MAT 2007


For the following questions answer them individually

Question 71

Three pipes are made of different shapes. The cross-sections of the pipes are an equilateral triangle, a hexagon and a circle. The perimeter of each of these cross-sections is equal. The flow through the pipes is proportional to the area of cross section. If it takes 8 minutes for the triangular pipe to fill up the tank, what will be the difference in the times taken by the hexagonal and circular pipes?

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Question 72

The Qutab Minar casts a shadow 150 m long at the same time when the Vikas Minar casts a shadow 120 m long on the ground. If the height of the Vikas Minar is 80 m, find the height of the Qutab Minar.

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Question 73

Due to global recession starting in January, Ram’s monthly salary of Rs. 8000 was cut by 10%. The monthly expenses, which were Rs. 6000, increased at the rate of 5% per month. Since which month will he have no savings if the recession lasted for a year ?

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Question 74

An oil refinery takes 100 litres of crude oil as input and after refining for 1 hour gives certain amount of output oil X litres. This can be sold in the market at a profit of Rs 30 per litre. If this oil is further refined for $$\frac{1}{2}$$ hour it gives oil Y litres. This can be sold at a profit of Rs. 50 per litre. Output and input ratio at both the stages is 90%. The maximum amount that can be earned from 1000 litres of crude input is

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Question 75

A mixture (40 litres) contains tonic and water in the ratio 3 : 1 to make the ratio 2 : 1, how much additional amount of water is required?

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Question 76

If 11,109,999 is divided by 1111, then what is the remainder?

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Question 77

If an angle of a triangle remains unchanged but each of its two including side is doubled, then by what factor does the area get multiplied ?

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Question 78

A number when divided by 765 leaves a remainder 42. What will be the remainder if the number is divided by 17 ?

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Question 79

If m and n are natural numbers such that $$ 2^{m}-2^{n}=960$$, what is the value of m ?

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Question 80

The radius of a cylindrical cistern is 10 metres and its height is 15 metres. Initially the cistern is empty, we start filling the cistern with water through a pipe whose diameter is 50 cm, water is coming out of the pipe with a velocity of 5 m/s. How many minutes will it take in filling the cistern with water?

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