MAT 2013 Question Paper


For the following questions answer them individually

Question 41

If 15 men, 24 women and 36 boys can do a piece of work in 12 days, working 8h per day, how many men must be associated with 12 women and 6 boys to do another piece of work $$2 \frac{1}{4}$$times as large in 30 days working 6 h per day?

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Question 42

The horizental distance between two towers is 60m. The angular elevation of the top of the taller tower as seen from the top of the shorter one is 30°. If the height of the taller tower is 150m, the height of the shorter one is

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Question 43

A boat travels upstream from B to A and downstream from A to B in 3 h. If the speed of the boat in still water is 9 km/h and the speed of the current is 3 km/h, what is the distance between A and B?

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Question 44

The electricity bill of a certain establishment is partly fixed and partly varies with the number of units of electricity consumed. When in a certain month 540 units are consumed, the bill is 1800. In another month 620 units are consumed and the bill is 2040. In yet another month 500 units are consumed. The bill for that month would be

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Question 45

A booster pump can be used for filling as-well-as for emptying a tank. The capacity of the tank to 2400 m3. The emptying capacity of the tank i8 10 m3 per min higher than its filling capacity and the pump needs 8 min lesser to empty the tank than it needs to fill it. What is the filling capacity of the pump?

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Question 46

A and B walk around a circular track. They start at 8 am from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other before 9:30 am?

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Question 47

The dimensions of a room are $$10 m \times 7 m \times 5 m$$. There are 2 doors and 3 windows in the room. The dimensions of the doors are $$1 m \times 3 m$$. One window is of size $$2 m \times 1.5 m$$ and the other two windows are of size $$ 1 m \times 1.5 m$$. The cost of painting the walls at ₹ 3 per $$m^2$$ is

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Question 48

There are two bags, one of which contains 3 black and 4 white balls, while the other contains 4 black and 3 white balls. A dice is cast. If the face 1 or 3 turns up, a ball is taken from the first bag and if any other face turns up a ball is chosen from the second bag. The probability of choosing a black ball is

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Question 49

A runs $$1\frac{2}{3}$$ times as fast as B. If A gives B a start of 3 80 in. How far must the winning post be so that A and B reach it at the same time?

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Question 50

A cistern, open at the top. is to be lined with sheet lead which weights $$27 kg/m^3$$". The cistern is 4.5 m long and 3 m wide and holds 50 $$m^3$$'. The weight of lead required is

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