Class CBSE Class 12 Mathematics Linear Programming Q #833
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
16. Which of the following points satisfies both the inequations $2x+y\le10$ and $x+2y\ge8$?
(A) $(-2,4)$
(B) $(3,2)$
(C) $(-5,6)$
(D) $(4, 2)$
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Step-by-Step Solution

  1. Check option (A) $(-2,4)$:

    • $2x+y = 2(-2) + 4 = -4 + 4 = 0 \le 10$ (Satisfies the first inequality)
    • $x+2y = -2 + 2(4) = -2 + 8 = 6 \ge 8$ (Does not satisfy the second inequality)

    So, option (A) is incorrect.

  2. Check option (B) $(3,2)$:

    • $2x+y = 2(3) + 2 = 6 + 2 = 8 \le 10$ (Satisfies the first inequality)
    • $x+2y = 3 + 2(2) = 3 + 4 = 7 \ge 8$ (Does not satisfy the second inequality)

    So, option (B) is incorrect.

  3. Check option (C) $(-5,6)$:

    • $2x+y = 2(-5) + 6 = -10 + 6 = -4 \le 10$ (Satisfies the first inequality)
    • $x+2y = -5 + 2(6) = -5 + 12 = 7 \ge 8$ (Does not satisfy the second inequality)

    So, option (C) is incorrect.

  4. Check option (D) $(4, 2)$:

    • $2x+y = 2(4) + 2 = 8 + 2 = 10 \le 10$ (Satisfies the first inequality)
    • $x+2y = 4 + 2(2) = 4 + 4 = 8 \ge 8$ (Satisfies the second inequality)

    So, option (D) is correct.

Correct Answer: (4, 2)

AI Suggestion: Option D

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the concept of linear inequalities to check which point satisfies both given conditions.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding the concept of inequalities and how points relate to the solution space defined by them.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the understanding and application of concepts related to linear inequalities, a standard topic in the syllabus.

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