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Jee Main 2025Medium JEE math MCQ

Let the line \( x + y = 1 \) meet the axes of \( x \) and \( y \) at \( A \) and \( B \), respectively. A right angled triangle \( AMN \) is inscribed in the triangle \( OAB \), where \( O \) is the origin and the points \( M \) and \( N \) lie on the lines \( OB \) and \( AB \), respectively. If the area of the triangle \( AMN \) is \( \frac{4}{5} \) of the area of the triangle \( OAB \) and \( AN : NB = \lambda : 1 \), then the sum of all possible value(s) of \( \lambda \) is
  1. A. 2
  2. B. \( \frac{5}{2} \)
  3. C. \( \frac{1}{2} \)
  4. D. \( \frac{13}{6} \)

Solution

The correct option is **A**. (A. 2)

MATH

mediumPYQ Reworded
Question
Read carefully, then pick the best option.
Let the line x+y=1 x + y = 1 meet the axes of x x and y y at A A and B B , respectively. A right angled triangle AMN AMN is inscribed in the triangle OAB OAB , where O O is the origin and the points M M and N N lie on the lines OB OB and AB AB , respectively. If the area of the triangle AMN AMN is 45 \frac{4}{5} of the area of the triangle OAB OAB and AN:NB=λ:1 AN : NB = \lambda : 1 , then the sum of all possible value(s) of λ \lambda is
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Jee Main 2025 — Medium JEE Mathematics MCQ | MyGoalPrep