MathsCBSE Class 12 · Sample paper, session 2026-27 · 1 mark · MCQ

CBSE Class 12 Mathematics sample paper 2026-27: question 9

From the official CBSE sample question paper for 2026-27, section A, question 9, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q9 · 1 mark · MCQApplication of Derivatives

If $y = a {x + 2 a sin (\frac{x}{a})}$ , $a > 0$ , $x \in [0, π a]$ ; is a decreasing function, then the interval in which $x$ lies is

(A) $(\frac{5 π}{6}, π]$
(B) $(\frac{2 π}{3}, π]$
(C) $(\frac{5 π a}{- 6}, π a]$
(D) $(\frac{2 π a}{3}, π a]$

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

Differentiate $y$ with respect to $x$ .

Hint 2

Find where $cos \frac{x}{a} < - \frac{1}{2}$ on $[0, π]$ .

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.

$y^{'} = a (1 + 2 cos \frac{x}{a})$ . For $y$ to decrease, $y^{'} < 0$ , so $cos \frac{x}{a} < - \frac{1}{2}$ .
Since $\frac{x}{a} \in [0, π]$ , we need $\frac{x}{a} \in (\frac{2 π}{3}, π]$ , i.e. $x \in (\frac{2 π a}{3}, π a]$ .
1 mark

Answer: Option (D)

Where the marks are

Solves $y^{'} < 0$ to get the interval (1 mark)

Revise the chapter

Chapter: Application of Derivatives (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Application of Derivatives, 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 9

Hints

Step-by-step solution

Revise the chapter

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