Assertion: The value of the integral -1^1 x-2 dx is 4 Reason: If f(-x)=f(x) then -a^af(x)dx=20^af(x)dx (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 but 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 12 · Sample paper, session 2026-27 · 1 mark · Assertion-reason

CBSE Class 12 Mathematics sample paper 2026-27: question 19

From the official CBSE sample question paper for 2026-27, 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-basedIntegrals

Assertion: The value of the integral $\int_{- 1}^{1} ∣ x - 2∣ d x$ is 4
Reason: If $f (- x) = f (x)$ then $\int_{- a}^{a} f (x) d x = 2 \int_{0}^{a} f (x) d x$

(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 but 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 2026-27.

Hints

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

Hint 1

Find the sign of $x - 2$ on $[- 1, 1]$ .

Hint 2

Check whether $∣ x - 2∣$ is an even function.

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.

On $[- 1, 1]$ we have $x - 2 < 0$ , so $∣ x - 2∣ = 2 - x$ . Then $\int_{- 1}^{1} (2 - x) d x = 4 - 0 = 4$ , so the Assertion is true.
The Reason is a true property of even functions. However, $∣ x - 2∣$ is not even, so the Reason does not explain the Assertion.
1 mark

Answer: Option (B)

Where the marks are

Evaluates the integral and judges the Reason correctly (1 mark)

Revise the chapter

Chapter: Integrals (notes, formulas, where marks are lost and every past question)
Topic: Properties of Definite Integrals

Practise this chapterBoard-style questions from Integrals, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2026-27: every question, by section.

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CBSE Class 12 Mathematics sample paper 2026-27: question 19

Hints

Step-by-step solution

Revise the chapter

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