1.A cylindrical tank 7 m in diameter, contains water to depth of 4
m. What is the total area of wetted surface?
(a) 110.5 sq.m
(a) 126.5 sq.m
(a) 131.5 sq.m
(a) 136.5 sq.m
2.The inner and outer radii of a 7 m long hollow iron right circular cylindrical pipe are 2 cm and 4 cm respectively. If 1000 cm^3 of iron weights 5 kg, what is the weight of the pipe?
(a) 264 kg
(b) 132 kg
(c) 396 kg
(d) None of these
3.A sphere is cut into two equal halves and both the halves are
painted from all the sides. The radius of the sphere is r unit and the rate of
painting is Rs. 8 per sq unit. What is the total cost of painting the two
halves of the sphere in rupees?
(a) 6 πr^2
(b) 32 πr^2
(c) 48 πr^2
(d) Insufficient data to answer
4.Shyam bought 2 articles for Rs. 5.50/- each, and 3 articles for
Rs. 3.50/- each and 3 articles for Rs. 5.50/- each and 5 articles for Rs.
1.50/- each. The average price for one article is:
(a) Rs. 3/-
(b) Rs. 3. 10/-
(c) Rs. 3. 50/-
(d) Rs. 2/-
5.Four runners started running simultaneously from a point on a
circular track. They took 200 sec, 300 sec, 360 sec and 450 sec to complete one
round. After how much time do they meet at the starting point for the first
time?
(a) 1800 seconds
(b) 3600 seconds
(c) 2400 seconds
(d) 4800 seconds
6.Water is flowing at the rate of 5 km/hr through a pipe of
diameter 14 cm into a rectangular tank which is 50 m long, 44 m wide. The time
taken, in hours, for the rise in the level of water in the tank to be 7 cm is
(a) 2
(b) 1 ½
(c) 3
(d) 2 ½
7.The ratio of the quantities of an acid and water in a
mixture is 1 : 3. If 5 litres of acid is further added to the mixture, the new
ration becomes 1 : 2. The quantity of new mixture in litres is:
(a) 32
(b) 40
(c) 42
(d) 45
8.The cost of an apple is twice that of a banana and the cost of a
banana is 25% loss than that of a guava. If the cost of each type of fruit
increase by 10%, then the percentage increase in cost of 4 banana, 2 apples and
3 guavas is
(a) 10%
(b) 12%
(c) 16%
(d) 18%
9.If I walk at 5 km/hour, I miss a train by 7 minutes. If,
however, I walk at 6 km/hour, I reach the station 5 minutes before the
departure of the train. The distance (in km) between my house and the station
is
(a) 6
(b) 5
(c) 4
(d) 3
10.The average age of 11 players of a cricket team is increased by
2 months when two of them aged 18 years and 20 years are replaced by two
new players. The average age of the new players is
(a) 19 years 1 month
(b) 19 years 6 month
(c) 19 years 11 month
(d) 19 years 5 month
ANSWERS AND SOLUTION :
1.(b) ; Required surface area = πr^2+ 2πrh
= πr(r+2h)
= 22/7 * 7/2 (7/2 + 2 * 4)
= 11* (7 + 16)/2 = 11 * 23/2
= 126.5 sq.mt
2.(b) ; Required weight of pipe = Ï€(R^2 – r^2)h
= 22/7 (4^2 – 2^2) 700
= 26400 cm^2
= 26400 * 5/1000 kg
132 kg
3.(c) Total surface area of two halves = 3Ï€r^2 + 3Ï€r^2
= 6Ï€r^2
Required cost = 8 * 6Ï€r^2 = Rs. 48Ï€r^2
4.(c) Required average price
= (2 × 5.5 + 3 × 3.5 + 3 × 5.5 + 5 × 1.5)/((2+3+3+5))
