Evaluate :
To find: Value of 
Formula used: (i) 
(ii) (a+b)n = nC0an + nC1an-1b + nC2an-2b2 + …… +nCn-1abn-1 + nCnbn
(a+1)6 = 
⇒ 6C0a6 + 6C1a5 + 6C2a4 + 6C3a3 + 6C4a2 + 6C5a + 6C6 … (i)
(a-1)6 = 
⇒ 6C0a6 - 6C1a5 + 6C2a4 - 6C3a3 + 6C4a2 - 6C5a + 6C6 … (ii)
Adding eqn. (i) and (ii)
(a+1)6 + (a-1)6 = [6C0a6 + 6C1a5 + 6C2a4 + 6C3a3 + 6C4a2 + 6C5a + 6C6] + [6C0a6 - 6C1a5 + 6C2a4 - 6C3a3 + 6C4a2 - 6C5a + 6C6]
⇒ 2[6C0a6 + 6C2a4 + 6C4a2 + 6C6]
⇒ 2
⇒ 2[(1)a6 + (15)a4 + (15)a2 + (1)]
⇒ 2[a6 + 15a4 + 15a2 + 1] = (a+1)6 + (a-1)6
Putting the value of a = 
in the above equation
= 2[
6 + 15
4 + 15
2 + 1]
⇒ 2[8 + 15(4) + 15(2) + 1]
⇒ 2[8 + 60 + 30 + 1]
⇒ 2[99]
⇒ 198
Ans) 198
1