simplify: (8 × 2) ÷ 4 + 3. (1 mark)
(a) 7
(b) 10
(c) 5
(d) 8

Ans: (a)
Sol: Using BODMAS, parentheses first: 8 × 2 = 16. Then divide: 16 ÷ 4 = 4. Then add: 4 + 3 = 7.

Q9. If a = 4, what is the value of a²? (1 mark)
(a) 8
(b) 12
(c) 16
(d) 20

Ans: (c)
Sol: Substitute a = 4: a² = 4² = 16.

Q10. Which number is 1,00,000 more than 23,45,678? (1 mark)
(a) 24,45,678
(b) 23,55,678
(c) 22,45,678
(d) 24,55,678

Ans: (a)
Sol: Add 1,00,000 to 23,45,678: 23,45,678 + 1,00,000 = 24,45,678.

Q11. What is 0.25 written as a fraction in its simplest form? (1 mark)
(a) 1/4
(b) 2/5
(c) 1/5
(d) 25/100

Ans: (a)
Sol: 0.25 = 25/100. Simplify by dividing by 25: 25 ÷ 25 = 1, 100 ÷ 25 = 4. Thus, 1/4.

Q12. What is the coefficient of y in the expression 3y + 7? (1 mark)
(a) 3
(b) 7
(c) 1
(d) 0

Ans: (a)
Sol: The coefficient is the number multiplied by y, which is 3.

Section B

Q13. Write 7,89,45,123 in words using the Indian number system.  (2 marks)

Ans: Seven crore eighty-nine lakh forty-five thousand one hundred twenty-three.
Group digits: 7,89,45,123 = 7 crore + 89 lakh + 45 thousand + 123.

Q14. Simplify: 20 ÷ 4 + 6 × 2.  (2 marks)

Ans: Using BODMAS, divide first: 20 ÷ 4 = 5. Multiply: 6 × 2 = 12. Add: 5 + 12 = 17.

Q15. Convert 3.75 into a fraction in its simplest form.  (2 marks)

Ans: 3.75 = 375/100 (since 2 decimal places). 
Simplify: 375 ÷ 25 = 15, 100 ÷ 25 = 4. Thus, 15/4.

Q16. If p = 5, find the value of 3p – 7.  (2 marks)

Ans: Substitute p = 5: 3 × 5 – 7 = 15 – 7 = 8.

Q17. Arrange in descending order: 12,34,567; 1,23,45,678; 12,34,678.  (2 marks)

Ans: 1,23,45,678; 12,34,678; 12,34,567
Compare digits: 1,23,45,678 (8 digits) > 12,34,678 (7 digits) > 12,34,567 (7 digits, but 6 < 7 in ten-thousands place).

Q18. Evaluate: 2.4 × 1.5.  (2 marks)

Ans: 2.4 × 1.5 = 24/10 × 15/10 = (24 × 15)/(10 × 10) = 360/100 = 3.6.

Q19. Form an algebraic expression: "Five times a number x increased by 8."  (2 marks)

Ans: 5x + 8
​Five times x is 5x, increased by 8 gives 5x + 8.

Q20. Find the sum of 56,78,901 and 12,34,567.  (2 marks)

Ans: 69,13,468

Q21. Simplify: (15 + 5) ÷ (2 × 2).  (2 marks)

Ans: 5
Parentheses first: 15 + 5 = 20, 2 × 2 = 4. Then divide: 20 ÷ 4 = 5.

Q22. If m = 2, find the value of m² + 4m.  (2 marks)

Ans: 12
Substitute m = 2: m² = 2² = 4, 4m = 4 × 2 = 8. Then, 4 + 8 = 12.

Q23. Convert 5/8 into a decimal.  (2 marks)

Ans: 0.625
Divide 5 by 8: 5 ÷ 8 = 0.625 (5.000 ÷ 8 = 0.625).

Q24. Compare: 4.56 and 4.65 (use <, >, or =).  (2 marks)

Ans: 4.56 < 4.65
Integer part is same (4). Compare decimals: 0.56 vs 0.65. Since 5 < 6 in tenths place, 4.56 < 4.65.

Section C

Q25. A school has 2,45,678 students enrolled. If 1,23,456 more students join, how many students will there be in total?  (3 marks)

Ans: 3,69,134

Q26. Simplify: 24 ÷ (3 + 5) × 2 + 7.  (3 marks)

Ans: 13
Parentheses first: 3 + 5 = 8. Divide: 24 ÷ 8 = 3. Multiply: 3 × 2 = 6. Add: 6 + 7 = 13.

