MAT 2004 Question Paper
For the following questions answer them individually
Train A travelling at 60km/hr leaves Mumbai for Delhi at 6 p.m. Train B travelling at 90 km/hr also leaves Mumbai for Delhi at 9 p.m. Train C leaves Delhi for Mumbai at 9 p.m. If all the three trains meet at the some time between Mumbai and Delhi, then what is the speed of Train C if the distance between Delhi and Mumbai is 1260 km?
A boat, while going down-stream in a river covered a distance of 50 miles at an average speed of 60 miles per hour. While returning, because of the water resistance, it took one hour fifteen minutes to cover the same distance. What was the average speed during the whole journey?
What is the third term in a sequence of numbers that leave remainders of 1, 2 and 3 when divided by 2, 3 and 4 respectively?
In a special racing event, the person who enclosed the maximum area would be the winner and would get Rs 100 for every square meter of area covered by him/her. Johnson, who successfully completed the race and was the eventual winner, enclosed the area shown in figure below. What is the prize money won? (Note: The arc from C to D makes a complete semi-circle).
AB = 3 m, BC = 10 m, CD = BE = 2 m
A and B can finish a job in 10 days while B and C can do it in 18 days. A started the job, worked for 5 days, then B worked for 10 days and the remaining job was finished by C in 15 days. In how many days could C alone have finished the whole job?
If $$8^x 2^y = 512 and 3^{3 x + 2 y} = (3^2)^{(3 * 2)}$$ then what is the value of $$x$$ and $$y$$ ?
In his wardrobe, Timothy has 3 trousers. One of them is black, the second blue, and the third brown. In his wardrobe, he also has 4 shirts. One of them is black and the other 3 are white. He opens his wardrobe in the dark and picks out one shirt-trouser pair, without examining the colour. What is the likelihood that neither the shirt nor the trouser is black?
In a factory, producing parts for an automobile, the parts manufactured on the shop floor are required to go through three quality checks, each conducted after a specific part of the processing on the raw material is completed. Only parts that are not rejected at one stage are put through the subsequent stages of production and testing. If average rejection rates at these three testing machines during a month are 10%, 5% and 2% respectively, then what is the effective rejection rate for the whole plant?
A country follows a progressive taxation system under which the income tax rate applicable varies for different slabs of income. Total tax is computed by calculating the tax for each slab and adding them up. The rates applicable are as follows:
If my annual income is Rs. 1,70,000, then what is the tax payable by me?
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