If J 5
​
(4)=aJ 2
​
(4)+bJ 3
​
(4), where J is the Bessel's function of the first kind, then a= a) 17 b) 2 c) 13 d) 21 e) -2 The Fourier-Legendre expansion of f(x)=x 10
on [−1,1] is ∑ n=0
[infinity]
​
c n
​
P n
​
(x). Then c 2
​
= a) 45/112 b) 35/97 c) 35/87 d) 50/143 e) 40/99 f) 55/112