The maximum value of ${sin}^{2} x {cos}^{3} x$ is

\frac{6 \sqrt{3}}{25 \sqrt{5}}

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\frac{9 \sqrt{3}}{25 \sqrt{5}}

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\frac{9 \sqrt{2}}{6 \sqrt{5}}

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\frac{\sqrt{2}}{\sqrt{5}}

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Solution

The correct option is A $\frac{6 \sqrt{3}}{25 \sqrt{5}}$
Maximum value of $s i n^{p} x c o s^{q} x$ is $(\frac{p^{p} q^{q}}{(p + q)^{p + q}})^{\frac{1}{2}}$
So, here $p = 2, q = 3$
Maximum value of $f (x) = (\frac{2^{2} 3^{3}}{5^{5}})^{\frac{1}{2}} = \frac{6 \sqrt{3}}{25 \sqrt{5}}$

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Similar questions

Find each of the following products :

(i) $\frac{3}{5} \times \frac{- 7}{8}$ (ii) $\frac{- 9}{2} \times \frac{5}{4}$ (iii) $\frac{- 6}{11} \times \frac{- 5}{3}$

(iv) $\frac{- 2}{3} \times \frac{6}{7}$ (v) $\frac{- 12}{5} \times \frac{10}{- 3}$ (vi) $\frac{25}{- 9} \times \frac{3}{- 10}$

(vii) $\frac{5}{- 18} \times \frac{- 9}{20}$ (viii) $\frac{- 13}{15} \times \frac{- 25}{26}$ (ix) $\frac{16}{- 21} \times \frac{14}{5}$

(x) $\frac{- 7}{6} \times 24$ (xi) $\frac{7}{24} \times (- 48)$ (xii) $\frac{- 13}{5} \times (- 10)$

25 x^{2} - 9

$T h e v a l u e o f \frac{2}{3} \times \frac{5}{6} / \frac{4}{9} - \frac{3}{4} + \frac{2}{9} \times \frac{5}{9} = ?$

If ${9 x}^{2} + {25 y}^{2} = 181$ and xy = - 6. Find the value of 3x + 5y

[(- 4) \times (- 9) \times (- 25)] \div [(- 2) \times (- 3) \times (- 5)]

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