MAT 2005 MS Slot 1 Questions & Answer Key

The number of ways in which four letters of the word MATHEMATICS  can be arranged is

A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is 50% more than its height. If the diameter is same for both the bowl and the cylinder, the volume of the beverage in the cylindrical vessel is

The price of copper rose by 25 per cent and then fell by 20 per cent. The price after these changes was

A right circular cone and a right circular cylinder have equal base and equal height. If the radius of the base and the height are in the ratio 5 : 12, then the ratio of the total surface area of the cylinder to that of the cone is

Tom reads at an average rate of 30 pages per hour, while Jan reads at an average rate of 40 pages per hour. If Tom start reading a novel at \(4 : 30\) and Jan begins reading an identical copy of the same book at \(5 : 20\), at what time will they be reading the same page

A contract is to be completed in 46 days and 117 men were set to work, each working 8 hours a day. After 33 days \(\frac{4}{7}\) of the work is completed. How many additional men may be employed so that the work may be completed in time, each man now working 9 hours a day?

The area of a field in the shape of a trapezium measures 1440 \(m^2\). The perpendicular distance between its parallel sides is 24 m. If the ratio of the parallel sides is 5 : 3, the length of the longer parallel side is

Ten different letters are given. Words with five letters are formed from these given letters. The number of words which have at least one letter repeated is

A man rows to a place 48 km distant and back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. the rate of the stream is

A shopkeeper purchased 150 identical pieces of calculators at the rate of Rs. 250 each. He spent an amountof Rs. 2500 on transport and packaging. He fixed the labelled price of each calculator at Rs. 320. However, he decided to give a discount of 5% on the labelled price. Whatis the percentageprofit earned by him?

If \(\log 2 = 0.30103\), find the number of digits in \(2^{56}\).

A cricket club has 15 members, of whom only 5 can bowl. If the names of the 15 members are put into a box and 11 drawn at random, then the chance of obtaining an eleven containing at least 3 bowlers is

From the top of a light-house 60 m high with its base at the sea-level, the angle of depression of a boat is \(15^\circ\). The distance of the boat from the foot of the light-house is

How many multiples of 3 are there among the integers 15 to 105 inclusive?

The traffic lights at three different road crossings change after every 48 sec., 72 sec. and 108 sec., respectively. If they all change simultaneously at \(8 : 20 : 00\) hours, then at what time will they again change simultaneously ?

There are two temples, one on each bank of a river, just opposite to each other. One temple is 54 m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are \(30^\circ\) and \(60^\circ\) respectively. Find the width of the river and the difference of heights of the temples.

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. The height of the cone is

A train 108 m long moving at a speed of 50 km/hr crosses a train 112 m long coming from the opposite direction in 6 seconds. The speed of the second train is

George takes 8 hours to copy a 50 page manuscript while Sonya can copy the same manuscript in 6 hours. How many hours would it take them to copy a 100 page manuscript, if they work together?

Rajan got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marriage. The age of Rajan's sister is

Shekhar started a business investing Rs. 25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajeev joined him with an amount of Rs. 35,000. In 2001, Shekhar invested another additional amount of Rs. 10,000 and then Jatin joined them with an amount of Rs. 35,000. What will be Rajeev’s share in the profit of Rs. 1,50,000 earned at the end of 3 years from the start of the business in 1999?

A person lent out a certain sum on simple interest and the same sum on compound interest at a certain rate of interest per annum. He noticed that the ratio between the difference of compound interest and simple interest of 3 years and that of 2 years is \(25 : 8\). The rate of interest per annum is

An empty fuel tank of a car was filled with A type petrol. When the tank was half-empty, it was filled with B type petrol. Again when the tank was half-empty, it was filled with A type petrol. When the rank was half-empty again, it was filled with B type petrol. What is the percentage of A type petrol at present in the rank ?

A and are two alloys of gold and copper prepared by mixing metals in the ratio \(7 : 2\) and \(7 : 11\) respectively. If equal quantities of the alloys are melted to form a third alloy C, the ratio of gold and copper in C will be

The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ratio of the number of boys to the number of girls in the class is

Bombay Express left Delhi for Bombay at 14.30 hrs, travelling at a speed of 60 kmph and Rajdhani Express left Delhi for Bombay on the same day at 16.30 hrs. travelling at speed of 80 kmph. How far away from Delhi will the two trains meet?

A man is watching from the top of a tower a boat speeding away from the tower. The boat makes an angle of depression of \(45^\circ\) with the man's eye when at a distance of 60 meters from the tower. After 5 seconds, the angle of depression become \(30^\circ\). What is the approximate speed of the boat, assuming that it is running in still water?

Simplify : \(\left[\frac{1}{\log_{xy} (xyz)} + \frac{1}{\log_{yz} (xyz)} + \frac{1}{\log_{zx} (xyz)}\right]\)

A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and 26 cm. Whatis the area of the circle?

The banker's discount on a certain sum due 2 years hence is 11/10 of the true discount.The rate percentis

A cistern has two taps whichfill it in 12 minutes and 15 minutes respectively. There is also
a waste pipe in the cistern. Whenall the three are opened, the empty cistern is full in 20
minutes. How long will the waste pipe take to empty the full cistern?

A spherical ball of lead, 3 cm in diameter is melted and recast into three spherical balls.
The diameter of two of these are 1.5 cm and 2 cm respectively. The diameter of the third
ball is

A man buys a watch for Rs. 1950 in cash andsells it for Rs. 2200 at a credit of 1 year. If
the rate of interest is 10% per annum, the man.

A pole 50 m high stands on a building 250 m high. To an observerat a height of 300 m, the building and the pole subtend equal angles. The distance of the observer from the top of the pole will be

A man and his wife appear in an interview of two vacancies in the same post. The probability of the husband's selections \(\frac{1}{7}\) and the probability of the wife's selections \(\frac{1}{5}\). What is the probability that only one of them is selected?

A container contains 40 liters of milk. From this container 4 liters of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?

A garrison of 3300 men had provisions for 32 days, when given at the rate of 850 gms per head. At the end of 7 days a reinforcement arrives and it was found that the provisions will last 17 days more, when given at the rate of 825 gms per head. What is the strength of the reinforcement?

A man sells Rs. 5000, 12% stock at 156 and invests the proceeds partly in 8% stock at 90 and the balance in 9% stock at 108. He thereby increase his income by Rs. 70. How much of the proceeds were invested in each stock?

If an 'anglet’ is defined as 1 per cent of 1 degree, then how many anglets are there in a circle?

In how many different ways can the letters of the word MATHEMATICS be arranged so that the vowels always come together?