76 . 
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? 

Answer & Explanation
Answer : Option
A


Explanation : 







77 . 
In the given triangle, AB is parallel to PQ. AP = c, PC= b,PQ = a, AB= x. What is the value of x? 

Answer & Explanation
Answer : Option
D


Explanation : 







78 . 
What is the number of points in the plane of a $\Delta$ABC which are at equal distance from the vertices of the triangle? 

Answer & Explanation
Answer : Option
B


Explanation : 







79 . 
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? 

Answer & Explanation
Answer : Option
A


Explanation : 







80 . 
42 men take 25 days to dig a pond. If the pond would have to be dug in 14 days, then what is the number of men to be employed? 

Answer & Explanation
Answer : Option
B


Explanation : 







81 . 
There are two taps Aand Bto fill up a water tank. The tank can be filled in 40 min, if both taps are on. The same tank can be filled in 60 min, if tap Aalone is on. How much time will tap Balone take, to fill up the same tank? 

Answer & Explanation
Answer : Option
D


Explanation : 

Work done by tap Bin 1 min = $1 \over 40$  $1 \over 60$ = $3  2 \pver 120$ = $1 \over 120$ 





82 . 
A train started from a station with a certain number of passengers. At the first halt, $1\over 3$rd of its passengers got down and 120 passengers got in. At the second halt, half of the passengers got down and 100 persons got in. Then, the train left for its destination with 240 passengers. How many passengers were there in the train when it started ? 

Answer & Explanation
Answer : Option
D


Explanation : 







83 . 
If the HCF of$x^ 3$ + m$x^ 2$  x+ 2mand $x^ 2$ + mx 2 is a linear polynomial, then what is the value of m? 

Answer & Explanation
Answer : Option
A


Explanation : 







84 . 
A person has four iron bars whose lengths are 24 m, 36 m, 48 m and 72 m respectively. This person wants to cut pieces of same length from each of four bars. What is the least number of total pieces if he is to cut without any wastage? 

Answer & Explanation
Answer : Option
B


Explanation : 

24 = 12 $\times$ 2,
36 = 12 $\times$ 3,
48 = 12 $\times$ 4,
and 72 = 12 $\times$ 6
HCF (24, 36, 48, 72) = 12
Total pieces = 2 + 3 + 4 + 6 = 15 





85 . 
If mean of y and $1\over y$ is M, then what is the mean of $y\over 3$ and $1 \over {y^3}$ 

Answer & Explanation
Answer : Option
D


Explanation : 







86 . 
From a series of 50 observations, an observation with value 45 is dropped but the mean remains the same. What was the mean of 50 observations? 

Answer & Explanation
Answer : Option
C


Explanation : 

Let the observation mean = x
Sum of 50 observations = 50x
According to question
$50x  45 \over 49$ = x
50x  45 = 49x
x = 45 





87 . 
Read the following information carefully to answer the questions that follow
The average age of 6 persons living in a house is 23.5 years. Three of them are majors and their average age is 42 years. The difference in ages of the three minor children is same What is the mean of the ages of minor children? 

Answer & Explanation
Answer : Option
C


Explanation : 

Total age of six persons = 23.5 $\times$ 6 = 141 years
Total age of three major persons = 42 $\times$ 3 = 126 years
Total age of three minor children = 141  126 = 15 years
The difference in ages of the three minor children is same.
Therefore, we take ages may be:
5, 5, 5; 3, 5, 7; 2, 5, 8 and 1, 5, 9
In all the cases, median will be 5 years
Ans: Mean age of minor children = $15 \over 3$ = 5 years 





88 . 
Read the following information carefully to answer the questions that follow What is the median of the ages of minor children? 

Answer & Explanation
Answer : Option
B


Explanation : 

Total age of six persons = 23.5 $\times$ 6 = 141 years
Total age of three major persons = 42 $\times$ 3 = 126 years
Total age of three minor children = 141  126 = 15 years
The difference in ages of the three minor children is same.
Therefore, we take ages may be:
5, 5, 5; 3, 5, 7; 2, 5, 8 and 1, 5, 9
In all the cases, median will be 5 years
ANS: Median age of minor children = 5 years 





89 . 
In how many ways can a committee of 4 people be chosen out of 8 people ? 

Answer & Explanation
Answer : Option
C


Explanation : 







90 . 
Study the following Piechart carefully and answer the questions given below
What is the ratio of the male Engineers and Designers to the sameoccupation female professionals in the town? 

Answer & Explanation
Answer : Option
D


Explanation : 

Male Engineers + Male Designers
40% of (18% of 10500) + 65% of (16% of 10500)
Female Engineers + Female Designers
= 60% of (18% of 10500) + 35% of (16% of 10500)
Required ratio = (40 $\times$ 18)
+ (65 $\times$ 16) : (60 $\times$ 18 + 35 $\times$ 16)
= (720 + 1040) : (1080 + 560)
= 1760 : 1640 = 44 : 41 





