# ssc cgl tier 1 :: quantitative aptitude :: qa test 53

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

1 .
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

2 .
A round balloon of unit radius subtends an angle of 90° 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?
$1\over \sqrt 2$
$\sqrt 2$
2
$1 \over 2$

3 .
If the area of a circle, inscribed in an equilateral triangle is 4$\pi$$cm^ 2 , then what is the area of the triangle? 12\sqrt$$cm^2$
9$\sqrt$$cm^2 8\sqrt$$cm^2$
18$cm^2$

4 .
The difference between the area of a square and that of an equilateral triangle on the same base is $1/over4$ $cm^ 2$ . What is the length of side of triangle?
$(4 - \sqrt 3)^{1 \over 2}$ cm
$(4 + \sqrt 3)^{1 \over 2}$ cm
$(4 - \sqrt 3)^{- 1 \over 2}$ cm
$(4 + \sqrt 3)^{- 1 \over 2}$ cm

5 .
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%

6 .
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

7 .

In the given triangle, AB is parallel to PQ. AP = c, PC= b,PQ = a, AB= x. What is the value of x?
a + $ab \over c$
a + $bc \over a$
b + $ca \over b$
a + $ac \over b$

8 .
What is the number of points in the plane of a $\Delta$ABC which are at equal distance from the vertices of the triangle?
0
1
2
3

9 .
An obtuse angle made by a side of a parallelogram PQRS with other pair of parallel sides is 150°. If the perpendicular distance between these parallel sides (PQand SR) is 20 cm, what is the length of the side RQ?
40 cm
50 cm
60 cm
70 cm