`(sqrt2+1)/sqrt3`

The ratio of the area of triangle inscribed in ellipse x^2/a^2+y^2/b^2=1 to that of triangle formed by the corresponding points on the auxiliary circle is 0.5. Then, find the eccentricity of the ellipse. (A) 1/2 (B) sqrt3/2 (C) 1/sqrt2 (D) 1/sqrt3

Let p=1+1/(sqrt(2))+1/(sqrt(3))+...+1/(sqrt(120)) and q=1/(sqrt(2))+1/(sqrt(3))+...+1/(sqrt(121)) then

For all n in N, 1 + 1/(sqrt(2))+1/(sqrt(3))+1/(sqrt(4))++1/(sqrt(n))

Find the sum (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+.......... upto 99 terms.

can -1/(2sqrt(2))-1/sqrt(2),-1/sqrt(3) be the direction cosines of any directed line? Justify your answer.

([(sqrt(2)+isqrt(3))+(sqrt(2)-isqrt(3))])/([(sqrt(3)+1sqrt(2))+(sqrt(3)-1sqrt(2))])

If sqrt(2)=1.414,sqrt(3)=1.732 , find the value of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)" "(ii)(sqrt(3)-1)/(sqrt(3)+1)" "(iii)(2+sqrt(6))/(sqrt(2))

Solve sqrt(2x+1)+sqrt(3x+2)=sqrt(5x+3)

Solve the equation sqrt(2x-1)+sqrt(3x-2)=sqrt(4x-3)+sqrt(5x-4).

Solve x^(2)-(sqrt3+1)x+sqrt3=0 .