MathsCBSE Class 10 · Basic · Board exam 2024, set 430/3/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Basic 2024: question 19

Set in the CBSE Class 10 board exam of 2024, paper 430/3/1, section A, question 19, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q19 · 1 mark · Assertion-reasonCompetency-basedCoordinate Geometry

Directions: In question numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option from the following: (A) Both Assertion (A) and Reason (R) are true. Reason (R) is the correct explanation of Assertion (A). (B) Both Assertion (A) and Reason (R) are true. Reason (R) is not the correct explanation of Assertion (A). (C) Assertion (A) is true, but Reason (R) is false. (D) Assertion (A) is false, but Reason (R) is true.

Assertion (A): The distance of $P (a, b)$ from origin is $a^{2} + b^{2}$ .

Reason (R): The distance between two points $A (x_{1}, y_{1})$ and $B (x_{2}, y_{2})$ is $(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}$ .

(A)Both Assertion (A) and Reason (R) are true. Reason (R) is the correct explanation of Assertion (A).
(B)Both Assertion (A) and Reason (R) are true. Reason (R) is not the correct explanation of Assertion (A).
(C)Assertion (A) is true, but Reason (R) is false.
(D)Assertion (A) is false, but Reason (R) is true.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2024 board paper, set 430/3/1.

Hints

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

Hint 1

Is the Reason, the distance formula, correct as written?

Hint 2

Apply the distance formula to O(0, 0) and P(a, b). What do you get?

Hint 3

The distance is √(a² + b²), but the Assertion claims a² + b² without the square root.

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.

Reason (R) is the distance formula $(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}$ , which is a true statement.
Using R with $O (0, 0)$ and $P (a, b)$ : $O P = (a - 0)^{2} + (b - 0)^{2} = a^{2} + b^{2}$ , not $a^{2} + b^{2}$ . So the Assertion is false while the Reason is true. Option (D).
1 mark

Answer: (D) Assertion (A) is false, but Reason (R) is true.

Where the marks are

Recognises that OP = √(a² + b²) ≠ a² + b², so A is false while R (distance formula) is true; chooses option (D) (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 paper2024 board paper, set 430/3/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Basic 2024: question 19

Hints

Step-by-step solution

Revise the chapter

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