MathsCBSE Class 12 · Sample paper, session 2023-24 · 1 mark · MCQ

CBSE Class 12 Mathematics sample paper 2023-24: question 11

From the official CBSE sample question paper for 2023-24, section A, question 11, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q11 · 1 mark · MCQLinear Programming

The feasible region corresponding to the linear constraints of a Linear Programming Problem is given below. Which of the following is not a constraint to the given Linear Programming Problem?

(A) $x + y \geq 2$
(B) $x + 2 y \leq 10$
(C) $x - y \geq 1$
(D) $x - y \leq 1$

Figure in the paper: Graph with shaded feasible region bounded by lines x+y=2 (through (2,0) and (0,2)), x-y=1 (through (1,0)), and x+2y=10 (through (10,0) and (0,5)); the shaded region has corner points near (0,5) and (0,2) on the y-axis, and lies to the left of the line x-y=1. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

Pick a point inside the shaded region.

Hint 2

Check which inequality that point fails.

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 shaded region contains points near the origin side, such as $(0, 3)$ . Test $(0, 3)$ in $x - y \geq 1$ : $0 - 3 = - 3 \neq \geq 1$ . So that half-plane does not contain the region.
Hence $x - y \geq 1$ is not a constraint; the region in fact satisfies $x - y \leq 1$ . The answer is option (C).
1 mark

Answer: $x - y \geq 1$ , option (C)

Where the marks are

Tests a point of the region against $x - y \geq 1$ and rejects it (1 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 2023-24: 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 2023-24: question 11

Hints

Step-by-step solution

Revise the chapter

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