MathsCBSE Class 12 · Sample paper, session 2025-26 · 2 marks · Very short answer

CBSE Class 12 Mathematics sample paper 2025-26: question 23(B)

From the official CBSE sample question paper for 2025-26, section B, question 23(B), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q23(B) · 2 marks · Very short answerApplication of Integrals

Find out the area of shaded region in the enclosed figure.

Figure in the paper: Parabola $x^{2} = y$ with vertex O at origin, and the horizontal line $y = 4$ meeting the parabola at A (left) and B (right); N is the point where y=4 meets the Y-axis. The shaded region is the part between the parabola and the line y=4 on the right of the Y-axis (region ONB). See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2025-26.

Hints

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

Hint 1

The region is bounded on the left by the Y-axis, so integrate with respect to $y$ .

Hint 2

Express $x$ in terms of $y$ from $x^{2} = y$ and integrate from 0 to 4.

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 region ONB lies between the Y-axis and the parabola $x^{2} = y$ (right branch $x = y$ ), from $y = 0$ to $y = 4$ . So Area $= \int_{0}^{4} x d y = \int_{0}^{4} y d y$ .
1 mark
$= [\frac{2}{3} y^{3/2}]_{0}^{4} = \frac{2}{3} (8 - 0) = \frac{16}{3}$ sq. units.
1 mark

Answer: $\frac{16}{3}$ sq. units

Where the marks are

Sets up area as $\int_{0}^{4} y d y$ (1 mark)
Evaluates to $16/3$ sq. units (1 mark)

Revise the chapter

Chapter: Application of Integrals (notes, formulas, where marks are lost and every past question)
Topic: Area Under Lines and Modulus Graphs

Practise this chapterBoard-style questions from Application of Integrals, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2025-26: every question, by section.

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CBSE Class 12 Mathematics sample paper 2025-26: question 23(B)

Hints

Step-by-step solution

Revise the chapter

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