The maximum value M of $3^x + 5^x – 9^x + 15^x –25^x$ , as x varies over reals, satisfies –

A.3<M<5

B.0<M<2

C.5<M<25

D.0<M<9

B. 0<M<2

$\begin{aligned}
& M=a+b-a^2+a b-b^2 \quad \frac{a^2+b^2}{2} \geq a b \\
& \mathrm{a}^2+\mathrm{b}^2 \geq 2 \mathrm{ab} \\
& -\left(a^2+b^2\right) \leq-2 a b \\
& \mathrm{M} \leq \mathrm{a}+\mathrm{b}-\mathrm{ab} \\
& \mathrm{M}<\mathrm{1}-(\mathrm{a}-\mathrm{l})(\mathrm{b}-1) \quad \min \text { is zero } \\
& \text { hence } 0<\mathrm{M}<2 \\
&
\end{aligned}$