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Q.

Let $y = \sin^{2} x + \cos^{4} x$ Then, for all real x

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a

$y \geq \frac{1}{4}$

b

The minimum value of y is 3/4

c

$y \leq 1$

d

The maximum value of y is 2

answer is B, C.

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Detailed Solution

$\begin{matrix} y = \cos^{4} x - \cos^{2} x + 1 \\ = (\cos^{2} x - \frac{1}{2}) + \frac{3}{4} \\ ∴ y_{min} = \frac{3}{4} and y is maximum when {(\cos^{2} x - \frac{1}{2})}^{2} is then maximum \end{matrix}$
$∴ y_{max} = \frac{1}{4} + \frac{3}{4} = 1$

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