Linear InequalitiesMCQPYQ Sep 24Question 1136 of 146
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The shaded area is represented by which of the following option?

Options

Ax+y<6;2xy>0;x<0\displaystyle x+y<6; 2x-y>0; x<0
Bx+y<6;2xy>0;x>0\displaystyle x+y<6; 2x-y>0; x>0
Cx+y>6;2xy<0;x<0\displaystyle x+y>6; 2x-y<0; x<0
Dx+y>6;2xy<0;x>0\displaystyle x+y>6; 2x-y<0; x>0
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Correct Answer

Option bx+y<6;2xy>0;x>0\displaystyle x+y<6; 2x-y>0; x>0

All Options:

  • Ax+y<6;2xy>0;x<0\displaystyle x+y<6; 2x-y>0; x<0
  • Bx+y<6;2xy>0;x>0\displaystyle x+y<6; 2x-y>0; x>0
  • Cx+y>6;2xy<0;x<0\displaystyle x+y>6; 2x-y<0; x<0
  • Dx+y>6;2xy<0;x>0\displaystyle x+y>6; 2x-y<0; x>0

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Detailed Solution & Explanation

Let's analyze the inequalities in Option B to verify the shaded region:
1) x+y<6\displaystyle x + y < 6 represents the half-plane below the line x+y=6\displaystyle x + y = 6, since testing (0,0)\displaystyle (0,0) gives 0<6\displaystyle 0 < 6 (True).
2) 2xy>0    y<2x\displaystyle 2x - y > 0 \implies y < 2x represents the half-plane below the boundary line y=2x\displaystyle y = 2x.
3) x>0\displaystyle x > 0 restricts the region to the right side of the y\displaystyle y-axis (first and fourth quadrants).

The intersection of these half-planes perfectly represents the shaded triangle in the first quadrant bounded by the lines x+y=6\displaystyle x+y=6, y=2x\displaystyle y=2x, and the y\displaystyle y-axis (x=0\displaystyle x=0). This region lies entirely in the first quadrant where x>0\displaystyle x > 0.

Hence, **Option B** is the correct answer.

About This Chapter: Linear Inequalities

Paper

Paper 3: Quantitative Aptitude

Weightage

1-3 Marks

Key Topics

Linear Inequalities in one & two variables

This chapter covers Linear Inequalities in one & two variables and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 1-3 Marks weightage. Focus on understanding core concepts rather than memorizing.

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