MAT 2005 Question Paper


For the following questions answer them individually

Question 71

A cistern has two taps whichfill it in 12 minutes and 15 minutes respectively. There is also
a waste pipe in the cistern. Whenall the three are opened, the empty cistern is full in 20
minutes. How long will the waste pipe take to empty the full cistern?

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Question 72

A spherical ball of lead, 3 cm in diameter is melted and recast into three spherical balls.
The diameter of two of these are 1.5 cm and 2 cm respectively. The diameter of the third
ball is

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Question 73

A man buys a watch for Rs. 1950 in cash andsells it for Rs. 2200 at a credit of 1 year. If
the rate of interest is 10% per annum, the man.

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Question 74

A pole 50 m high stands on a building 250 m high. To an observerat a height of 300 m, the building and the pole subtend equal angles. The distance of the observer from the top of the pole will be

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Question 75

A man and his wife appear in an interview of two vacancies in the same post. The probability of the husband's selections $$\frac{1}{7}$$ and the probability of the wife's selections $$\frac{1}{5}$$. What is the probability that only one of them is selected?

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Question 76

A container contains 40 liters of milk. From this container 4 liters of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?

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Question 77

A garrison of 3300 men had provisions for 32 days, when given at the rate of 850 gms per head. At the end of 7 days a reinforcement arrives and it was found that the provisions will last 17 days more, when given at the rate of 825 gms per head. What is the strength of the reinforcement?

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Question 78

A man sells Rs. 5000, 12% stock at 156 and invests the proceeds partly in 8% stock at 90 and the balance in 9% stock at 108. He thereby increase his income by Rs. 70. How much of the proceeds were invested in each stock?

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Question 79

If an 'anglet’ is defined as 1 per cent of 1 degree, then how many anglets are there in a circle?

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Question 80

In how many different ways can the letters of the word MATHEMATICS be arranged so that the vowels always come together?

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