MAT 2001 MS Slot 1 Questions & Answer Key

Walking at \(\frac{3}{4}\) of his usual pace, a man reaches his office 20 minutes late. Find his usual time.

If the difference between the simple and the compound interests on some principal amount at 20% for 3 years is Rs 48, then the principal amount must be

In a zoo, there are rabbits and pigeons. If their heads are counted, these are 90 while their legs are 224. Find the number of pigeons in the zoo.

The sides of a rectangular field are in the ratio 3 : 4 with its area as 7500 sq m. The cost of fencing the field @ 25-paise per metre is

A and B together can do a piece of work in 6 days. A alone can doit in 10 days. What time will B require to do it alone ?

A square and an equilateral triangle have the same perimeter. If the diagonal of the square is \(12 \surd2\) cm, then the area of the triangle is

Acistern is filled in 5 hours and it takes 6 hours when thereis a leak in its bottom. If the cistern is full, in what time shall the leak empty it?

The radius of the circumcircle of an equilateral triangle of side 12 cm is

The sides of a triangle are 6 cm, 11 cm and 15cm. The radiusofits incircle is

The sum of the interior angles of a polygon is 1620. The number of sides of the polygon must be

The distance between the tops of two trees 20 m and 28 m high is 17 m. The horizontal distance between the two trees is

Rs 770 have been divided among A, B and C such that A receives 2/9th of what B and C together receive. Then A's share is

What least number must be subtracted from each of the numbers 14, 17, 34 and 42 so that the remainders are proportional ?

\(\frac{3\pi}{5}\) radians is equal to

If \(\sin A : \cos A = 4 : 7\), then the value of \(\frac{(7 \sin A - 3 \cos A)}{(7 \sin A+ 2 \cos A)}\) is

A tree breaks due to storm and the broken part bends so that the top of the tree first touches the ground, making an angle of 30 with the horizontal. The distance from the foot of the tree to the point where the top touches the ground is 10 m. The height of the tree is

If \(pqr = 1\) then 

\(\left(\left(\frac{1}{(1 + p + q^{-1})}\right) + \left(\frac{1}{(1 + q + r^{-1})}\right) + \left(\frac{1}{(1 + r + p^{-1})}\right)\right)\) is equal to

An edge of a cube measures 10 cm. If the largest possible cone is cut out of this cube, then the volume of the cone is

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 a and b are the roots of the equation \(x^2 - 6x + 6 = 0\), then the value of \(a^2 + b^2\) is

If \(a : b = 2 : 5\) then \((3a + 4b) : (5a + 6b)\) is equal to

The value of 

\((1^3 + 2^3 + 3^3 + ........ + 15^3) - (1 + 2 + 3 + ......... + 15)\) is

In the figure given below, O is the centre of the circle. If \(\angle OBC = 37^\circ\), the \(\angle BAC\) is equal to

A horse is tethered to one corner of a rectangular grassy field 40 m by 24 m with a rope 14 m long. Over how much area of the field can it graze ?

A two-digit number is such that the product of the digits is 14. When 45 is added to the number, then the digits interchange their places. Find the number.

Vishal goes to a shop to buy a radio costing Rs 2568. The rate of sales tax is 7%. He tells the shopkeeperto reduce the price of the radio to such an extent that he has to pay Rs 2568, inclusive of sales tax. Find the reduction needed in the price of the radio.

Dinesh travels 760 km to his home, partly by train and partly by car. He takes 8 hoursif he travels 160 km bytrain and the rest by car. He takes 12 minutes moreif he travels 240 km bytrain and the rest by car. The speedsof the train and the car respectively are

A person on tour has Rs 360 for his daily expenses. If he extends his tour for 4 days, he hasto cut his daily expensesby Rs3. Find the original duration of the tour.

Rs 6500 were divided equally among a certain number of persons. Had there been 15 more persons, each would have got Rs 30 less. Find the original number of persons.

Pipes A and B running together can fill a cistern in 6 minutes. If B takes 5 minutes more than A to fill the cistern, then the times in which A and will fill the cistern separately will be respectively

In a flight of 3000 km, an aircraft was slowed down by bad weather. Its average speed for the trip was reduced by 100 km/hour and the time increased by one hour. Find the original duration of the flight.

Students of a class are made to stand in rows. If 4 students are extra in a row, there would be 2 rows less. If 4 students are less in a row, there would be 4 more rows. Find the numberof students in the class.

Four different objects 1, 2, 3, 4 are distributed at random in four places marked 1, 2, 3, 4. What is the probability that none of the objects occupy the place corresponding to its number ?

A boat goes 24 km upstream and 28 km dowstream in 6 hours. If it goes 30 km upstream and 21 km downstream in 6 hours and 30 minutes, find the speed of the stream.

The diameter of a cycle wheel is 70 cm. A cyclist takes 30 hours to reach a destination at the speed of 22 km/hr. How many revolutions will the wheel make during this journey?

Shyam had 85 currency notes in all, some of which were of Rs 100 denomination and the remaining of Rs 50 denomination. The total amountof all these currency notes was Rs 5000. How much amountin rupeesdid he have in the denomination of Rs 50?

Acar owner buyspetrol at Rs 7.50, Rs 8.00 and Rs 8.50 per litre for three successive years. What approximately is the average costper litre of petrol if he spends Rs 4000 each year?

lf 10 years are subtracted from the present age of Ram and the remainderdivided by 14, then you would get the preset age of his grandson Shyam. If Shyam is 9 years younger to Sunder whose age is 14, then whatis the present age of Ram?

Sunder purchased an office bag with a price tag of Rs 600 in a sale where 25%discount was being offered on the tag price. He was given a further discount of 10% on the amount arrived at after giving usual 25%discount. What wasthe final amount paid by Sunder?

The mean of 30 values was 150. It was detected on rechecking that one value 165 was wrongly copied as 135 for the computation of the mean. Find the correct mean.