MathsCBSE Class 12 · Sample paper, session 2025-26 · 1 mark · MCQ

CBSE Class 12 Mathematics sample paper 2025-26: question 16

From the official CBSE sample question paper for 2025-26, section A, question 16, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q16 · 1 mark · MCQLinear Programming

A student of class XII studying Mathematics comes across an incomplete question in a book.

Maximise $Z = 3 x + 2 y + 1$
Subject to the constraints $x \geq 0, y \geq 0, 3 x + 4 y \leq 12$ ,

He/She notices the below shown graph for the said LPP problem, and finds that a constraint is missing in it:
Help him/her choose the required constraint from the graph.
The missing constraint is

(A) $x + 2 y \leq 2$
(B) $2 x + y \geq 2$
(C) $2 x + y \leq 2$
(D) $x + 2 y \geq 2$

Figure in the paper: Graph with a shaded (hatched) feasible region in the first quadrant bounded by the axes, the line 3x+4y=12 (intercepts (4,0) and (0,3)) and another line passing through about (1,0) and (0,2) (the missing constraint line); the shaded region lies between the two lines. 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

Write the equation of the line through the two intercepts.

Hint 2

Is the origin inside the shaded region?

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 line through $(1, 0)$ and $(0, 2)$ is $2 x + y = 2$ .
The feasible region lies away from the origin (testing $(0, 0)$ gives $0 \geq 2$ , false, and the origin is not shaded), so the constraint is $2 x + y \geq 2$ . Option (B).
1 mark

Answer: $2 x + y \geq 2$ , option (B)

Where the marks are

Finds the line $2 x + y = 2$ and picks the side not containing the origin (1 mark)

Revise the chapter

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

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 2025-26: 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 2025-26: question 16

Hints

Step-by-step solution

Revise the chapter

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