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The feasible region of a… (Class 12 Maths SQP 2025-26, Q17)

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

CBSE Class 12 Mathematics sample paper 2025-26: question 17

From the official CBSE sample question paper for 2025-26, section A, question 17, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q17 · 1 mark · MCQLinear Programming

The feasible region of a linear programming problem is bounded but the objective function attains its minimum value at more than one point. One of the points is .

Then one of the other possible points at which the objective function attains its minimum value is

  1. (A)
  2. (B)
  3. (C)
  4. (D)

Figure in the paper: Graph with a shaded bounded feasible region in the first quadrant: a triangle-like region with vertices near (5,0), (10,0) and (0,16), bounded by two lines (one through (5,0) and (0,16), another steeper line) and the x-axis. 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

When the optimum occurs at two points, it occurs on the whole segment joining them.

Hint 2

Which option lies on the boundary line through ?

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.

  1. If the minimum occurs at more than one point, it occurs all along a boundary edge. The edge through and is .

  2. satisfies , so it lies on that edge. Option (A).

    1 mark

Answer: , option (A)

Where the marks are

  • Identifies the edge through and checks that lies on it (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.