Q13. 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) 2019 — Paper 30/5/1

80 marks · 3 hours · 30 questions (41 with the OR choices)

3 of its 41 questions have been set in other papers too (each one says where); the other 38 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 1–6 · 1 mark each

Q1 1 mark

This question is in the full bank. Sign up free to see it.
Q2(a) 1 mark

This question is in the full bank. Sign up free to see it.

OR

Q2(b) 1 mark

This question is in the full bank. Sign up free to see it.
Q3 1 mark

This question is in the full bank. Sign up free to see it.
Q4(a) 1 mark

This question is in the full bank. Sign up free to see it.

OR

Q4(b) 1 mark

Also in 2020 · 430/2/1 (Q16(a))

This question is in the full bank. Sign up free to see it.
Q5 1 mark

This question is in the full bank. Sign up free to see it.
Q6 1 mark

This question is in the full bank. Sign up free to see it.

Questions 7–12 · 2 marks each

Q7(a) 2 marks

This question is in the full bank. Sign up free to see it.

OR

Q7(b) 2 marks

This question is in the full bank. Sign up free to see it.
Q8 2 marks

This question is in the full bank. Sign up free to see it.
Q9 2 marks

This question is in the full bank. Sign up free to see it.
Q10(a) 2 marks

This question is in the full bank. Sign up free to see it.

OR

Q10(b) 2 marks

This question is in the full bank. Sign up free to see it.
Q11 2 marks

This question is in the full bank. Sign up free to see it.
Q12 2 marks

This question is in the full bank. Sign up free to see it.

Questions 13–22 · 3 marks each

Q13 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)), 2020 · 30/2/1 (Q35), 2020 · 30/4/1 (Q27)

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.

Step-by-step solution →
Q14 3 marks

This question is in the full bank. Sign up free to see it.
Q15(a) 3 marks

This question is in the full bank. Sign up free to see it.

OR

Q15(b) 3 marks

This question is in the full bank. Sign up free to see it.
Q16(a) 3 marks

This question is in the full bank. Sign up free to see it.

OR

Q16(b) 3 marks

This question is in the full bank. Sign up free to see it.
Q17 3 marks

This question is in the full bank. Sign up free to see it.
Q18(a) 3 marks

This question is in the full bank. Sign up free to see it.

OR

Q18(b) 3 marks

This question is in the full bank. Sign up free to see it.
Q19 3 marks

Also in 2026 · 30(B) (Q29(a)), 2025 · 30/2/1 (Q26(a)), 2025 · 430/S/1 (Q31), 2024 · 30/4/1 (Q31), 2024 · 30/5/1 (Q28), 2024 · 30(B)/S (Q26(a)), 2024 · 430/5/1 (Q29(a)), 2023 · 430/2/1 (Q28(b)), 2022 · 430/6/1 (Q12(a)), 2020 · 30(B) (Q23), 2020 · 430/3/1 (Q32), 2015 · 30(B) (Q25)

This question is in the full bank. Sign up free to see it.
Q20 3 marks

This question is in the full bank. Sign up free to see it.
Q21 3 marks

This question is in the full bank. Sign up free to see it.
Q22(a) 3 marks

This question is in the full bank. Sign up free to see it.

OR

Q22(b) 3 marks

This question is in the full bank. Sign up free to see it.

Questions 23–30 · 4 marks each

Q23(a) 4 marks

This question is in the full bank. Sign up free to see it.

OR

Q23(b) 4 marks

This question is in the full bank. Sign up free to see it.
Q24 4 marks

This question is in the full bank. Sign up free to see it.
Q25 4 marks

This question is in the full bank. Sign up free to see it.
Q26 4 marks

This question is in the full bank. Sign up free to see it.
Q27(a) 4 marks

This question is in the full bank. Sign up free to see it.

OR

Q27(b) 4 marks

This question is in the full bank. Sign up free to see it.
Q28(a) 4 marks

This question is in the full bank. Sign up free to see it.

OR

Q28(b) 4 marks

This question is in the full bank. Sign up free to see it.
Q29 4 marks

This question is in the full bank. Sign up free to see it.
Q30 4 marks

This question is in the full bank. Sign up free to see it.

Other 2019 papers

All CBSE Class 10 Maths papers →