= (11.0 + 10.5 + 16.5 + 7.5)/13
= 45.5/13
= Rs. 3.50/-
5.(a) Required time = L.C.M of (200, 300, 360 and 450) second
= 1800 seconds
6.(a); Quantity of water flows in 1 hour = πr^2h
= (22 ×7 ×7 ×5000)/(7 ×100 ×100) = 77 cm^3
Volume of water in pipe = (50 ×44 ×7)/100 154 cm^3
so Required time = 154/77 = 2 hours
7.(d) ; Let quantity of acid in mixture = x
And quantity of water in mixture = 3x
According to question,
x + 5/3x = 1/2
=> 3x = 2x + 10
=> x = 10 litres
So, Total quantity of new mixture
= x +3x + 5 = 4x + 5
= 4 * 10 + 5 = 45 litres
8.(a); Let price of a banana be = Rs. 100/-
then, price of an apple and a guava respectively will be Rs. 200/- and Rs. 250/-
Sum of prices of 4 bananas, 2 apples and 3 guavas
= 400 + 400 + 750
= Rs. 1550/-
Sum of prices of 4 bananas, 2 apples and 3 guavas
= 110/100 * 400 * 110/100 * 400 + 110/100 * 750
= 440 + 440 + 825 = Rs. 1705/-
So, increased percentage = (1705 – 1550)/1550 * 100
= 155/1550 * 100 = 10%
9.(a) Let distance between house and station be x km
According to question
x/5 – x/6 = (7+5)/60
(6x – 5x)/30 = 12/60
7x = (30* 12)/60 = 6 km
10.(c) Total increment in age = 11 * 2 = 22 months
so Total ages of two new players
= (18 + 20) years + 22 months
= 38 years + 22 months
1.(b) ; Required surface area = πr^2+ 2πrh
= πr(r+2h)
= 22/7 * 7/2 (7/2 + 2 * 4)
= 11* (7 + 16)/2 = 11 * 23/2
= 126.5 sq.mt
2.(b) ; Required weight of pipe = Ï€(R^2 – r^2)h
= 22/7 (4^2 – 2^2) 700
= 26400 cm^2
= 26400 * 5/1000 kg
132 kg
3.(c) Total surface area of two halves = 3Ï€r^2 + 3Ï€r^2
= 6Ï€r^2
Required cost = 8 * 6Ï€r^2 = Rs. 48Ï€r^2
4.(c) Required average price
= (2 × 5.5 + 3 × 3.5 + 3 × 5.5 + 5 × 1.5)/((2+3+3+5))
= (11.0 + 10.5 + 16.5 + 7.5)/13
= 45.5/13
= Rs. 3.50/-
5.(a) Required time = L.C.M of (200, 300, 360 and 450) second
= 1800 seconds
6.(a); Quantity of water flows in 1 hour = πr^2h
= (22 ×7 ×7 ×5000)/(7 ×100 ×100) = 77 cm^3
Volume of water in pipe = (50 ×44 ×7)/100 154 cm^3
so Required time = 154/77 = 2 hours
7.(d) ; Let quantity of acid in mixture = x
And quantity of water in mixture = 3x
According to question,
x + 5/3x = 1/2
=> 3x = 2x + 10
=> x = 10 litres
So, Total quantity of new mixture
= x +3x + 5 = 4x + 5
= 4 * 10 + 5 = 45 litres
8.(a); Let price of a banana be = Rs. 100/-
then, price of an apple and a guava respectively will be Rs. 200/- and Rs. 250/-
Sum of prices of 4 bananas, 2 apples and 3 guavas
= 400 + 400 + 750
= Rs. 1550/-
Sum of prices of 4 bananas, 2 apples and 3 guavas
= 110/100 * 400 * 110/100 * 400 + 110/100 * 750
= 440 + 440 + 825 = Rs. 1705/-
So, increased percentage = (1705 – 1550)/1550 * 100
= 155/1550 * 100 = 10%
9.(a) Let distance between house and station be x km
According to question
x/5 – x/6 = (7+5)/60
(6x – 5x)/30 = 12/60
7x = (30* 12)/60 = 6 km
10.(c) Total increment in age = 11 * 2 = 22 months
so Total ages of two new players
= (18 + 20) years + 22 months
= 38 years + 22 months
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