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)`

(a) sqrt(175) (b) 2sqrt(112) (c) sqrt(125) (d) 5sqrt(119)

The centre of a hyperbola is at (2,4), the coordinates of one of its vertices are (6,4) and eccentricity is sqrt(5) , find its equation.

Prove that the triangle formed by the points 1,(1+i)/(sqrt(2)) ,and i as vertices in the Argand diagram is isosceles.

Prove that the triangle formed by the points 1,(1+i)/(sqrt(2)),a n di as vertices in the Argand diagram is isosceles.

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

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

A B C D is a square of unit area. A circle is tangent to two sides of A B C D and passes through exactly one of its vertices. The radius of the circle is (a) 2-sqrt(2) (b) sqrt(2)-1 (c) sqrt(2)-1/2 (d) 1/(sqrt(2))

root(5)(x^(8).sqrt(x^(6).sqrt(x^(-4))

Simplify : 2sqrt(-18)+3sqrt(-50)-6sqrt(-8)