" (i) "(x+(1)/(x))" incenti (ii) "((2x)/(3)-(3)/(2x))^(6)" [Roorkee "

ii) (2x+6)(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)

(ii) (2x+1)(3x-2)=6(x+1)(x-2)

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)

If 2x - (1)/(2x) =4 , find : (ii) 8x^(3) - (1)/( 8x^3)

Find each of the following products: (i) (x - 4)(x - 4) (ii) (2x - 3y)(2x - 3y) (iii) ((3)/(4) x - (5)/(6) y) ((3)/(4)x - (5)/(6) y) (iv) (x - (3)/(x)) (x - (3)/(x)) (v) ((1)/(3) x^(2) - 9) ((1)/(3) x^(2) - 9) (vi) ((1)/(2) y^(2) - (1)/(3) y) ((1)/(2) y^(2) - (1)/(3) y)

Find the term independent of x in the expansion of : (i) (2x+1/(3x^(2)))^(9) (ii) ((3x^(2))/2-1/(3x))^(6) (iii) (x-1/x^(2))^(3n) (iv) (3x-2/x^(2))^(15)

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

Evaluate : (i) int(3x^(2))/((1+x^(6)))dx (ii) int(x^(3))/((x^(2)+1)^(3))dx (iii) (x^(8))/((1-x^(3))^(1//3))dx