List of top Mathematics Questions asked in MAT

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 metal cube of edge 12 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 6 cm and 8 cm, then find the edge of the third smaller cube.
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.
Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cyclindrical tank, the radius of whose base is 60 cm. By how much will the level of water rise in 30 minutes?
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
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 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?
An iron pipe 20 cm long has exterior diameter equal to 25 cm. If the thickness of the pipe is 1 cm, then the whole surface of the pipe 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.
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?
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 student is to answer 10 out of 13 questions in an examination such that he must choose atleast 4 from the first five questions. The number of choices available to him is
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 club consists of members whose ages are in AP, the common difference being 3 months. If the youngest member of the club is just 7 years old and the sum of the ages of all the members is 250 years, then the number of members in the club are
A plane left 30 minutes later than the scheduled time and in order to reach the destination 1500 km away in time, it had to increase the speed by 250 km/hr from the usual speed. Find its usual speed.
A can do \(50\%\) more work as B can do in the same time. B alone can do a piece of work in 20 hours. A, with help of B, can finish the same work in how many hours?
R and S start walking each other at 10 AM at the speeds of 3 km per hour and 4 km per hour respectively. They were initially 17.5 km apart. At what time do they meet?
A sink contains exactly 12 litres of water. If water is drained from the sink until it holds exactly 6 litres of water less than the quantity drained away, then how many litres of water were drained away?
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.
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.
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 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?
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 school has 4 sections of Chemistry in Class X having 40, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the 4 sections. Determine the overall average of marks per student.