MAT 2002 MS Slot 1 Questions & Answer Key

In a group of 15 women, 7 have nose studs, 8 have ear rings and 3 have neither. How many of these have both nose studs and ear rings?

Shatabadi Express has a capacity of 500 seats of which 10% are in the Executive Class and the rest being Chair Cars. During one journey, the train was booked to 85% of its capacity. If Executive Class was booked to 96% of its capacity, then how many Chair Car seats were empty during that journey?

A person pays Rs. 975 in monthly instalments, each monthly instalment being less than the former by Rs. 5. The amount of the first instalment is Rs. 100. In what time, will the entire amount be paid?

p% of a number P is q% more than r% of the number R. If the difference between P and R is r% of R and if the sum of P and is 210, then which of the following statements is always true ?

A vessel is fully filled with a special liquid. Four litres of liquid is drawn out of this vessel and is replaced with water. If the ratio of the special liquid to the water becomes 1 : 2, then what is the capacity of the vessel?

The weight of a solid cone having diameter 14 cm and vertical height 51 cm is ..........., if the material of solid cone weighs 10 grams per cubic cm.

A box contains 10 balls out of which 3 are red and the rest are blue. In how many ways can a random sample of 6 balls be drawn from the bag so that at the most 2 red balls are included in the sample and no sample has all the 6 balls of the same colour?

‘A’ wants to secure an annual income of Rs. 1500 by investing in 15% debentures of face value Rs. 100 each and available for Rs. 104 each. If the brokerage is 1%, then the sum of money he should invest is

A cycle agent buys 30 bicycles, of which 8 are first grade and the rest are second grade, for Rs. 3150. Find at what price he must sell the first grade bicycles so that if he sells the second grade bicycles at three quarters of the price, he may make a profit of 40% on his outlay?

If \(\log_{x} a,  a^{\frac{x}{2}} and  \log b  x\) are in GP then \(x\) is

The angles of elevation of an artificial satellite measured from two earth stations are \(30^\circ\)and \(40^\circ\) respectively, if the distance between the earth stations is 4000 km, then the height of the satellite is

By selling 33 metres of cloth, a shopkeeper gains the price of 11 metres of cloth. His gain percent is

A cricket team of 11 players is to be formed from 20 players including 6 bowlers and 3 wicket keepers. The number of ways in which a team can be formed having exactly 4 bowlers and 2 wicket keepers is

Sanjay borrowed a certain sum from Anil at a certain rate of simple interest for 2 years. He lent this sum to Ram at the same rate of interest compounded annually for the same period. At the end of two years, he received Rs. 4200 as compound interest but paid Rs. 4000 only as simple interest. Find the rate of interest.

A man in a train notices that he can count 21 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling?

A race course is 400 metres long. A and B run a race and A wins by 5 metres. B and C run over the same course and B wins by 4 metres. C and D run over it and D wins by 16 metres. If A and D run over it, then who would win and by how much?

A track is in the form of a ring whose inner circumference is 352 m and the outer circumference is 396 m. The width of the track is

At a dinner party, every two guests used a dish of rice between them. Every three guests used a dish of daal and every four used a dish of meat between them. There were altogether 65 dishes. How many guests were present?

In an examination paper there are two groups, each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 questions be selected?

In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?

The average (arithmetic mean) of x and y is 40. If z = 10, then what is the average of x, y and z ?

If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius then the surface area of each ball is

If 7% of the sale price of an article is equivalent to 8% of its cost price and 9% of its sale price exceeds 10%of its cost price by Re. 1, then what is the costprice of the article?

Two passengers boarding a flight were found to have between them 34.5 kg of luggage. As per the excess luggage policy of the flight operator, the two passengers were made to pay Rs. 3.75 and Rs. 6.00 for the excess weight of their luggage. Later they found out that if the same luggage were to belong to just one person, then the excess luggage fee would have been Rs. 13.50. How much free luggage is allowed for each passenger?

A person wishes to make a 100 sq m rectangular garden. Since he has only 30 m barbed wire for fencing, he fences only three sides letting the house wall act as the fourth side The width of the garden is

A daily wage worker was paid Rs. 1,700 during a period of 30 days. During this period he was absent for 4 days and was fined Rs. 15 per day for absence. He was paid the full salary only for 18 days as he came late on the other days. Those who came late were given only half the salary for that day. What was the total salary paid per month to a worker who came on time every day and was never absent?

The number of rectangles that you can find on a chessboard is

A car driver travels from the plains to the hill station, which are 200 km apart, at an average speed of 40 km/h. In the return trip, he covers the same distance at an average speed of 20 km/h. The average speed of the car over the entire distance of 400 km is

The area of a square increases by ........... if its side increases by 30%

The monthly incomes of two persons are in the ratio of 4 : 5 and their monthly expenditures are in the ratio of 7 : 9. If each saves Rs. 50 a month, then what are their monthly incomes?

A's age is \(\frac{1}{6}\)th of B's age. B's age will be twice of C's age after 10 years. If C's eighth birthday was celebrated two years ago, then the present age of A must be

A manufacturer offers a 20% rebate on the marked price of a product. The retailer offers another 30% rebate on the reduced price. The two reductions are equal to a single reduction of

A leak was found in a ship when it was 77 km from the shore. It was found that the leak admits 2.25 tonnes of water in 5.5 minutes. 92 tonnes will suffice to sink the ship. But the pumps can throw out the water @ 12 tonnes an hour. Find the average rate of sailing at which the ship may reach the shore as it begins to sink.

Suppose six coins are flipped. Then the probability of getting at least one tail is

In the figure, ABCD is a square with side 10. BFD is an arc of a circle with centre C. BGD is an arc of a circle with centre A. What is the area of the shaded region

Three boys and three girls are to be seated around table in a circle. Among them the boy X does not want any girl neighbour and the girl Y does not want any boy neighbour. How many such arrangements are possible?

We have an angle of \(2\left(\frac{1^\circ}{2}\right)\). How big will it look through a glass that magnifies things three times?

A circular running path is 726 metres in circumference. Two men start from the same point and walk in opposite directions @ 3.75 km/h and 4.5 km/h respectively. When will they meet for the first time?

How many ml of water must be added to 48 ml of alcohol to make a solution that contains 25% alcohol ?

When a bus started from the first stop, the number of male passengers to the number of female passengers was 3: 1. At the first stop, 16 passengers got down and 6 more female passengers got in. The ratio of the male to female passengers now became 2 : 1. What was the total number of passengers in the bus when it started from the first stop?