The length of the longest rod that can be fitted in a cubical vessel of edge `10 c m\ ` long, is (a) `10\ c m` (b) `10\ sqrt(2)\ c m` (c) `10\ sqrt(3)\ c m` (d) `20\ c m`

The area of the circle that can be inscribed in a square of side 10 cm is (a) 40pi\ c m^2 (b) 30pi\ c m^2 (c) 100\ pi\ c m^2 (d) 25\ pi\ c m^2

If the length of each side of an equilateral triangle of area 4sqrt(3)\ c m^2,\ is (a) 4\ c m (b) 4/(sqrt(3))c m\ (c) (sqrt(3))/4\ c m (d) 3\ c m

The radius of a circle is 6 cm. The perpendicular distance from the centre of the circle to the chord which is 8 cm in length, is (a) sqrt(5)\ c m (b) 2sqrt(5)\ c m (c) 2\ sqrt(7)\ c m (d) sqrt(7)\ c m

The length of the tangent drawn from a point 8cm away from the centre of a circle of radius 6cm is (a) sqrt(7)c m (b) 2sqrt(7)c m (c) 10 c m (d) 5c m

A B\ a n d\ C D are two parallel chords of a circle with centre O such that A B=6\ c m\ a n d\ C D=12\ c mdot The chords are on the same side of the centre and the distance between them is 3 cm. The radius of the circle is (a) 6\ c m (b) 5\ sqrt(2)\ c m (c) 7\ c m (d) 3\ sqrt(5)\ c m

The area of a square is 50 c m^2 . The length of its diagonal is (a) 5sqrt(2)\ c m (b) 10 cm (c) 10sqrt(2)\ c m (d) 8\ c m

In Figure, if A P=10 c m , then B P= (a) sqrt(91)c m (b) sqrt(127)c m (c) sqrt(119)c m (d) sqrt(109)c m

The length of a rectangle is three times of its width. If the length of the diagonal is 8sqrt(10)m , then the perimeter of the rectangle is: (a) 15sqrt(10)\ m (b) 16sqrt(10)\ m (c) 24sqrt(10)\ m (d) 64 m

If area of an equilateral triangle is 3sqrt(3)\ c m^2, then its height is (a)3 cm (b) sqrt(3)\ c m (c)6 cm (d) 2sqrt(3)\ c m

Each side of an equilateral triangle is 8 cm. Its area is (a) 16sqrt(3)\ c m^2 (b) 32sqrt(3)\ c m^2 (c) 24sqrt(3)\ c m^2 (d) 8sqrt(3)\ c m^2