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Differential Equations question

2024 · Shift 1 · Q18

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PYQ Library
JEE Advanced
Mathematics
Differential Equations
2024 · Shift 1 · Q18

Differential Equations question

2024 · Shift 1 · Q18

JEE AdvancedMathematicsDifferential EquationsMCQ+3 / −1

Let

f(x)

be a continuously differentiable function on the interval

(0, \infty)

such that

f(1)=2

and

\lim\limits_{t \rightarrow x} \frac{t^{10} f(x)-x^{10} f(t)}{t^9-x^9}=1

for each

x\gt 0

. Then, for all

x\gt 0, f(x)

is equal to :

A
$\frac{31}{11 x}-\frac{9}{11} x^{10}$
B
$\frac{9}{11 x}+\frac{13}{11} x^{10}$
C
$\frac{-9}{11 x}+\frac{31}{11} x^{10}$
D
$\frac{13}{11 x}+\frac{9}{11} x^{10}$

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