MISSION CGL MAINS 2015 : Advanced Quant Quiz

1.If  the incentre of an equilateral triangle lies inside the triangle and its radius is 3 cm, then the side of the equilateral triangle is

(1) 9√3 cm

(2) 6√3 cm

(3) 3√3 cm

(4) 6 cm

2.Suppose ∆ABC be a right-angled triangle where ∠A = 90⁰ and AD perpendicular on BC. If ∆ ABC = 40 cm^2, ∆ACD = 10 cm^2 and AC = 9 cm, then the length of BC is

(1) 12 cm

(2) 8 cm

(3) 4 cm

(4) 6 cm

3.Two circles touch each other externally at P. AB is a direct common tangent to the two circles, A and B are points of contact and ∠PAB = 35⁰ Then ∠ABP is

(1) 35⁰

(2) 55⁰

(3) 65⁰

(4) 75⁰

4.The length of the common chord of two intersecting circles is 24 cm. If the diameters of the circles are 30 cm and 26 cm, then the distance between the centres in cm is

(1) 13

(2) 14

(3) 15

(4) 16

5.In ∆ABC, D and E are points on AB and AC respectively such that DE ‖ BC and DE divides the ∆ABC into two parts of equal areas. Then ratio of AD and BD is 

(1) 1 : 1

(2) 1 : √2-1 

(3) 1 : √2

(4) 1 : √2 + 1

6.The area of the square inscribed in a circle of radius 8 cm is

(1) 256 sq. cm

(2) 250 sq. cm

(3) 128 sq. cm

(4) 125 sq. cm

7.X and Y are centres of circles of radii 9 cm and 2 cm respectively, XY = 17 cm. Z is the centre of a circle of radius r cm which touches the above circles externally. Given that ∠XZY = 90⁰, the value of r is

(1) 13 cm

(2) 6 cm

(3) 9 cm

(4) 8 cm

8.I is the incentre of a triangle ABC. If ∠ABC = 65⁰ and ∠ACB = 55⁰, then the value of ∠BIC is

(1) 130⁰

(2) 120⁰

(3) 140⁰

(4) 110⁰

9.If the radii of two circles be 6 cm and 3 cm and the length of the transverse common tangent be 8 cm, then the distance between the two centres is

(1) √145 cm

(2) √140 cm

(3) √150

(4) √135

10.The ratio between the number of sides of two regular polygons is 1 : 2 and the ratio between their interior angles is 2 : 3. The number of sides of these polygons is respectively

(1) 6, 12

(2) 5, 10

(3) 4, 8

(4) 7, 14

Answers and Solution: