Q26. 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) 2023 — Paper 30/C/B

80 marks · 3 hours · 38 questions (44 with the OR choices)

5 of its 44 questions have been set in other papers too (each one says where); the other 39 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

Q1 1 mark

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Q2 1 mark

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Q10 1 mark

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Q11 1 mark

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Q12 1 mark

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Q13 1 mark

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Questions 21–25 · 2 marks each

Q21 2 marks

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Q22 2 marks

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Q23(a) 2 marks

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Q23(b) 2 marks

Also in 2025 · 30/1/1 (Q28)

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Q24 2 marks

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Q25(a) 2 marks

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Q25(b) 2 marks

Also in 30(B)/5 (Q30)

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Questions 26–31 · 3 marks each

Q26 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)), 30/1/1 (Q27), 30/4/1 (Q27), 430/C/1 (Q29(b)), 2020 · 30/2/1 (Q35), 2020 · 30/4/1 (Q27), 2019 · 30/5/1 (Q13)

Prove that $5$ is an irrational number.

Show answer

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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Q27 3 marks

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Q28 3 marks

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Q29(a) 3 marks

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Q29(b) 3 marks

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Q30(a) 3 marks

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Q30(b) 3 marks

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Q31 3 marks

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Questions 32–35 · 5 marks each

Q32(a) 5 marks

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Q32(b) 5 marks

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Q33(a) 5 marks

Also in 2025 · 30/1/1 (Q26(b)), 2024 · 430/4/1 (Q27(a)), 2019 · 30/3/1 (Q19(b))

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Q33(b) 5 marks

Also in 2025 · 430(B)/S (Q33(b)), 2024 · 430/5/1 (Q29(b)), 430/C/1 (Q33), 2016 · 30/1 (Q22), 2016 · 30/3 (Q27), 2015 · 30/1 (Q24)

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Q34 5 marks

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Q35 5 marks

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Questions 36–38 · 4 marks each

Q36 4 marks

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Q37 4 marks

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Q38 4 marks

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Other 2023 papers

All CBSE Class 10 Maths papers →