MathsCBSE Class 12 · Board exam 2023, set 65/1/1 · 1 mark · MCQ

CBSE Class 12 Mathematics 2023: question 18

Set in the CBSE Class 12 board exam of 2023, paper 65/1/1, section A, question 18, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q18 · 1 mark · MCQLinear Programming

The number of corner points of the feasible region determined by the constraints $x - y \geq 0$ , $2 y \leq x + 2$ , $x \geq 0$ , $y \geq 0$ is :

(A) $2$
(B) $3$
(C) $4$
(D) $5$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 65/1/1.

Hints

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

Hint 1

Draw $y = x$ and $y = (x + 2) /2$ .

Hint 2

Find where they meet and check the origin.

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.

Lines $y = x$ and $2 y = x + 2$ meet at (2,2); region with $y \leq x$ , $2 y \leq x + 2$ , $y \geq 0$ is unbounded, bounded by $y = 0$ from (0,0), and edges from (0,0) to (2,2) and beyond along $2 y = x + 2$ .
½ mark
Corner points: (0,0) and (2,2), i.e. 2. Option (A).
½ mark

Answer: 2, option (A)

Where the marks are

Identifies corners (0,0),(2,2) (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 paper2023 board paper, set 65/1/1: 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.

CBSE Class 12 Mathematics 2023: question 18

Hints

Step-by-step solution

Revise the chapter

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