Sample Question Paper Class 7 Mathematics Set 3 (Solutions)

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 (12 × 1 = 12 Marks)

Q1. Write the smallest 8-digit number in the Indian place value system.
(a) 10,00,000
(b) 1,00,00,000
(c) 1,00,000
(d) 10,00,00,000

Ans: (b)
An 8-digit number begins from one crore, written as 1,00,00,000.

Q2. Which triangle congruence condition uses the hypotenuse?
(a) SSS
(b) SAS
(c) RHS
(d) ASA

Ans: (c)
RHS is used only for right-angled triangles and includes the hypotenuse and one side.

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

Ans: (a)
According to BODMAS, multiplication is done first: 4 × 3 = 12, then 10 + 12 = 22.

Q4. The LCM of two different prime numbers m and n is:
(a) 1
(b) m + n
(c) m × n
(d) m - n

Ans: (c)
Since prime numbers have no common factors, their LCM is their product.

Q5. What is the decimal form of 9/25?
(a) 0.36
(b) 0.9
(c) 0.25
(d) 0.09

Ans: (a)
9 ÷ 25 = 0.36.

Q6. If a data set has an even number of values, the median is:
(a) The middle value
(b) The total sum
(c) The average of the two middle values
(d) The mode

Ans: (c)
For an even number of observations, the median is the average of the two middle values.

Q7. Can sides 2 cm, 6 cm and 8 cm form a triangle?
(a) Yes
(b) No
(c) Only acute
(d) Only obtuse

Ans: (b)
The sum of two sides (2 + 6 = 8) is equal to the third side, so a triangle cannot be formed.

Q8. Dividing a number by 0.1 is equivalent to multiplying it by:
(a) 0.1
(b) 1
(c) 10
(d) 100

Ans: (c)
Dividing by 0.1 shifts the decimal one place to the right, which is multiplying by 10.

Q9. What is the parity of the sum of three odd numbers?
(a) Even
(b) Odd
(c) Zero
(d) Cannot be determined

Ans: (b)
Odd + Odd = Even, and Even + Odd = Odd.

Q10. A 60° angle can be constructed using which polygon?
(a) Square
(b) Regular hexagon
(c) Equilateral triangle
(d) Pentagon

Ans: (c)
Each angle of an equilateral triangle measures 60°.

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

Ans: (a)
0.8 = 8/10 = 4/5 after simplification.

Q12. Which term was used by Bhaskaracharya for "Mean"?
(a) Samarajju
(b) Samamiti
(c) Samikarana
(d) Bijaganita

Ans: (b)
"Samamiti" refers to equal distribution, which represents the mean.

Section B (12 × 2 = 24 Marks)

Q13. Write 8,12,34,567 in words using the Indian number system.

Ans:
Eight crore twelve lakh thirty-four thousand five hundred sixty-seven.

Q14. Find the prime factorisation of 105.

Ans:
105 ÷ 3 = 35
35 ÷ 5 = 7
So, 105 = 3 × 5 × 7.

Q15. Simplify: 30 ÷ 5 + 4 × 2.

Ans:
30 ÷ 5 = 6
4 × 2 = 8
6 + 8 = 14.

Q16. Solve: 4k + 1 = 13.

Ans:
4k = 12
k = 3.

Q17. Convert 1.25 into a fraction in simplest form.

Ans:
1.25 = 125/100 = 5/4.

Q18. Find the HCF of 84 and 180.

Ans: Write all factors of 84 and 180 and determine the highest common factor
HCF = 12.

Q19. Form an algebraic expression for "Twice a number p increased by 10."

Ans:
2p + 10.

Q20. Solve: 2y = 60.

Ans:
y = 30.

Q21. Convert 7/20 into a decimal.

Ans:
7 ÷ 20 = 0.35.

Q22. Evaluate: 0.018 × 0.012.

Ans:
0.000216.

Q23. Compare 6.78 and 6.87.

Ans:
6.78 < 6.87.

Q24. Define the RHS congruence condition.

Ans:
Two right-angled triangles are congruent if their hypotenuse and one corresponding side are equal.

Section C - 3 Marks Each

Q25. A factory produced 4,56,789 units in one month. In the next month, it produced 1,78,901 more units.
(a) Find the total production for the two months.
(b) State the place value of digit 5 in the total production.

Ans:
Step 1: Write the numbers in column form.
  4,56,789
+1,78,901
-----------
Step 2: Add column by column from right to left.
Total = 6,35,690 units.
Step 3: Identify the digit 5 in 6,35,690.
It is in the thousands place.
(a) Total production = 6,35,690 units
(b) Place value of 5 = 5,000

Q26. Simplify: 20 ÷ (5 - 3) × 4 + 2.
Also, explain which operation is performed first and why.

