Find the value of r if the coefficients of (2r+4)th and (r - 2) th term in the expansion of `(1+ x)^18` are equal.

For what value of m, the coefficients of (2m + 1)^(th) and (4m+5)^(th) terms in the expansion of (1 + x)^10 are equal ?

Find the 6th term in the expansion of (x+3)^9 .

Find the 4th term in the expansion of (x-2y)^12 .

If the coefficients of 5th, 6th , and 7th terms in the expansion of (1+x)^n are in A.P., then n=

Find the 6th term in the expansion of (3x^2-1/3x)^8

Find 5th term in the expansion of (2x^2-1/3x)^11 .

Find a if the 17th and 18th terms in the expansion of (2+a)^50 are equal.

Find the 13th term in the expansion of (9x-1/(3sqrtx))^18 , x ne 0 .

If the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the expansion of (1+x)^(14) are in A.P., then r is/are a. 5 b. 11 c. 10 d. 9

If the coefficient of the rth, (r+1)th and (r+2)th terms in the expansion of (1+x)^(n) are in A.P., prove that n^(2) - n(4r +1) + 4r^(2) - 2=0 .