Identify the function whose graph is given below: (A) ^-1 (x/2 ) (B) ^-1(2x) (C) π-^-1x (D) π+^-1x

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

CBSE Class 12 Mathematics sample paper 2026-27: question 1

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

Q1 · 1 mark · MCQInverse Trigonometric Functions

Identify the function whose graph is given below:

(A) $cos^{- 1} (\frac{x}{2})$
(B) $cos^{- 1} (2 x)$
(C) $π - cos^{- 1} x$
(D) $π + cos^{- 1} x$

Figure in the paper: Graph on X-Y axes (x from -2 to 2, y marked -π, π, 2π, 3π) showing a decreasing curve starting near x=-1 at y about 2π... ending near x=1 at y about π, passing through about (0, 3π/2). See it in the official paper.

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

Read the domain and the range from the graph.

Hint 2

Compare these with the domain and range of $cos^{- 1} x$ .

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 curve is defined only for $x \in [- 1, 1]$ and decreases, like $cos^{- 1} x$ , whose range is $[0, π]$ .
Its values run from $2 π$ at $x = - 1$ down to $π$ at $x = 1$ , so it is $cos^{- 1} x$ shifted up by $π$ . Check: at $x = 0$ , $π + \frac{π}{2} = \frac{3 π}{2}$ . Hence the function is $π + cos^{- 1} x$ .
1 mark

Answer: $π + cos^{- 1} x$ , option (D)

Where the marks are

Identifies the graph as $cos^{- 1} x$ shifted up by $π$ (1 mark)

Revise the chapter

Chapter: Inverse Trigonometric Functions (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Inverse Trigonometric Functions, 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 1

Hints

Step-by-step solution

Revise the chapter

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