Ans:
Step 1: Solve the bracket first.
5 - 3 = 2
Step 2: Divide.
20 ÷ 2 = 10
Step 3: Multiply.
10 × 4 = 40
Step 4: Add.
40 + 2 = 42
According to the BODMAS rule, brackets are solved first, followed by division and multiplication, and finally addition.

Q27. Simplify: 17.05 - [5.8 + (1.23 - 0.7)].
Also, verify your answer using estimation.

Ans:
Step 1: Solve the inner bracket.
1.23 - 0.7 = 0.53
Step 2: Solve the square bracket.
5.8 + 0.53 = 6.33
Step 3: Subtract.
17.05 - 6.33 = 10.72
Verification (Estimation):
17 - 6 ≈ 11, which is close to 10.72.

Q28. If a = 3 and b = 4, find the value of 2a² + b².
Also, state whether the result is even or odd.

Ans:
Step 1: Find a².
a² = 3² = 9
Step 2: Multiply by 2.
2a² = 2 × 9 = 18
Step 3: Find b².
b² = 4² = 16
Step 4: Add.
18 + 16 = 34
Step 5: Check parity.
34 is divisible by 2, so it is even.

Q29. Write 7,89,12,345 in expanded form using powers of 10.
Also, write the highest place value.

Ans:
Expanded form:
7 × 10⁷ + 8 × 10⁶ + 9 × 10⁵ + 1 × 10⁴ + 2 × 10³ + 3 × 10² + 4 × 10¹ + 5 × 10⁰
Highest place value = 7 × 10⁷

Q30. ΔABC and ΔXYZ have ∠B = ∠Y = 50°, ∠C = ∠Z = 30°, and BC = YZ = 5 cm. Are the triangles congruent? Justify

Ans:

Given:
∠B = ∠Y = 50°
∠C = ∠Z = 30°
BC = YZ

Here, two angles and the included side of ΔABC are equal to the corresponding two angles and included side of ΔXYZ.

Therefore, by the ASA (Angle-Side-Angle) congruence condition,
ΔABC ≅ ΔXYZ.

Q31. Form and simplify an algebraic expression for:
"A number n multiplied by 5 and decreased by four times the same number."

Ans:
Step 1: Five times the number = 5n
Step 2: Four times the number = 4n
Step 3: Decreased by means subtraction.
Expression = 5n - 4n = n

Q32. Convert 0.625 into a fraction and verify your answer by converting it back into a decimal.

Ans:
Step 1: Convert decimal to fraction.
0.625 = 625/1000
Step 2: Simplify by dividing by 125.
625 ÷ 125 = 5
1000 ÷ 125 = 8
Fraction = 5/8
Verification:
5 ÷ 8 = 0.625

Section D - 4 Marks Each

Q33. Maya fills a 2 x 2 grid with prime numbers such that the product of the first row is 15 and the second row is 35. The first column's product is 21, and the second column's is 25. What are the numbers?

Ans:

 Grid:

• Row 1: a × b = 15 (primes: 3 × 5).
• Row 2: c × d = 35 (primes: 5 × 7).
• Column 1: a × c = 21 (primes: 3 × 7).
• Column 2: b × d = 25 (primes: 5 × 5).

Solve:

• b = 5, d = 5 (from column 2).
• a = 3 (from row 1, since b = 5).
• c = 7 (from column 1, since a = 3).
• Check row 2: c × d = 7 × 5 = 35, correct.
  Grid:

The numbers are 3, 5, 7, 5.

Q34. Simplify the expression 5(4p - 2q) - 3(p - 5q) + 10.
Then evaluate it for p = 1 and q = -1.

Ans:
Step 1: Expand brackets.
5(4p - 2q) = 20p - 10q
-3(p - 5q) = -3p + 15q
Step 2: Combine like terms.
20p - 10q - 3p + 15q + 10 = 17p + 5q + 10
Step 3: Substitute values.
17(1) + 5(-1) + 10 = 17 - 5 + 10 = 22

Q35. A trader buys an item for ₹56.45 and sells it for ₹78.95.
(a) Find the profit.
(b) Express the profit as a fraction.

Ans:
a)
Profit = Selling Price - Cost Price
= 78.95 - 56.45 = ₹22.50
b)
22.5 = 225/10 = 45/2
Hence, Profit = ₹22.50, Fraction = 45/2

Q36. If x = 3 and y = 5, evaluate x² + 2xy - y².
Also, comment on whether the result is positive or negative.

Ans:
x² = 9
2xy = 30
y² = 25
9 + 30 - 25 = 14
14 is greater than 0, so the result is positive.

Q37. Two consecutive numbers in the Virahanka sequence are 987 and 1597.
(a) Find the next two numbers.
(b) Find the previous two numbers.

Ans:
a)
987 + 1597 = 2584
1597 + 2584 = 4181
b)
1597 - 987 = 610
987 - 610 = 377
Next numbers: 2584, 4181
Previous numbers: 610, 377