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MHTCET 2016 Math Solved Paper

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Question : 17 of 50

Marks: +1, -0

If

y=e^{m} \sin^{-1} x

(1-x^{2}) = A y^{2},

A

is equal to

m
-m
$m^{2}$
$- m^{2}$

Solution:

(c) Given,

y=e^{m\; \sin^{-1} x}

.......(i)

After differentiating on both sides w.t.

x,

we get

\frac{d y}{d x}

=

e^{m \sin^{-1} x} \frac{d}{d x} (m \sin^{-1} x)

⇒

\frac{d y}{d x}

=

{e^m}^{\sin^{-1} x} \left(m \times \frac{1}{\sqrt{1-x^{2}}}\right)

⇒

\sqrt{1-x^{2}} \frac{d y}{d x} = m y

[From eq. (i)]

After squaring on both sides, we get

(1-x^{2}) \left( \frac{d y}{d x} \right)^{2} = m^{2} y^{2}

As,

(1-x^{2}) \left( \frac{d y}{d x} \right)^{2} = A y^{2}

Hence,

A=m^{2}

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