## Home SSC / SSC CHSL Quantitative Aptitude Questions and Answers

61 .
The letters of the word SOCIETY are placed at random in a row. The probability that the three vowels come together is
$1 \over 6$
$1 \over 7$
$2 \over 7$
$5 \over 6$
62 .
There are three events $E_ 1$ , $E_ 2$ and $E_ 3$ . One of which must, and only one can happen. The odds are 7 to 4 against $E_ 1$ and 5 to 3 against $E_ 2$. The odds against $E_ 3$ is
4 : 11
3 : 8
23 : 88
65 : 23
63 .
If 27 $\times$ $(81)^{2n + 3}$ - $3^m$=0 , then what is m equal to?
2n + 5
5n+ 6
8n+ 3
8n+ 15
64 .
What is $\sqrt 5 + \sqrt 3 \over \sqrt 5 - \sqrt 3$ + $\sqrt 5 - \sqrt 3 \over \sqrt 5 + \sqrt 3$ equal to ?
16
8
4
$\sqrt {15}$
65 .
A trader marked a watch 40% above the cost price and then gave a discount of 10%. He made a net profit of Rs.468 after paying a tax of 10% on the gross profit. What is the cost price of the watch?
Rs. 1200
Rs.1800
Rs.2000
Rs.2340
66 .
By selling 8 dozen pencils, a shopkeeper gains the selling price of 1 dozen pencils. What is the gain?
12$1 \over 2$ %
13$1 \over 7$ %
14$2 \over 7$ %
87$1 \over 2$ %
67 .
For what value of k, will the expression 3$x^ 3$ - k$x^ 2$ + 4x + 16 be divisible by (x - $k \over 2$) ?
4
- 4
2
0
68 .
What is the value of 2 + $\sqrt 2$ + $1 \over 2 + \sqrt 2$ - $1 \over 2 - \sqrt 2$ ?
2
2 - $\sqrt 2$
4 + $\sqrt 2$
2$\sqrt 2$
69 .
If a cos $\theta$- b sin $\theta$= c, then what is the value of a sin $\theta$+ b cos $\theta$?
± $\sqrt {a^2 + b^2 + c^2}$
± $\sqrt {a^2 - b^2 + c^2}$
± $\sqrt {a^2 + b^2 - c^2}$
± $\sqrt {a^2 - b^2 - c^2}$
70 .
If 2$x^ 2$ cos 60° - 4 $cot^ 2$ 45° - 2 tan 60° = 0, then what is the value of x?
2
3
$\sqrt 3$ - 1
$\sqrt 3$ + 1
71 .
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
72 .
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
$1 \over 2$
73 .
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$cm^2$
74 .
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
75 .
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%