Class CBSE Class 12 Mathematics Linear Programming Q #832
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
15. The solution set of the inequation $3x+5y<7$ is:
(A) whole $xy$-plane except the points lying on the line $3x+5y=7$.
(B) whole $xy$-plane along with the points lying on the line $3x+5y=7$.
(C) open half plane containing the origin except the points of line $3x+5y=7$.
(D) open half plane not containing the origin.
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Step-by-Step Solution

  1. Consider the inequality $3x + 5y < 7$.
  2. To determine the solution set, we can test a point, such as the origin (0,0).
  3. Substitute x=0 and y=0 into the inequality: $3(0) + 5(0) < 7$, which simplifies to $0 < 7$.
  4. Since $0 < 7$ is true, the origin (0,0) is part of the solution set.
  5. The solution set is an open half-plane because the inequality is strict ($<$), meaning the points on the line $3x + 5y = 7$ are not included.
  6. Since the origin is part of the solution, the solution set is the open half-plane containing the origin.

Correct Answer: (C) open half plane containing the origin except the points of line $3x+5y=7$.

AI Suggestion: Option C

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires students to apply their understanding of linear inequalities to determine the solution set in a coordinate plane.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of the concept of solution sets for linear inequalities and their graphical representation.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly assesses the knowledge of linear inequalities and their solutions, a standard topic in the syllabus.

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