DIRECTION: In the question number 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. Assertion(A): The sequence -1, -1 - 1, …, -1 is an AP. Reason(R): In an AP, a_n - an-1 is constant where n ≥ 2 and n N (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 · Basic · Sample paper, session 2024-25 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Basic sample paper 2024-25: question 19

From the official CBSE sample question paper for 2024-25, 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-basedArithmetic Progressions

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

Assertion(A): The sequence $- 1, - 1 - 1, \dots, - 1$ is an AP.

Reason(R): In an AP, $a_{n} - a_{n - 1}$ is constant where $n \geq 2$ and $n \in N$

(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 2024-25.

Hints

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

Hint 1

Find the difference between consecutive terms.

Hint 2

Is a constant sequence an AP?

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 terms are constant (each is -1), so every difference is 0, which is constant. Hence the sequence is an AP and A is true.
R is the definition of an AP, so it is true and correctly explains A: option (A).
1 mark

Answer: Option (A)

Where the marks are

Recognises common difference 0 and that R is the definition of an AP (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 2024-25 (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 sample paper 2024-25: question 19

Hints

Step-by-step solution

Revise the chapter

More questions from Arithmetic Progressions