1. A polygon has 54 diagonals. The number of sides in the polygon is :
(a) 7
(b) 9
(c) 12
(d) None of these
2. The sum of all the interior angles of a regular polygon is four times the sum of its exterior angles. The polygon is :
(a) hexagon
(b) triangle
(c) decagon
(d) nonagon
3. O is the centre of a circle and arc ABC subtends an angle of 130° at O. AB is extended to P. Then angle PBC is:
(a) 75°
(b) 70°
(c) 65°
(d) 80°
4. AB and BC are two chords of a circle with centre O. If P and Q are the mid-points of AB and BC respectively, then the quadrilateral OQBP must be
(a) a rhombus
(b) concyclic
(c) a rectangle
(d) a square
6. O is the circum centre of the triangle ABC with circumradius 13 cm. BC = 24 cm and OD is perpendicular to BC. Then the length of OD is.
(a) 7 cm
(b) 3 cm
(c) 4 cm
(d) 5 cm
8. P is point outside a circle and is 13 cm away from its centre. A secant drawn from the point P intersects the circle at points A and B in such a way that PA = 9 cm and AB = 7 cm. The radius of the circle is :
(a) 5.5 cm
(b) 5 cm
(c) 4 cm
(d) 4.5 cm
10. N is the foot of the perpendicular from a point P of a circle with radius 7 cm, on a diameter AB of the circle. If the length of the chord PB is 12 cm, the distance of the point N from the point B is
(a) 6(5/7)cm
(b) 12(2/7)cm
(c) 3(5/7)cm
(d) 10(2/7)cm
