MathsCBSE Class 12 · Sample paper, session 2026-27 · 2 marks · Very short answer

CBSE Class 12 Mathematics sample paper 2026-27: question 25

From the official CBSE sample question paper for 2026-27, section B, question 25, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q25 · 2 marks · Very short answerLinear Programming

The feasible region of a linear programming problem is shown in the given figure:

Write all the constraints on the decision variables involved

Figure in the paper: Graph with X and Y axes, origin O. Lines $x + 2 y = 6$ and $3 x + 2 y = 10$ are drawn. The shaded feasible region is the triangle ABC lying above the x-axis: A is the x-intercept of $3 x + 2 y = 10$ on the x-axis, B is the x-intercept of $x + 2 y = 6$ on the x-axis, and C is the intersection of the two lines. Region is bounded by the x-axis and the two lines, to the right of line 3x+2y=10 and below line x+2y=6. 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

For each boundary line, check which side the shaded region lies on by testing a point such as the origin.

Hint 2

The region is bounded below by the x-axis, which gives one more constraint.

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 lies on the side of $3 x + 2 y = 10$ away from the origin, so $3 x + 2 y \geq 10$ . It lies on the origin side of $x + 2 y = 6$ , so $x + 2 y \leq 6$ . (Check with the interior point $(4, 0.5)$ : $13 \geq 10$ and $5 \leq 6$ .)
1½ marks
The region lies above the x-axis, so $y \geq 0$ . ( $x \geq 0$ is then automatically satisfied.)
½ mark

Answer: $3 x + 2 y \geq 10, x + 2 y \leq 6, y \geq 0$

Where the marks are

Writes $3 x + 2 y \geq 10$ and $x + 2 y \leq 6$ (1½ marks)
Writes $y \geq 0$ (½ mark)

Revise the chapter

Chapter: Linear Programming (notes, formulas, where marks are lost and every past question)
Topic: Feasible Region and Constraints

Practise this chapterBoard-style questions from Linear Programming, one at a time, marked against the answer key and marking points.Back to the full paperSample paper 2026-27: 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 12 Mathematics sample paper 2026-27: question 25

Hints

Step-by-step solution

Revise the chapter

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