List of top Questions asked in MAT- 2006

A train covered a certain distance at a uniform speed. If the train had been 6 km/hr faster, then it would have taken 4 hours less than the scheduled time. And, if the train were slower by 6km/hr, then the train would have taken 6 hours more than the scheduled time. The length of the journey is
A train covers 180 km distance in 4 hours. Another train covers the same distance in 1 hour less.What is the difference in the distances covered by these trains in one hour?
An aeroplane flying at a height of 300 metres above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are \(60^\circ\) and \(45^\circ\), respectively. Then the height of the lower plane from the ground, in metres, is
A ladder 15 m long reaches a window which is 9 m above the ground on one side of a street.Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 12 m high. Find the width of the street.
A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank of the river is \(60^\circ\) and when he retires 40 metres away from the tree, the angle of elevation becomes \(30^\circ\). The breadth of the river is
A man on the top of a vertical tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from \(30^\circ\) to \(45^\circ\), then how soon, after this, will the car reach the tower?
The horizontal distance between two trees of different heights is 60 m. The angle of depression of the top of the first tree when seen from the top of the second tree is \(45^\circ\). If the height of the second tree is 80 m, then find the height of the first tree.
In each of these questions, there is given a Statement followed by two Assumptions numbered I and II. Consider the Statement and the following Assumptions to decide which of the Assumptions is implicit in the Statement. 
Statement:
An advertisement of a Bank, "Want to open a bank account! Just dial our 'room service' and we will come at your doorsteps".
Assumptions:
I. There is a section of people who require such services at their home.
II. Nowadays banking has become very competitive.
The number of ways in which a committee of 3 ladies and 4 gentlemen can be appointed from a meeting consisting of 8 ladies and 7 gentlemen, if Mrs X refuses to serve in a committee if Mr Y is its member, is
A circular grassy plot of land, 42 m in diameter, has a path 3.5 m wide running around it outside.The cost of gravelling the path at Rs 4 per square metre is
There are 4 candidates for the post of a lecturer in Mathematics and one is to be selected by votes of 5 men. The number of ways in which the votes can be given is
A metallic sheet is of rectangular shape with dimensions 48 cm \(\times\) 36 cm. From each one of its corners, a square of 8 cm is cut off. An open box is made of the remaining sheet. Find the volume of the box.
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by
A plot of land in the form of a rectangle has a dimension 240 m × 180 m. A drainlet 10m wide is dug all around it (outside) and the earth dug out is evenly spread over the plot, increasing its surface level by 25 cm. The depth of the drainlet is
A room has 3 lamps. From a collection of 10 light bulbs of which 6 are not good, a person selects 3 at random and puts them in a socket. The probability that he will have light is
Speed of a speedboat when moving in the direction perpendicular to the direction of the current is 16 km/hr. Speed of the current is 3 km per hour. So the speed of the boat against the current will be (in km/hr)
Profits of a business are distributed among three partners A, B and C in such a way that 4 times the amount received by A is equal to 6 times the amount received by B and 11 times the amount received by C. The ratio in which the three received the amount is
A part of monthly expenses of a family is constant and the remaining varies with the price of wheat. When the rate of wheat is Rs 250 a quintal, the total monthly expenses of the family are Rs 1000 and when it is Rs 240 a quintal, the total monthly expenses are Rs 980. Find the total monthly expenses of the family when the cost of wheat is Rs 350 a quintal.
A well 22.5 deep and of diameter 7m has to be dug out. Find the cost of plastering its inner curved surface at Rs 3 per sq metre.
Company C sells a line of 25 products with an average retail price of Rs 1,200. If none of these products sells for less than Rs 420 and exactly 10 of the products sell for less than Rs 1,000, then what is the greatest possible selling price of the most expensive product?
Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that atleast one of the selected persons will be a woman is
The probability that a certain electronic component fails when first used is 0.10. If it does not fail immediately, then the probability that it lasts for one year is 0.99. The probability that a new component will last for one year is
Population of a district is 2,96,000 of which 1,66,000 are males. \(50\%\) of the population is literate. If \(70\%\) males are literate, then the number of women who are literate, is
In a certain laboratory, chemicals are identified by a colourcoding system. There are 20 different chemicals. Each one is coded with either a single colour or a unique twocolour pair. If the order of colours in the pair doesn't matter, then what is the minimum number of differentcolours needed to code all the 20 chemicals with either a single colour or a unique pair of colours?
A rectangular tank is 225 m by 162 m at the base. With what speed must water flow into it through an aperture 60 cm by 45 cm that the level may be raised 20 cm in 5 hours?