Question

1) (nC0)(2nCn) - (nC1)(2n-2Cn) + (nC2)(2n-4Cn) .... equals to
Ans: 2^n
2) If a(r) is the co-efficient of X^r in the expansion of (1 + X + X^2)^n, then
a(1) - 2*a(2) + 3*a(3) - ... 2n*a(2n) = ? Ans: -n
3) Find the co-efficient of X^r in the expansion of 1 + (1+X) + (1+X)^2 + ... + (1+X)^n.
4)The greatest integer less than or equal to (2^(1/2) + 1)^6 is
(a) 196 (b) 197 (c) 198 (d) 199