SEBA Class 10 Mathematics Revision (R-1) All Question Answers

Are you preparing for your SEBA HSLC Examination? The Revision Chapter (R-1) in the General Mathematics textbook is crucial for building a strong foundation. This chapter covers essential topics like Ratio (অনুপাত), Proportion (সমানুপাত), and Variation (বিচৰণ).

Below, we have provided the complete solved answers for Exercise R-1. These solutions are designed for both English and Assamese medium students to understand the logic easily.

Q1. Which of the following ratios form a proportion?

Original Question (Assamese): তলৰ কোনটো অনুপাত একোটা সমানুপাত হ’ব?

To check if two ratios form a proportion, their simplified forms must be equal ($ \frac{a}{b} = \frac{c}{d} $).

• Option (a): 12 : 21 and 32 : 56
  Simplifying 12/21 (divide by 3) = 4/7
  Simplifying 32/56 (divide by 8) = 4/7
  Result: They are equal.


• Option (b): 18 : 30 and 14 : 21
  Simplifying 18/30 = 3/5
  Simplifying 14/21 = 2/3
  Result: Not equal.

Q2. Which of the following sets of numbers are in proportion?

Original Question (Assamese): তলৰ কোনবোৰ সংখ্যা ক্ৰমে সমানুপাতত থাকিব?

For numbers to be in proportion, the ratio of the first two must equal the ratio of the last two.

• (a) 2, 6, 6, 8: 2/6 = 1/3, but 6/8 = 3/4. (Not Proportional)
• (b) 10, 20, 30, 60:
  10/20 = 1/2
  30/60 = 1/2
  They are proportional.

Q3. Fill in the blanks (Variation Problems)

Original Question (Assamese): খালী ঠাই পূৰোৱা

(i) Area of a Circle

Formula: A = πr²

• If A increases, then radius (r) increases (বাঢ়ে).
• If r decreases, then Area (A) decreases (কমে).

(ii) Time (t) and Distance (d) Table

Time (t)	1	2	3	4	5	6	7	8	9
Dist (d)	4	8	12	16	20	24	28	32	36

Analysis: Since d/t is always 4, this is Direct Variation.

• (a) t and d vary directly (প্ৰত্যক্ষ ভাবে).
• (b) If t = 6, then d = 4 × 6 = 24.
• (c) If d = 28, then t = 28 ÷ 4 = 7.
• (d) If d = 36, then t = 36 ÷ 4 = 9.

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Q4. Direct Proportion Calculation

Question: If p ∝ q and p = 6 when q = 30, find q when p = 2.

Solution:
Since p varies directly as q, p = k × q.
First, find k: 6 = k × 30 → k = 1/5.
Now, put p = 2:
2 = (1/5) × q
q = 2 × 5
q = 10

Q5. Inverse Variation (Table Calculation)

Question: Find the value of y in the table.

x	1	2	4	8
y	32	16	8	?

Solution:
Check the product of x and y:
1 × 32 = 32
2 × 16 = 32
Since the product is constant, this is Inverse Variation.
To find the missing value:
8 × y = 32
y = 32 ÷ 8
y = 4