a^(3)-(1)/(a^(3))-2a+(2)/(a)

Factorise : x^(3)+(1)/(x^(3))-2x-(2)/(x)

A line passes through the point (6, -7, -1) and (2, -3, 1). The direction cosines of the line so directed that the angle made by it with the positive direction of x-axis is acute, are: a) (2)/(3),(-2)/(3),(-1)/(3) b) (2)/(3),(2)/(3),(-1)/(3) c) (2)/(3),(-2)/(3),(1)/(3) d) (2)/(3),(2)/(3),(1)/(3)

[{((1)/(3))^(-3)-((1)/(2))^(-3)}-:((1)/(5))^(-2)]

Evaluate : [((1)/(2))^(3)-((1)/(3))^(2)]times((3)/(5))^(2)times((-2)/(3))^(3)

Let H_(n)=1+(1)/(2)+(1)/(3)+ . . . . .+(1)/(n) , then the sum to n terms of the series (1^(2))/(1^(3))+(1^(2))/(1^(3))+(2^(2))/(2^(3))+(1^(2)+2^(2)+3^(2))/(1^(3)+2^(3)+3^(3))+ . . . , is

((3(2)/(3))^(2)-(2(1)/(2))^(2))/((4(3)/(4))^(2)-(3(1)/(3))^(2))-:(3(2)/(3)-2(1)/(2))/(4(3)/(4)-3(1)/(3))=?(37)/(97) (b) (74)/(97)( c) 1(23)/(74) (d) None of these

Prove that the two parabolas y^(2)=4ax and x^(2)=4by intersects at an angle of tan^(1)[(3a^((1)/(3))b^((1)/(3)))/(2(a^((2)/(3))+b^((2)/(3))))]

The sum of (1^(3))/(1)+(1^(3)+2^(3))/(1+2)+ (1^(3)+2^(3)+3^(3))/(1+2+3)+.. . upto 10 terms is

Simplify ((3(2)/(3))^(2)-(2 (1)/(2)))/((4(3)/(4))^(2)-(3(1)/(3))^(2))+(3(2)/(3)-2(1)/(2))/(4(3)/(4)-3(1)/(3))

S_(n)=(1)/(1^(3))+(1+2)/(1^(3)+2^(3))+(1+2+3)/(1^(3)+2^(3)+3^(3))+......+(1+2+....+n)/(1^(3)+2^(3)+......+n^(3)).100S_(n)=n then n is equal to :