The distance between the points ( 30°, 30°) and ( 60°, - 60°) is (A) 0 unit (B) √(3) units (C) 1 unit (D) √(2) units

MathsCBSE Class 10 · Basic · Sample paper, session 2025-26 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic sample paper 2025-26: question 7

From the official CBSE sample question paper for 2025-26, section A, question 7, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q7 · 1 mark · MCQCoordinate Geometry

The distance between the points $(cos 3 0^{\circ}, sin 3 0^{\circ})$ and $(cos 6 0^{\circ}, - sin 6 0^{\circ})$ is

(A)0 unit
(B) $3$ units
(C)1 unit
(D) $2$ units

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

Open one hint at a time and try again before the next.

Hint 1

First write down the values of cos 30°, sin 30°, cos 60° and sin 60°.

Hint 2

Then apply the distance formula.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

The points are $(\frac{3}{2}, \frac{1}{2})$ and $(\frac{1}{2}, - \frac{3}{2})$ .
$d^{2} = (\frac{3 - 1}{2})^{2} + (\frac{1 + 3}{2})^{2} = \frac{( 4 - 2 3 ) + ( 4 + 2 3 )}{4} = 2$ .
So $d = 2$ units, option (D).
1 mark

Answer: $2$ units, option (D)

Where the marks are

Substitutes the trigonometric values in the distance formula and gets $2$ (1 mark)

Revise the chapter

Chapter: Coordinate Geometry (notes, formulas, where marks are lost and every past question)
Topic: Distance Formula

Practise this chapterBoard-style questions from Coordinate Geometry, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2025-26 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic sample paper 2025-26: question 7

Hints

Step-by-step solution

Revise the chapter

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