The first three terms in the expansion of a power of a binomial are respectivley 128, 2240 and 16800. Find the binomial and the index (or exponent ) of the power.

The first three terms in the expansion of a binomial are 1, 10 and 40. Find the expansion.

The coefficients of three consecutive terms in the expansion of (1+a)^n are in the ratio : 6: 33: 110. Find n.

Find the expansion of (3x^2 -2ax+ 3a^2)^3 using binomial theorem.

The sum of the coefficients of the first three terms of the expansion (x-3/x^2)^m, x ne 0 , m being a natural number, is 559. Find the term in the expansion containing x^3 .

Find the coefficient of x^n in the expansion of e^(a+bx) in powers of x.

Find the value of x for which the sixth term of : (sqrt(2^(log(10-3^x)))+ root (5)(2^((x-2)log 3)))^n is equal to 21, if it is known that the binomial coefficient of the 2nd, 3rd and 4th term in the expansion represent respectively the 1st, 3rd and 5th term of an A.P. (the symbol log stands for logarithm to the base 10).

The coefficient of the middle term in the binomial expansion in powers of x of (1+ alpha x)^4 and of (1-alpha x)^6 is the same, if alpha equals :

Consider the binomial expansion of (sqrt(x)+(1/(2x^(1/4))))^n n in NN , where the terms of the expansion are written in decreasing powers of x. If the coefficients of the first three terms form an arithmetic progression then the statement(s) which hold good is(are)