# ssc cgl tier 1 :: quantitative aptitude :: qa test 58

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

1 .
If Ais the area of a right angled triangle and bis one of the sides containing the right angle, then what is the length of the altitude on the hypotenuse?
$2Ab \over \sqrt {b^4 + 4 A^2}$
$2A^2 b \over \sqrt {b^4 + 4 A^2}$
$2Ab^2 \over \sqrt {b^4 + 4 A^2}$
$2A^2 b^2 \over \sqrt {b^4 + 4 A^2}$

2 .
A parallelogram and a rectangle stand on the same base and on the same side of the base with the same height. If $I_ 1$ , $I_ 2$ be the perimeters of the parallelogram and the rectangle respectively, then which one of the following is correct?
$I_ 1$ < $I_ 2$
$I_ 1$ = $I_ 2$
$I_ 1$ > $I_ 2$ but $I_ 1$ $\neq$2$I_ 2$
$I_ 1$ = 2$l_ 2$

3 .
The diameter of two circles are 18 cm and 8 cm. The distance between their centres is 13 cm. What is the number of common tangents?
1
2
3
None of the above

4 .
What is the geometric means of the observations

125, 729, 1331?
495
1485
2221
None of the above

5 .
The mean of 100 values is 45. If 15 is added to each of the first forty values and 5 is subtracted from each of the remaining sixty values, the new mean becomes
45
48
51
55

6 .
A cylindrical tube open at both ends is made of metal. The internal diameter of the tube is 6 cm and length of the tube is 10 cm. If the thickness of the metal used is 1 cm, then the outer curved surface area of the tube is
140$\pi$sq cm
146.5 $\pi$sq cm
70 $\pi$sq cm
None of the above

7 .
For a plot of land of 100 m $\times$ 80 m, the length to be raised by spreading the earth from stack of a rectangular base 10 m $\times$ 8 m and vertical section being a trapezium of height 2 m. The top of the stack is 8 m $\times$ 5 m. How many centimeters can the level raised?
3 cm
2.5 m
2 cm
1.5 cm

8 .
If $3^ x$ + 27($3^ {-x}$ ) = 12, then what is the value of x?
Only 1
Only 2
1 or 2
0 or 1

9 .
For which value of kdoes the pair of equations$x^ 2$ - $y^ 2$ = 0 and $(x- k)^ 2$ + $y^ 2$ = 1 yield a unique positive solution of x?
2
0
$\sqrt 2$
- $\sqrt 2$
The expression $sin^ 2$ x +$cos^ 2$ x - 1 = 0 is satisfied by how many values of x?