`(v i i)(3/2x^2-1/(3x))^6`

Expand using binomial theorem: (i) (1-2x)^(4) " " (ii) (x+2y)^(5) (iii) (x-(1)/(x))^(6) " "(iv) ((2x)/(3)=(3)/(2x))^(5) (v) (x^(2) +(2)/(x))^(6)" "(vi) (1+(1)/(x^(2)))^(4)

int(x+root(3)(x^(2))+root(6)(x))/(x(1+root(3)(x)))dx is equal to (i)(3)/(2)x(1+root(3)(x))(3)/(2)x^((2)/(3))+6tan^(-1)x^(6)+C( iii) (3)/(2)x^((2)/(3))+6tan^(-1)x^((1)/(6))+C( iv) (2)/(3)x^((2)/(3))+5tan^(-1)x^(6)+C

(i) int (3x^2)/(x^6+1) dx (ii) int (3x)/(1+2x^4) dx

(i) (2x+3) (3x-5) (ii) x(1+x)^(3) (iii) (sqrtx + 1/x) (x -1/sqrtx) (iv) (x-1/x)^(2) (v) (x^(2) + 1/x^(2))^(3) (vi) (2x^(2) +5x-1) (x-3)

(a) Write the conjugates of the following: (i) 3+i (ii) 3-i (iii) -sqrt(5)-sqrt(7)i (iv) -sqrt(5)i (v) (4)/(5) (vi) 49-(i)/(7) (vii) (1-i)/(1+i) (viii) (1+i)^(2) (ix) (2+5i)^(2) (x) (-2-(1)/(3)i)^(3) (b) Find the real number x and y if: (i) (x-iy)(3+5i) is the conjugate of -6-24 i (ii) -3+ix^(2)y and x^(2)+y+4i are congugate of each other.

Expand (i) ((2x)/3-(3)/(2x))^(6) , (ii) (2/x-x/2)^(5)

Expand (i) ((2x)/3-(3)/(2x))^(6) , (ii) (2/x-x/2)^(5)

Find x and y if (x^4+2x i)-(3x^2+y i)=(3-5i)+(1+2y i)

Factorize: (i) 6x^2-13 x+6 (ii) -2x^2-3x+2

Evaluate : (i) (3x + (1)/(2) ) (2x + (1)/(3) )