The coefficient of `x^9` in `(1+9x+27x^2+27x^3)^6` is

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

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

The value of (3x ^(3) + 9x ^(2) + 27x)div 3x is

If two of the roots of 8x^(4) - 2x^(3) - 27x^(2) + 6x + 9 = 0 are being equal in magnitude but opposite in sign then the roots are

Let's resolve into factors the following agebraic expressions : - 1 + 9x + 27x^2 + 28x^3

The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,4x^2,1+8x^3] , [3x, 9x^2,1+27x^3]|=10 is (A) 0 (B) 1 (C) 2 (D) 3

The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,4x^2,1+8x^3] , [3x, 9x^2,1+27x^3]|=10 is (A) 0 (B) 1 (C) 2 (D) 3

The total number of distinct x in R for which |[x, x^2, 1+x^3] , [2x,4x^2,1+8x^3] , [3x, 9x^2,1+27x^3]|=10 is (A) 0 (B) 1 (C) 2 (D) 3