Statement A (Assertion): -5, (-5)/(2), 0, 5/2, … is in Arithmetic Progression. Statement R (Reason): The terms of an Arithmetic Progression cannot have both positive and negative rational numbers. (A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) (B) Both assertion (A) and reason (R) are true and 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.

MathsCBSE Class 10 · Standard · Sample paper, session 2023-24 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard sample paper 2023-24: question 20

From the official CBSE sample question paper for 2023-24, section A, question 20, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q20 · 1 mark · Assertion-reasonCompetency-basedArithmetic Progressions

Statement A (Assertion): $- 5, \frac{- 5}{2}, 0, \frac{5}{2}, \dots$ is in Arithmetic Progression.

Statement R (Reason): The terms of an Arithmetic Progression cannot have both positive and negative rational numbers.

(A)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
(B)Both assertion (A) and reason (R) are true and 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 sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Check whether successive differences are equal.

Hint 2

Does the given sequence itself contradict R?

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 differences are $- \frac{5}{2} - (- 5) = \frac{5}{2}$ , $0 - (- \frac{5}{2}) = \frac{5}{2}$ and $\frac{5}{2} - 0 = \frac{5}{2}$ . They are constant, so A is true.
This very AP contains both negative and positive terms, so R is false. Option (C).
1 mark

Answer: Option (C)

Where the marks are

Shows the common difference is $\frac{5}{2}$ (A true) and R is false, option (C) (1 mark)

Revise the chapter

Chapter: Arithmetic Progressions (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Arithmetic Progressions, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2023-24 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2023-24: question 20

Hints

Step-by-step solution

Revise the chapter

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