MAT 2006 MS Slot 1 Questions & Answer Key

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

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 student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him 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 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 22.5m 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 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°. If the height of the second tree is 80 m, then find the height of the first tree.

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 of which Mr Y is its member, is

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° and 45°, 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° and when he retires 40 metres away from the tree, the angle of elevation becomes 30°. The breadth of the river 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

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

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

At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is 5/12. On walking 192 metres towards the tower, the tangent of the angle of elevation is 3/4. The height of the tower 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° to 45°, then how soon, after this, will the car reach the tower?

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.

The average score of boys in an examination of a school is 71 and that of girls is 73. The average score of the school in that examination is 71.8. Find the ratio of the number of boys to the number of girls that appeared in the examination.

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?

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 chemist has 10 litres of a solution that is 10 per cent nitric acid by volume. He wants to dilute the solution to 4 per cent strength by adding water. How many litres of water must he add?

A company received two shipments of ball bearings. In the first shipment, 1 per cent of the ball bearings were defective. In the second shipment, which was twice as large as the first, 4.5 percent of the ball bearings were defective. If the company received a total of 100 defective ball bearings, then how many ball bearings were there in the first shipment?

In a certain laboratory, chemicals are identified by a colour coding system. There are 20 different chemicals. Each one is coded with either a single colour or a unique two colour pair. If the order of colours in the pair doesn't matter, then what is the minimum number of different colours needed to code all the 20 chemicals with either a single colour or a unique pair of colours?

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

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?

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)

R and S start walking towards 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 shopkeeper marks up his goods to gain 35%. But he allows 10% discount for cash payment. His profit on the cash transaction therefore, in percentage, is

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?

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 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 6 km/hr, then the train would have taken 6 hours more than the scheduled time. The length of the journey is

Students of a class are made to stand in rows. If 4 students are extra in each row, then there would be 2 rows less. If 4 students are less in each row, then there would be 4 more rows. The number of students in the class 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 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 metallic sheet is of rectangular shape with dimensions 48 cm × 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.