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Assertion (A) : Consider a… (Class 12 Maths 2026, Q20)

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MathsCBSE Class 12 · Board exam 2026, set 65/5/1 · 1 mark · Assertion-reason

CBSE Class 12 Mathematics 2026: question 20

Set in the CBSE Class 12 board exam of 2026, paper 65/5/1, section A, question 20, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q20 · 1 mark · Assertion-reasonCompetency-basedLinear Programming

Assertion (A) : Consider a Linear Programming Problem with minimise subject to constraints , , which gives minimum Z at infinitely many points. The corner points of feasible region are (0, 3) and (6, 0).

Reason (R) : If two corner points produce the same minimum value of the objective function, then every point on the line segment joining the points will give the same minimum value.

  1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
  2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
  3. (C)Assertion (A) is true, but Reason (R) is false.
  4. (D)Assertion (A) is false, but Reason (R) is true.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 65/5/1.

Hints

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

Hint 1

Evaluate Z at both corners.

Hint 2

Region is unbounded — check x+2y<6.

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. Unbounded region with corners (0,3) and (6,0): Z=6 at both. Half-plane x+2y<6 has no common point with region, so min 6 holds on whole segment — infinitely many points. A true.

    ½ mark

  2. R is the standard result that explains A. Option (A).

    ½ mark

Answer: Option (A)

Where the marks are

  • Z = 6 at both corners, min verified (½ mark)
  • R explains A (½ mark)

Revise the chapter

Practise this chapterBoard-style questions from Linear Programming, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 65/5/1: 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.