If the coefficients of the `(2r+4)t h ,(r-2)t h` term in the expansion of `(1+x)^(18)` are equal, then the value of `r` is.

If the coefficients of the rth, (r+1)t h ,(r+2)t h terms is the expansion of (1+x)^(14) are in A.P, then the largest value of r is.

If the coefficients of (r-5)^th and (2r - 1)^th terms in the expansion of (1 + x)^34 are equal, find r.

If the coefficients of rth and (r+1)t h terms in the expansion of (3+7x)^(29) are equal, then r equals a. 15 b. 21 c. 14 d. none of these

In the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the binomial expansion of (1+y)^m are in A.P., then prove that m^2-m(4r+1)+4r^2-2=0.

If the coefficients of the r^(th) term and the (r + 1)^(th) term in the expansion of (1 + x)^(20) are in the ratio 1:2 , then r is equal to

r and n are positive integers r gt 1 , n gt 2 and coefficient of (r + 2)^(th) term and 3r^(th) term in the expansion of (1 + x)^(2n) are equal, then n equals

If the coefficients of r^(th),(r + 1)^(th) and (r + 2)^(th) terms in the binomial expansion of (1 + y)^(m) are in A.P., then m and r satisfy the equation

If (r+1)t h term is the first negative term in the expansion of (1+x)^(7//2), then find the value of rdot

Column I, Column II The coefficient of the two consecutive terms in the expansion of (1+x)^n will be equal, then n can be, p. 9 If 15^n+23^n is divided, by 19, then n can be, q. 10 ^10 C_0^(20)C_(10)-^(10)C_1^(18)C_(10)+^(10)C_2^(16)C_(10)- is divisible by 2^n ,t h e nn can be, r. 11 If the coefficients of T_r , T_(r+1),T_(r+2) terms of (1+x)^(14) are in A.P., then r is less than, s. 12