GATEWAY TO CGL MAINS 2015 : Quiz on Advanced Maths

1.In the given figure O is the centre of the circle. If ∠BAC = 38°, then ∠OCD is

(a) 76° 

(b) 52°

(c) 38° 

(d) 19°

2.In the given figure, O is the centre of the circle. If ∠OBC = 20°, the∠BAC:—

(a) 80° 

(b) 70°

(c) 100° 

(d) 140°

3.The value of x: - 

(a) 2.2 cm 

(b) 1.6 cm

(c) 3 cm 

(d) 2.6 cm 

4.The number of common tangents that can be drawn to two given intersecting circles is at the most

(a) 1 

(b) 2

(c) 3 

(d) 4

5.Three circles touch each other external1y.The distance between their centres is 5 cm, 6 cm and 7 cm.Find radii of the circles:-

(a) 2 cm, 3 cm, 4 cm

(b) 3 cm, 4 cm, 1 cm

(c) 1 cm, 2 cm, 4 cm

(d) None of these

6.In the given figure, ABCD is cyclic quadrilateral and diagonals bisect each other at P. If∠DBC = 60°, and ∠BAC = 30° then ∠BCD is

(a) 90° 

(b) 60°

(c) 80° 

(d) None of these 

7.Two circles of radii 4 cm and 9 cm respectively touch each other eternally at a point and a common tangent touches them at the points P and Q respectively. Then the area of square with one side PQ, is: 

(a) 97 sq. cm 

(b) 194. Sq.cm 

(c) 72 sq. cm 

(d) 144 sq. cm 

8.In the following figure, if OA = 10 and AC = 16, then OB must be: 

(a) 5

(b) 6

(c) 3 

(d) 4

9.Find the value of ∠x in the given figure : - 

(a) 40° 

(b) 45°

(c) 50° 

(d) 60°

10.Two circles of radius 4cm and 6 cm touch each other internally. Find the longest chord of the bigger circle which is outside of the smaller circle? 

(a) 8 √2  cm 

(b) 4√2  cm

(c) 6√2 cm

(d) 3√2 cm 

ANSWERS AND SOLUTION: 
1.(c)∠ODC = ∠BAC = 38° (Angle made by same are BC) 
And OC = OD = Radius 
so ∠OCD = ∠ODC = 38°

2.(b)OB = OC ⇒∠OCB= ∠OBC=20°
so ∠BOC=180°-(20+20)=140°
so ∠BAC=1/2 ∠BOC=70°

3.(a) PT^2= PA * PB => 36 = 5(5 + x) 
=>5 + x = 36/5 = 7.2 
=>x = 2.2 cm 

4.(b) 
5.(a) 
6.(a)∠BDC = ∠BAC = 30°
so ∠BCD = ∠BDC + ∠DBC = 180°
so ∠BCD = 180°-(30°+60°)
=90°
7.(d) 
8.(b) 
9.(d) 
10(a)