1. Four equal circles are described about the four corners of a square so that each touches two of the others. If each side of the square is 14 cm, then the area enclosed between the circumferences of the circles is –
1) 24 sq. meters
2) 42 sq. meters
3) 154 sq. meters
4) 196 sq. meters
2. The length of a room is double the breadth. The cost of colouring the roof at Rs. 50 per square meter is Rs.10,000 and the cost of painting the four walls at Rs. 480 per square meter is Rs. 129,600. Find the height of the room.
1) 4.5 meters
2) 5.7 meters
3) 4.6 meters
4) 5.6 meters
5) None of these
3. A sphere of radius 6 cm. is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 12 cm. If the sphere is submerged completely, then the surface of the water is increased by –
1) 1 cm
2) 3 cm
3) 2 cm
4) 5 cm
5) None of these
4. The diameter of the wheel of a bus is 70 cm. How many revolutions per minute must the wheel make in order to keep a speed of 33 km/hr?
1) 350
2) 250
3) 341
4) 441
5) None of these
5. If the probability of police raid on any given day in the house of a criminal is 50%, then what is the probability that the police raids on exactly 3 days in a five-day period?
1) 3/16
2) 4/16
3) 8/11
4) 7/9
5) None of these
6. Three of the men participating in a race are A, B and C. The probability of A winning the race is 1/12, the probability for B winning the race is 1/5 and for C is 2/13. If dead heat among them is possible, what is the robability that only one of the three winning the race?
1) 253/768
2) 263/768
3) 453/786
4) 373/441
5) None of these
7. Ajay marks up the prices of articles by 50% and he sells only 40% of those at this price. He sells half of the remaining at 14 2/7% discount and remaining at 25% discount. What is net profit of Ajay?
1) 23.5%
2) 8 3/14%
3) 24.5%
4) 44.5%
5) None of these
8. The price of a commodity to sell it was set in a manner so that the shopkeeper earns 25% profit. Had he bought it at 15% less and sold it at Rs. 35 less then he would have earned 30% profit. Find the cost price. (in Rs.)
1) 241 11/29
2) 231 44/49
3) 37.375
4) 4035
5) None of these
9. The difference between the compound interest and simple interest earned on a sum of Rs. 23,700 in 3 years is Rs. 1253.6589. Find the rate per cent.
1) 11%
2) 12%
3) 13%
4) 14%
5) None of these
10. 4 litres of wine are drawn from a cask containing 40 litres of wine and It is replaced by water. The process is repeated 5 times. Find out the ratio of wine to water finally. (Approximately)
1) 3 : 2
2) 2 : 3
3) 4 : 5
4) 5 : 6
5) None of these
Answers:
1. 2
Area of the square = 196 sq cm
Area of the four quadrants = Area of the circle with radius
= 7 cm
= 22/7 × 72 = 154 sq. cm.
Required Area = 196 – 154 = 42 sq. cm.
2. 1
Let the length be l so breadth = l/2
Now, l × l/2 = 10000/50
l^2 = 400
l = 20
Now, 2lh + 2 × l/2 × h = 129600/480
3lh = 27
h = 270/(3*20)
h = 4.5 m.
3. 3
Let h be the height up to the level of water in the cylinder.
Volume of water in the cylinder = 22/7 r^2 h = 22/7 * 144 * h
Let h1 be the height to which the water level is raised.
22/7 * 144 * (h1 - h) = 4/3 * 22/7 * 216
h1 - h = 2cm
4. 2
Distance in 60 minutes = 33000 meters
In 1 min distance = 33000/60 = 550 m
Hence, number of revolutions per minute = 550/(2*22/7*0.35) = 250
5. 5
Probability that the house could be raided on any day in 5–
day period = 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1/32
Required probability = 5C3 * 1/32 = 10/32 = 5/16
6. 5
The probability of any one winning the race given that
dead heat is possible is
P (A wins, B loses and C loses) + P (B wins, A loses and C loses) + P (C wins, B loses and A loses), i.e.,
1/12 * 4/5 * 11/13 * 1/5 * 11/12 11/13 * 2/13 * 11/12 * 4/5
= 11/195 + 121/780 + 22/195
= 33/195 + 121/780
= 253/780
7. 2; Let the no. of articles be 100
Let the C.P of 1 article = Rs. 1
Total C. P = Rs. 100
Total selling price = 40×1.5 + 30 ×6/7 + 30×0.75 = 108 3/14
%Profit = 108 3/14 - 100 = 8 3/14%
8. 1
When difference in SP is Rs. 14.5 then C.P is Rs. 100
if difference in S.P is Rs. 35 then C.P = 100/14.5 * 35 = Rs. 241 11/29
9. 3; C.I – S.I = Rs. 1253.6589
1253.6589/23700 * 100 = 5.2897 % of the sum
We know that 13% is the required rate of interest because in 3 yrs, CI became 44.2897% of the sum and SI remains 39% of the sum, the difference is 5.2897%.
So option 3 is correct.
10. 1
Amount of wine left = 40 * 9/10 * 9/10 * 9/10 * 9/10 * 9/10 = 23.61 litres
Water = 40 - 23.61 = 16.38
Approximate ratio = 24 : 16 = 3 :2
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