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Straight Lines and Pair of Straight Lines question

2025 · 29 Jan · Shift 2 · Q33

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Mathematics
Straight Lines and Pair of Straight Lines
2025 · 29 Jan · Shift 2 · Q33

Straight Lines and Pair of Straight Lines question

2025 · 29 Jan · Shift 2 · Q33

JEE MainMathematicsStraight Lines and Pair of Straight LinesMCQ+4 / −1

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}{9}

of the area of the triangle OAB and AN : NB =

\lambda : 1

, then the sum of all possible value(s) of

\lambda

is:

A
$\frac{1}{2}$
B
$\frac{5}{2}$
C
2
D
$\frac{13}{6}$

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