The coefficient of x^r in (1+x)²/(1-2x)³ is

49ⁿ+16n+k is divisible by 64 for n?N. Then the numerically least –ve integer value of k is

The coefficient of x^r (0<r<n-1) in the expansion of (x+3)^n-1+(x+3)^n-2. (x+2)+ (x+3)^n-3. (x+2)²+……+(x+2)^n-1 is

ⁿC₀+ⁿC₁+ⁿC₂+………+ⁿC_n =

If the 5^th term is 24 times the 3^rd term in the expansion of (1+x)¹¹ then x=

If T_r+1 is the term independent of x in (3x-5/x³)⁸ then r=

The 4^th term of (1-2x)^-1 when x=1/3 is

If x^r occurs in the expansion (x+1/x²)²ⁿ, then its coefficient is:

The sum of the coefficients of (1+2x-4x²)³⁵ is

The number of non zero terms in the expansion of (x+a)¹⁰⁰ + (x-a)¹⁰⁰ is