Q25. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Since ∠PAB = ∠ABS = 90° and these are alternate angles made by the transversal AB, the tangents PQ and RS at the ends of the diameter AB are parallel. Hence proved.

CBSE Class 10 Maths (Standard) 2025 — Paper 30/3/1

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

3 of its 44 questions have been set in other papers too (each one says where); the other 41 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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Q3 1 mark

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Q10 1 mark

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Q11 1 mark

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Q15 1 mark

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Q20 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

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Q24(a) 2 marks

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Q24(b) 2 marks

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Q25 2 marks

Also in 430/4/1 (Q24(b)), 2024 · 30/5/1 (Q21(b)), 2024 · 30(B)/S (Q26(b))

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Show answer

Since $∠ P A B = ∠ A B S = 9 0^{\circ}$ and these are alternate angles made by the transversal $A B$ , the tangents $P Q$ and $R S$ at the ends of the diameter $A B$ are parallel. Hence proved.

Step-by-step solution →

Questions 26–31 · 3 marks each

Q26(a) 3 marks

Also in 2020 · 30/2/1 (Q30(a))

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Q26(b) 3 marks

Also in 2024 · 30(B)/S (Q33)

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Q27 3 marks

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Q28(a) 3 marks

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Q28(b) 3 marks

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Q29 3 marks

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Q30 3 marks

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Q31 3 marks

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Questions 32–35 · 5 marks each

Q32 5 marks

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Q33(a) 5 marks

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Q33(b) 5 marks

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Q34(a) 5 marks

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Q34(b) 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 2025 papers

All CBSE Class 10 Maths papers →