Q27. Add: 3.45 + 2.67 + 1.23.  (3 marks)

Ans: 7.35

Q28. If x = 3 and y = 2, find the value of 4x² + 3y.  (3 marks)

Ans: 42
Substitute x = 3, y = 2. Calculate: x² = 3² = 9, 4x² = 4 × 9 = 36, 3y = 3 × 2 = 6. Then, 36 + 6 = 42.

Q29. Write 9,87,65,432 in expanded form using powers of 10.  (3 marks)

Ans: 9 × 10⁷ + 8 × 10⁶ + 7 × 10⁵ + 6 × 10⁴ + 5 × 10³ + 4 × 10² + 3 × 10¹ + 2 × 10⁰
Each digit is multiplied by its place value: 9 (crore), 8 (ten lakh), 7 (lakh), etc.

Q30. Subtract 45,67,890 from 1,23,45,678 and verify by addition.  (3 marks)

Ans: 77,77,788
Subtraction:

Verification: 77,77,788 + 45,67,890 = 1,23,45,678 (add back to check).

Q31. Form an algebraic expression for: "A number y multiplied by 7, then decreased by twice the same number." Simplify it.  (3 marks)

Ans: 5y
Expression: 7y – 2y. Simplify: 7y – 2y = 5y.

Q32. Convert 0.375 into a fraction and verify by converting it back to a decimal.  (3 marks)

Ans: Fraction: 3/8
0.375 = 375/1000. Simplify: 375 ÷ 125 = 3, 1000 ÷ 125 = 8, so 3/8.
Verification: 3 ÷ 8 = 0.375 (decimal division confirms).

Section D

Q33. The population of a city is 12,34,56,789. If 2,34,567 people move out and 1,45,678 people move in, what is the new population? Show all steps.  (4 marks)

Ans: 12,33,67,900
Step 1: Subtract 2,34,567:

Step 2: Add 1,45,678:

Q34. Simplify the expression: 5 × (8 ÷ 2 + 4) – 3 × (6 ÷ 2). Show step-by-step working.  (4 marks)

Ans: 35
Step 1: Parentheses: 8 ÷ 2 = 4, 4 + 4 = 8; 6 ÷ 2 = 3.
Step 2: Expression becomes: 5 × 8 – 3 × 3.
Step 3: Multiply: 5 × 8 = 40, 3 × 3 = 9.
Step 4: Subtract: 40 – 9 = 31.
(Note: The answer 35 seems incorrect based on calculation; correct answer is 31. Possible typo in intent; solved as per expression.)

Q35. Q35. A basket has $\frac{\mathrm{<br>}}{}$$\frac{5}{8}$ kg kg of apples and $\frac{3}{4}$ kg of oranges.
a) Find the total weight of fruits in the basket.
b) If 1 kg of fruit costs ₹120, what is the total cost?  (4 marks)

Ans: 

a) Total weight

$\frac{5}{8}+\frac{3}{4}=\frac{5}{8}+\frac{6}{8}=\frac{11}{8}\hspace{0.17em}kg\backslash frac\{5\}\{8\}\; +\; \backslash frac\{3\}\{4\}\; =\; \backslash frac\{5\}\{8\}\; +\; \backslash frac\{6\}\{8\}\; =\; \backslash frac\{11\}\{8\}\; \backslash ,\; \backslash text\{kg\}$$kg=1\frac{3}{8}\hspace{0.17em}kg\backslash frac\{11\}\{8\}\; =\; 1\; \backslash tfrac\{3\}\{8\}\; \backslash ,\; \backslash text\{kg\}$kg

b) Total cost

$1\frac{3}{8}\times 120=\frac{11}{8}\times 120=\frac{1320}{8}=1651\; \backslash tfrac\{3\}\{8\}\; \backslash times\; 120\; =\; \backslash frac\{11\}\{8\}\; \backslash times\; 120\; =\; \backslash frac\{1320\}\{8\}\; =\; 165$

Q36. If a = 4 and b = 3, evaluate the expression 2a² + 3b² – ab. Show all substitutions and calculations.  (4 marks)

Ans: Substitute a = 4, b = 3:
a² = 4² = 16, so 2a² = 2 × 16 = 32.
b² = 3² = 9, so 3b² = 3 × 9 = 27.
ab = 4 × 3 = 12.
Expression: 32 + 27 – 12 = 59 – 12 = 47.
(Note: Recalculated; correct answer is 47, not 29, based on steps.)

Q37. Compare the numbers 78,90,123 and 78,09,123 using place value analysis and write the numbers in words.  (4 marks)

Ans: 78,90,123 > 78,09,123

• 78,90,123: Seventy-eight lakh ninety thousand one hundred twenty-three.
• 78,09,123: Seventy-eight lakh nine thousand one hundred twenty-three.

Place value analysis: Both have same digits up to lakh (78). 
In ten-thousands place: 9 vs 0, so 78,90,123 > 78,09,123.