1.A motorboat travelling at the somespeed, can cover 25 km upstream and 39 km downstream in 8 h. At the same speed, it can travel 35 km upstream and 52 km downstream in 11 h. The speed of the stream is
(a) 2 km/h
(b) 3 km/hr
(c) 4 km/h
(d) 5 km/h
(e)None of the above
1. (c); Let the speed of a boat & stream be x & y kmph.
According to question
25/(x-y)+39/(x+y)=8 …………(i)
&
35/(x-y)+52/(x+y)=11………..(ii)
From (i) and (ii)
x=9, y=4
Hence speed of stream, y=4
2.A box contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the box, the probability that it is green is 2/3. The number of blue balls in the box is
(a) 13
(b) 12
(c) 16
(d) 8
(e) None of the above
2. (d); Let the number of green marble=x
So, xC1/24C1=2/3
x=16
So, No. of blue marble=24-16=8
3.From 4 children, 2 women and 4 men, 4 persons are selected. The probability that there are exactly 2 children among the selected persons, is
(a) 11/21
(b) 9/21
(c) 10/21
(d) 5/21
(e) None of the above
3. (b); Total number of cases=10C4
Favourable number of cases=(4C2X6C2)/10C4=9/21
4.There are two bags containing white and black balls. In the first bag, there are 8 white and 6 black balls and in the second bag, there are 4 white and 7 black balls. One ball is drawn at random from any of these two bags. Find the probability of this ball being black.
(a) 5/9
(b) 7/19
(c) 41/77
(d) 9/17
(e) None of the above.
4(c); Probability of selecting black ball from 1st boy.=(1/2)X(6C1/14C1)=3/4
Probability of selecting black ball from 2nd boy=(1/2)X(7C1/11C1)=7/22
Required Probability=(3/14)+(7/22)=41/77
5.If the sum of the lengths of the diagonals of a rhombus is 10 m and if its area is 9 m2. Then, what is the sum of squares of the diagonals?
(a) 36 m2
(b) 64m2
(c) 80m2
(d) 100m2
(e) None of the above
5. (b); Let diagonals of rhombus be x & y.
Given x+y=10
½ x.y=9
xy=18
x^2+y^2=(x+y)^2-2xy
=(10)^2-2.18
=(10)^2-2.18
=64
6.Circumference of a circle A is 1(4/7) times perimeter of a square. Area of the square is 784 sq cm. What is the area of another circle B whose diameter is half the radius of the circle A?
(a) 154 sq cm
(b) 156 sq cm
(c) 35.8 sq cm
(d) 616 sq cm
(e) None of the above
6. (a); Side of square=(784)^(1/2)=28
2pi R=(11/4)X4X28
R=28
Diameter of another circle B=1/2 R=(1/2)X28=14
r=14/2=7
Area of circle=B=pi*7^2=154 cm^2
7.Floorof a square room of side 10 m is to be completed covered with square tiles, each having length 50 cm. The smallest number of tiles needed is
(a) 200
(b) 300
(c) 400
(d) 500
(e) None of these
7. (c); Number of tiles needed=(Area of square room)/(Area of tile)
=(10X100X10X100)/(50X50)
=400
8.The ratio of 1st and 2nd classes train fairs between two stations is 3 : 1 and that of the number of passengers travelling between these stations by 1st and 2nd classes is 1 : 50. If on a particular day, Rs. 2650 be collected from the passengers travelling between these stations, then find the amount collected from 2nd class passengers.
(a) Rs. 3000
(b) Rs. 3500
(c) Rs. 2800
(d) Rs. 2500
(e) None of these
8. (d); Ratio of the amount collected from 1st& 2nd class fairs=(3X1): (1X50)= 3 : 50
Required Amount=2650X(50/53)=2500
9.Nandita scores 80% marks in five subjects together, viz., Hindi, Science, Mathematics, English and Sanskrit, where in the maximum marks of each subject were 105. How many marks did Nandita score in Science, if she scored 89 marks in Hindi, 92 marks in Sanskrit, 98 marks in Mathematics and 81 marks in English?
(a) 60
(b) 75
(c) 65
(d) 75
(e) None of the above.
9. (a); 80% of total marks=80% of 105X5=420
So, obtained marks in Science=420-(89+92+98+81)=60
10.A person invests Rs. 12000 as fixed deposit at a bank at the rate of 10% per annum simple interest. But due to some pressing needs, he has to withdraw the entire money after 3 yr, for which the bank allowed him a lower rate of interest. If he gets Rs. 3320 less than, what he would have got at the end of 5 yr, the rate of interest allowed by bank is
(a) 7(8/9)%
(b) 8(7/9)%
(c) 7(8/9)%
(d) 7(7/9)%
(e) None of the above
10. (e); Let the rate of Interest allowed by bank be r%
(12000X5X10)/100)-((12000X3Xr)/100)=3320
r=7(4/9)%
Directions (Q. 11-15): Study the following graph carefully to answer the questions that follow.
Number of soldiers recruited (in thousand) in three different forces in six different years
11.What was the average number of soldiers recruited in the navy over all the years together?
(a) 25000
(b) 24000
(c) 2400
(d) 28000
(e) None of the above
11. (a); Required Average=(5000+10000+15000+30000+40000+50000)X1/6
=25000
12.Number of soldiers recruited in navy in the years 2009 was what percentage of number of soldiers recruited in army in the year 2006?
(a) 140
(b) 150
(c) 160
(d) 180
(e) None of the above
12. (c); Required Percentage=(40000/250000)X100=160%
13.If 30% of soldiers recruited in airforce in the year 2010 was female, what is the number of males recruited in airforce in that year?
(a) 63000
(b) 6300
(c) 61000
(d) 6100
(e) None of the above
14.What was the respective ratio between the number of soldiers recruited for airforce in the year 2005 and the number of soldiers recruited in army in the year 2009?
(a) 2 : 15
(b) 5 : 13
(c) 2 : 17
(d) 15 : 4
(e) None of the above.
15.What was the approximate percentage decrease in number of soldiers recruited in army in the year 2008 as compared to the previous year?
(a) 20
(b) 23
(c) 38
(d) 30
(e) 33
15 (e); Required Percentage=(45000-30000)X100)/45000
=33% Approx
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