If `(r)_n`, denotes the number `rrr... (n digits)`, where `r = 1,2,3,...,9` and `a=(6)_n,b=(8)_n,c=(4)_(2n)`, then

If (r)_(n'), denotes the number rrr...(ndigits), where r=1,2,3,...,9 and a=(6)_(n),b=(8)_(n),c=(4)_(2n), then

If S_r denotes the sum of the first r terms of an A.P. Then, S_(3n)\ :(S_(2n)-S_n) is n (b) 3n (c) 3 (d) none of these

Let a_n denote the number of all n-digit positive integers formed by the digits 0, 1, or both such that no consecutive digits in them are 0. Let b_n= The number of such n-digit integers ending with digit 1 and c_n= Then number of such n-digit integers with digit 0. The value of b_6 is

If ""(n)C_(0), ""(n)C_(1), ""(n)C_(2), ...., ""(n)C_(n), denote the binomial coefficients in the expansion of (1 + x)^(n) and p + q =1 sum_(r=0)^(n) r^(2 " "^n)C_(r) p^(r) q^(n-r) = .

For each positive integer n, let A_(n)=max{(C(n,r)0<=r<=n} then the number of elements n in {1,2...20} for 1.9<=(A_(n))/(A_(n-1))<=2 is

If N denotes the number of ways of selecting r objects of out of n distinct objects (rgeqn) with unlimited repetition but with each object included at least once in selection, then N is equal is a. .^(r-1)C_(r-n) b. .^(r-1)C_n c. .^(r-1)C_(n-1) d. none of these

If n is an even natural number and coefficient of x^(r) in the expansion of ((1+x)^(n))/(1-x) is 2^(n) then (A) r>((n)/(2))(B)r>=((n-2)/(2))(C)r =n