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JEE Main 202227 JuneEvening Shift
Exam
JEE Main
Year
2022
Date
27 June
Shift
Evening Shift
Subject
Mathematics
Chapter
Probability

JEE Main 2022 · 27 June · Evening Shift · Mathematics · Probability

If a point A(x, y) lies in the region bounded by the y -axis,...

If a point $A(x,y)A\left(x, y\right) lies in the region bounded by the yy-axis, straight lines 2y+x=6and2y + x = 6 and5x - 6y = 30,thentheprobabilitythat, then the probability thaty < 1$ isIf a point A(x, y) lies in the region bounded by the y -axis, straight lines 2y + x = 6 and 5x - 6y = 30 , then the

Options

  1. A16\dfrac{1}{6}
  2. B56\dfrac{5}{6}
  3. C23\dfrac{2}{3}
  4. D67\dfrac{6}{7}

Correct answer

B. 56\dfrac{5}{6}

Step-by-step solution

Plotting the diagram of the given straight line we get,

If a point A(x, y) lies in the region bounded by the y -axis, straight lines 2y + x = 6 and 5x - 6y = 30 , then the

Now by diagram, required probability =ar(ADEC)ar(ABC)= \dfrac{ar \left(ADEC\right)}{ar \left(ABC\right)}

=1−ar(BDE)ar(ABC)= 1 - \dfrac{ar \left(BDE\right)}{ar \left(ABC\right)}

=1−12×2×412×8×6=1−16=56= 1 - \dfrac{\dfrac{1}{2} \times 2 \times 4}{\dfrac{1}{2} \times 8 \times 6} = 1 - \dfrac{1}{6} = \dfrac{5}{6}

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