**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