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Differential Equations question

2023 · 10 Apr · Shift 2 · Q33

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JEE Main
Mathematics
Differential Equations
2023 · 10 Apr · Shift 2 · Q33

Differential Equations question

2023 · 10 Apr · Shift 2 · Q33

JEE MainMathematicsDifferential EquationsNumerical+4 / −1

Let the tangent at any point P on a curve passing through the points (1, 1) and

\left(\frac{1}{10}, 100\right)

, intersect positive

x

-axis and

y

-axis at the points A and B respectively. If

\mathrm{PA}: \mathrm{PB}=1: k

and

y=y(x)

is the solution of the differential equation

e^{\frac{d y}{d x}}=k x+\frac{k}{2}, y(0)=k

, then

4 y(1)-6 \log _{\mathrm{e}} 3

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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