Q27. Prove that √5 is an irrational number.

Assuming √5 = a/b with a, b coprime and b ≠ 0 leads to 5 dividing both a and b, contradicting that they are coprime. Hence the assumption is wrong and √5 is an irrational number.

CBSE Class 10 Maths (Standard) 2020 — Paper 30/4/1

80 marks · 3 hours · 40 questions (50 with the OR choices)

3 of its 50 questions have been set in other papers too (each one says where); the other 47 are only in this paper.

Take this paper as a timed mock

Free with an account: the board's time limit, marking at the end, and the answer to every question.

Questions 1–20 · 1 mark each

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Questions 21–26 · 2 marks each

Q21 2 marks

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Q22(a) 2 marks

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Questions 27–34 · 3 marks each

Q27 3 marks

Also in 2026 · 30/2/1 (Q26), 2026 · 30/3/1 (Q28), 2026 · 430/3/1 (Q26), 2026 · 430/4/1 (Q29), 2025 · 30/6/1 (Q26(a)), 2025 · 30(B) (Q26), 2025 · 430/2/1 (Q26(a)), 2024 · 30/2/1 (Q27), 2024 · 30(B)/S (Q29), 2024 · 430/S/1 (Q26(a)), 2023 · 30/1/1 (Q27), 2023 · 30/4/1 (Q27), 2023 · 30/C/B (Q26), 2023 · 430/C/1 (Q29(b)), 30/2/1 (Q35), 2019 · 30/5/1 (Q13)

Prove that $5$ is an irrational number.

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Assuming $5 = \frac{a}{b}$ with $a, b$ coprime and $b \neq = 0$ leads to $5$ dividing both $a$ and $b$ , contradicting that they are coprime. Hence the assumption is wrong and $5$ is an irrational number.

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Q28 3 marks

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Q29(a) 3 marks

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Q31(b) 3 marks

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Q32 3 marks

Also in 2025 · 30(B)/S (Q27(a))

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Q33 3 marks

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Questions 35–40 · 4 marks each

Q35(a) 4 marks

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Q35(b) 4 marks

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Q36 4 marks

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Q37(a) 4 marks

Also in 2026 · 30(B) (Q32(a)), 2026 · 430/4/1 (Q33(a)), 2026 · 430/5/1 (Q32(b)), 2025 · 30(B) (Q33), 2025 · 430/4/1 (Q34(a)), 2025 · 430/5/1 (Q33(a)), 2024 · 30/1/1 (Q34(a)), 2024 · 30/2/1 (Q33(a)), 2024 · 30(B)/S (Q34), 2024 · 430/1/1 (Q32(a)), 2023 · 430/2/1 (Q34), 2019 · 30/2/1 (Q23)

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Q37(b) 4 marks

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Other 2020 papers

All CBSE Class 10 Maths papers →