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Let \(y=f(x)=\sin ^3\left(\frac{\pi}{3}\left(\cos \left(\frac{\pi}{3 \sqrt{2}}\left(-4 x^3+5 x^2+1\right)^{\frac{3}{2}}\…

Q1

Let \(y=f(x)=\sin ^3\left(\frac{\pi}{3}\left(\cos \left(\frac{\pi}{3 \sqrt{2}}\left(-4 x^3+5 x^2+1\right)^{\frac{3}{2}}\right)\right)\right)\). Then, at \(x=1\),

[JEE Main 2023, 31 Jan (Shift 1)]

a

\(2{\mathrm{y}}^{'}+\sqrt{3}{\pi }^{2}\mathrm{y}=0\)

b

\(2{\mathrm{y}}^{'}+3{\pi }^{2}\mathrm{y}=0\)

c

\(\sqrt{2}{\mathrm{y}}^{'}-3{\pi }^{2}\mathrm{y}=0\)

d

\({\mathrm{y}}^{'}+3{\pi }^{2}\mathrm{y}=0\)

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