# ssc cgl tier 1 :: quantitative aptitude :: qa test 14

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

1 .
a
b
c
d

2 .Find the value of cot Î¸ tan(90Â°â€“ Î¸ )â€“ sec(90Â°â€“ Î¸ )cosec Î¸ + sin 2 25Â°+ sin 2 65Â° + $\sqrt3$ (tan 5Â°tan 15Â°tan 30Â°tan 75Â°tan 85Â°)
1
-1
2
0

3 .If (1 + sin Î± )(1 + sin Î² )(1 + sin Î³ ) = (1 â€“ sin Î± ) (1 â€“ sin Î² )(1 â€“ sin Î³ ), then each side is equal to
Â± cos Î± cos Î² cos Î³
Â± sin Î± sin Î² sin Î³
Â± sin Î± cos Î² cos Î³
Â± sin Î± sin Î² cos Î³

4 .There are two vertical posts, one on each side of a road, just opposite to each other. One post is 108 metre high. From the top of this post, the angles of depression of the top and foot of the other post are 30Â° and 60Â° respectively. The height of the other post is â€“
36 m
72 m
108 m
110 m

5 .If ABC is an equilateral triangle and D is a point on BC such that AD â”´BC, then
AB : BD = 1 : 1
AB : BD = 1 : 2
AB : BD = 2 : 1
AB : BD = 3 : 2

6 .ABC is a right angled triangle, right angled at C and pis the length of the perpendicular from C on AB. If a, band care the lengths of the sides BC, CA and AB respectively, then
A. $1\over p^2$= $1\over b^2$-$1\over a^2$

B. $1\over p^2$= $1\over a^2$+$1\over b^2$

C. $1\over p^2$+ $1\over a^2$+$1\over b^2$ = 0

D. $1\over p^2$= $1\over a^2$-$1\over b^2$
a
b
c
d

7 .Each edge of a regular tetrahedron is 3 cm, then its volume is â€“

A.$9\sqrt3\over4$ $cm^3$

B.$27\sqrt3$ $cm^3$

C.$4\sqrt3\over9$ $cm^3$

D.$9\sqrt3$ $cm^3$
a
b
c
d

8 .Three circles of radii 4 cm, 6 cm and 8 cm touch each other pair wise externally. The area of the triangle formed, by the line segments joining the centers of the three circles is â€“

A.$144\sqrt3$ sq.cm

B.$12\sqrt105$ sq.cm

C.$6\sqrt6$ sq.cm

D.$24\sqrt6$ sq.cm

a
b
c
d

9 .Let C be a point on a straight line AB, Circles are drawn with diameters AC and AB. Let P be any point on the circumference of the circle with diameter AB. If AP meets other circle at Q, then â€“

A.QC â•‘ PB

B. QC is never parallel to PB

C.QC = $1\over 2$ PB

D. QC â•‘ PB and QC =$1\over 2$ PB
a
b
c
d

10 .A prism has as the base a right-angled triangle whose sides adjacent to the right angles are 10 cm and 12 cm long. The height of the prism is 20 cm. The density of the material of the prism is 6 gm/cubic cm. The weight of the prism is â€“
6.4 kg
7.2 kg
3.4 kg
4.8 kg