DIRECTIONS: In the question number 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option out of the following. Assertion (A): a, b, c are in A.P. if and only if 2b = a + c. Reason (R): The sum of first n odd natural numbers is n². (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 · Board exam 2023, set 30/4/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2023: question 20

Set in the CBSE Class 10 board exam of 2023, paper 30/4/1, 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

DIRECTIONS: In the question number 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option out of the following.

Assertion (A): a, b, c are in A.P. if and only if $2 b = a + c$ .

Reason (R): The sum of first n odd natural numbers is $n^{2}$ .

(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 question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/4/1.

Hints

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

Hint 1

Check A using the idea of a common difference.

Hint 2

Check R using $S_{n} = \frac{n}{2} (a + l)$ , then ask whether R explains A.

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.

a, b, c are in A.P. $⟺ b - a = c - b ⟺ 2 b = a + c$ . Hence A is true.
$1 + 3 + \dots + (2 n - 1) = \frac{n}{2} [1 + (2 n - 1)] = n^{2}$ . Hence R is true.
R is about the sum of odd numbers and does not explain the condition for three numbers to be in A.P. The answer is option (B).
1 mark

Answer: Option (B): both true, R not the correct explanation of A

Where the marks are

Chooses option (B) (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 paper2023 board paper, set 30/4/1 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard 2023: question 20

Hints

Step-by-step solution

Revise the chapter

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