MAT 2007 Question Paper

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?

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.

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 ?

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

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?

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

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 ?

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

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

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?