Find the pattern puzzle
This seems likely:
$$7^2 + 5^2 = 74$$
$$5^2 + 21^2 = 466$$
$$21^2 + 7^2 = \boxed{490}$$
Zubin's method is good, but still I will show my attempt.
For first triplet ... $5*\color{red}{12}+7*\color{red}{2}=74$
For second triplet ... $5*\color{red}{26}+21*\color{red}{16}=466$
$12-2=10=26-16$
For first triplet we used bigger number for first multiplication, for second triplet we used smaller number for first multplication, so for third triplet we will use bigger number for first multiplication.
$21*\color{red}{(x+10)}+7*\color{red}{(x)}=\text{any one of the four options}$
$21x+210+7x=\text{any one of the four options}$
$28x=\text{any one of the four options}-210$
By observation option B,C and D gives fractional answer, so choosing option A gives,
$28x=490-210=280 \rightarrow x=10$
$21*\color{red}{(20)}+7\color{red}{(10)}=490$