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Let \(\mathrm{y}=\mathrm{f}\left(\mathrm{x}\right)={\sin }^{3}\left(\frac{\pi }{3}\left(\cos \left(\frac{\pi }{3\sqrt{2}…

Q1

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