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MHTCET 15 May 2024 Shift 2 Paper

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Question : 101 of 150

Marks: +1, -0

If

x=\sin \theta, y=\sin ^{3} \theta

\frac{d^{2} y}{d x^{2}}

\theta=\frac{\pi}{2}

is

0
2
3
6

Solution:

Concept:

The relation between

x

and

y

can be simplified before differentiating.

Explanation:

Given

x = \sin \theta

and

y = \sin^3 \theta

.

Since

y = (\sin \theta)^3

, we get

y = x^3

.

Differentiating with respect to

x

:

\frac{dy}{dx} = 3x^2

.

Differentiating again:

\frac{d^2y}{dx^2} = 6x

.

At

\theta = \frac{\pi}{2}

,

x = \sin \frac{\pi}{2} = 1

.

Therefore,

\left(\frac{d^2y}{dx^2}\right)_{\theta = \frac{\pi}{2}} = 6(1) = 6

.

Answer:

The correct option is D. 6.

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