If the third in the expansion of `(1+x)^(m)" is "-(1)/(8) x^(2)`. Then find the value of m.

If x^(4) , occurs in the rth term in the expansion of (x^(4)+(1)/(x^(3)))^(15) , then find the value of r.

If the middle term in the expansion of (x^(2)+1//x)^(n)" is "924x^(6) , then find the value of n.

The first three terms in the expansion of (1+ax)^(n)(n ne 0) are 1,6x, and 16x^(2) . Then find the value of a and n.

If the middle term in the expansion of (x^m+2/x)^6 is independent of x,find the value of m.

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

If the coefficients of three consecutive terms in the expansion of (1+x)^(n) are in the ratio 1:7:42, then find the value of n.

find the middle term in the expansion of (3x+2y)^8

If 21^st and 22^nd terms in the expansion of (1+x)^44 are equal then find the value of x.

Find the general term in the expansion of (x-1/x)^14

Find the middle term in the expansion of (x^(2)+(1)/(x^(2))+2)^(n)