1. Which rule gives the perimeter of a square whose side is l?
- Al + 4
- B2l
- Cl × l
- D4l
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Answer: D) 4l
A square has four equal sides, so perimeter = l + l + l + l = 4l. (l × l gives the area, not the perimeter.)
Class 6 Rules and Formulas with Variables — practice questions with answers
Algebra · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. Each side of this regular pentagon is s. Which rule gives its perimeter?
- As + 5
- B5s
- C6s
- D4s
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Answer: B) 5s
A pentagon has 5 sides, all equal to s, so perimeter = 5 × s = 5s.
3. A circle has diameter d. Which rule gives its radius?
- A2d
- B
- Cd + 2
- Dd − 2
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Answer: B)
The radius is half the diameter, so r = . Example: d = 10 cm gives r = 5 cm.
4. A rectangular hall has area 72 sq m and length 9 m. Using A = l × b, what is its breadth?
- A8 m
- B81 m
- C63 m
- D18 m
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Answer: A) 8 m
9 × b = 72, so b = 72 ÷ 9 = 8 m. (63 = 72 − 9; 18 is half of 36.)
5. Raghav says the rule "a − b = b − a" is true because 4 − 4 = 4 − 4. Which choice shows he is wrong?
- Aa = 0, b = 0
- Ba = 7, b = 7
- Ca = 5, b = 5
- Da = 9, b = 2
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Answer: D) a = 9, b = 2
One example where it fails is enough: 9 − 2 = 7 but 2 − 9 is not 7. When a = b both sides are 0, so those choices do not test the rule.
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