In the expansion of `(2x^2-1/(3x))^9` find the coefficients of ` x`

Consider the expansion of (x^2-1/(3x))^9 Find the coefficient of x^9 .

Consider the expansion of (3x^2-1/(3x))^9 find the coefficient of x^6 and the term independent of x.

The sum of the binomial coefficients in the expansion of (x^2+1/x)^n is 1024. find the coefficient of x^11 in the binomial expansion.

Find the coefficient of : (i) x^3 in the expansion of (1 - x)^(-1/4) (ii) x^2 in the expansion of (5 - 3x)^(-1/3)

If the coefficient x^(2) and x^(3) in the expansion of (1 + 8x + bx^(2))(1 - 3x)^(9) in the power of x are equal , then b is :

If the coefficient x^(2) and x^(3) in the expansion of (1 + 8x + bx^(2))(1 - 3x)^(9) in the power of x are equal , then b is :

Prove that the coefficient of x^3 in the expansion of (1+x+2x^2) (2x^2 - 1/(3x))^9 is -224/27.

Find the coefficient of (i) x^(5)" in the expansion of "(x+3)^(8) (ii) x^(6) " in the expansion of "(3x^(2) - a/(3x))^(9) (iii) x^(-15) " in the expansion of " (3x^(2) - a/(3x^(3)))^(10). (iv) a^(7)b^(5)" in the expansion of "(a-2b)^(12) .