If center of a regular hexagon is at the origin and one of the vertices on the Argand diagram is `1+2i` , then its perimeter is `2sqrt(5)` b. `6sqrt(2)` c. `4sqrt(5)` d. `6sqrt(5)`

If the area of regular hexagon is 96sqrt(3) , what is its perimeter?

(sqrt(6+2sqrt(5)))(sqrt(6-2sqrt(5)))

The distance between the directrices of the hyperbola x=8s e ctheta,\ y=8\ t a ntheta, a. 8sqrt(2) b. 16sqrt(2) c. 4sqrt(2) d. 6sqrt(2)

Multiply 6sqrt(5) by 2sqrt(5) .

The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the center of the circle lies on x-2y=4. The radius of the circle is (a) 3sqrt(5) (b) 5sqrt(3) (c) 2sqrt(5) (d) 5sqrt(2)

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)

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)

The centroid of an equilateral triangle is (0, 0). If two vertices of the triangle lie on x+y=2sqrt(2), then one of them will have its coordinates. (a) (sqrt(2)+sqrt(6),sqrt(2)-sqrt(6)) (b) (sqrt(2)+sqrt(3),sqrt(2)-sqrt(3)) (c) (sqrt(2)+sqrt(5),sqrt(2)-sqrt(5)) (d) none of these

If the angles of a triangle are in the ratio 4:1:1, then the ratio of the longest side to the perimeter is (a) sqrt(3):(2+sqrt(3)) (b) 1:6 (c) 1:2+sqrt(3) (d) 2:3

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