If a lim √(1+√(1+x^4)) - √2 / x^4 ; x ∈ (x→0) and b =

Question

If a = \(\lim\limits_{x \to 0} \frac {\sqrt {1 +\sqrt {1 +x^4}}-\sqrt{2}}{x^4}\) and b = \(\lim\limits_{x \to 0} \frac {sin ^2 x}{\sqrt {2}-\sqrt {1 +cos \,x}}\) find a.b³

(1) 16 

(2) 32

(3) –16 

(4) 48

Answer 1

Correct option is (2) 32