# ssc cgl tier 1 :: quantitative aptitude :: qa test 3

## Home ssc cgl tier 1 / quantitative aptitude Questions and Answers

1 .If 2x 2 cos 60Âº â€“ 4 cot 2 45Âº â€“ 2 tan 60Âº = 0, then what is the value of x?
A.2, B.3 , C.$\sqrt{3}$-1 , D.$\sqrt{3}$+1
a
b
c
d

2 .Two houses are collinear with the base of a tower and are at distance 3 m and 12 m from the base of the tower. The angles of elevation from these two houses of the top of the tower are complementary. What is the height of the tower?
4 m
6 m
7.5 m
36 m

3 .A round balloon of unit radius subtends an angle of 90Âº at the eye of an observer standing at a point, say A. What is the distance of the centre of the balloon from the point A?
A. $^1\over\sqrt{2}$ , B.$\sqrt{2}$ , C.2 , D.$^1\over2$
a
b
c
d

4 .If the area of a circle, inscribed in an equilateral triangle is 4pcm 2 , then what is the area of the triangle?
A.$12\sqrt{3}$ $cm^2$ , B. $9\sqrt{3}$ $cm^2$ , C. $8\sqrt{3}$ $cm^2$ , D. $18cm^2$
a
b
c
d

5 .The difference between the area of a square and that of an equilateral triangle on the same base is 1/4 cm 2 . What is the length of side of triangle?
a.$\left(4-\sqrt{3}\right)$$^{1/2}cm , b.\left(4+\sqrt{3}\right)$$^{1/2}$cm
c.$\left(4-\sqrt{3}\right)$$^{-1/2}cm , d.\left(4+\sqrt{3}\right)$$^{+1/2}$cm
a
b
c
d

6 .If the diameter of a wire is decreased by 10%, by how much per cent (approximately) will the length be increased to keep the volume constant?
5%
17%
20%
23%

7 .A cone is inscribed in a hemisphere such that their bases are common. If C is the volume of the cone and H that of the hemisphere, then what is the value of C : H?
1 : 2
2 : 3
3 : 4
4 : 5

8 .
30Âº
35Âº
45Âº
55Âº

9 .
a
b
c
d

10 .What is the number of points in the plane of a DABCwhich are at equal distance from the vertices of the triangle?
0
1
2
3