If the extremities of the diagonal fo a square are (1,-2,3) and (2,-3,5), then the length of the side is `sqrt(6)` b. `sqrt(3)` c. `sqrt(5)` d. `sqrt(7)`

One vertex of an equilateral triangle is (2,2) and its centroid is (-2/sqrt3,2/sqrt3) then length of its side is (a) 4sqrt(2) (b) 4sqrt(3) (c) 3sqrt(2) (d) 5sqrt(2)

In a triangle, the lengths of the two larger sides are 10 and 9, respectively. If the angles are in A.P., then the length of the third side can be 5-sqrt(6) (b) 3sqrt(3) (c) 5 (d) 5+sqrt(6)

In a triangle, the lengths of the two larger sides are 10 and 9, respectively. If the angles are in A.P, then the length of the third side can be (a) 5-sqrt(6) (b) 3sqrt(3) (c) 5 (d) 5+sqrt(6)

The ratio of the area of a square of side a and that of an equilateral triangle of side a , is (a) 2:1\ (b) 2:sqrt(3)\ (c) 4:3 (d) 4:sqrt(3)

The eccentricity of the ellipse 4x^2+9y^2=36 is a. 1/(2sqrt(3)) b. 1/(sqrt(3)) c. (sqrt(5))/3 d. (sqrt(5))/6

The eccentricity of the ellipse 4x^2+9y^2=36 is a. 1/(2sqrt(3)) b. 1/(sqrt(3)) c. (sqrt(5))/3 d. (sqrt(5))/6

If a diagonal of a rectangle is thrice its smaller side, then its length and breadth are in the ratio (a) 3:1 (b) sqrt(3)\ :1 (c) sqrt(2)\ :1 (d) 2sqrt(2)\ :1

If one root x^2-x-k=0 is square of the other, then k= a. 2+-sqrt(5) b. 2+-sqrt(3) c. 3+-sqrt(2) d. 5+-sqrt(2)

A parallelopiped is formed by planes drawn through the points (1,2,3) and (9,8,5) parallel to the coordinate planes. The length of its diagonal is (A) 2sqrt(14) units (B) 2sqrt(26) units (C) 6sqrt(3) units (D) 2sqrt(21) units

The side of an equilatetral triangle has the same length as the diagonal of a square. What is the area of the square? (1) The height of the equilateral triangle is equal to 6sqrt(3) . (2) The area of the equilateral triangle is equal to 36sqrt(3) .