MAT 2003 MS Slot 1 Questions & Answer Key

The sum of the \(6^{th}\) and \(15^{th}\) elements of an arithmetic progression is equal to the sum of \(7^{th}\), \(10^{th}\) and \(12^{th}\) elements of the same progression. Which element of the series should necessarily be equal to zero?

Mr. X's salary is increased by 20%. On the increase, the tax rate is 10% higher. The percentage increase in tax liability is

Rohit, Harsha and Sanjeev are three typists who, working simultaneously, can type 216 pages in four hours. In one hour, Sanjeev can type as many pages more than Harshs as Harsha can type more than Rohit. During a period of five hours, Sanjeev can type as many pages as Rohit can during seven hours How many pages does each of them type pei hour?

A box of light bulbs contains 24 bulbs. A worker replaces 17 bulbs in the shipping department and 13 bulbs in the accounting department. How many boxes of bulbs did the worker use?

If there are 3 different roads from Delhi to Mumbai and 4 different roads from Mumbai to Chennai, then how many roadsare there from Delhi to Chennai that go through Mumbai?

What will Rs. 1000 be worth after three yearsif it earns interest at the rate of 5% compounded annually?

A bag contains 2 red, 3 green and 2 blue balls. 2 balls are to be drawn randomly. Whatis the probability that the balls drawn contain no blue ball?

If \(p, q, r, s\) are in harmonic progression and \(p > s\), then

A worker makes a basket in \(\frac{2}{3}\) of an hour. If he works for \(7 \left(\frac{1}{2}\right)\) hours, then how many baskets will he make?

The slope of a function \(y = x^3 + kx  at  x = 2\) is equal to the area under the curve \(z = a^2 + a\) between points a = 0 and a = 3 Then the value of k is

If 5 men take an hour to dig a ditch, then how long should 12 men take to dig a ditch of the same type?

The difference between the logarithms of sum of the squares of two positive numbers A and B and the sum of logarithms of the individual numbers is a constant C. If A = B, then C is

How muchinterest will Rs- 10,000 earn in 9 months at an annual rate of 6 per cent?

There are four prime numbers written in ascending order. The product of the first three is 385 and that of the last three is 1001. The first number is

A train can travel 20%faster than a car. Both start from the point A at the same time and reach point B 75 km away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is

Pintoo dealt some cards to Minto and himself from a full pack of playing cards andlaid the rest aside. Pintoo then said to Mintoo, "If you give me a certain number of your cards I will have 4 times as many cards as you have. If I give you the same numberof cards, I will have thrice as many cards as you have." How manycards did Pintoo have?

An express train travelled at an average speed of 100 kmph, stopping for 3 minutes after every 75 km.A local train travelled at a speed of 50 kmph, stopping for 1 minute after every 25 km. If the trains began travelling at the same time, then how many kilometres did the local train travel in the time it took the express train to travel 600 km?

For an acute angle \(\theta, \sin \theta + \cos \theta\) takes the greater value when \(\theta\) is

HCF of 3240, 3600 and a third number is 36 and their LCM is \(2^4 \times 3^5 \times 5^2 \times 7^2\). The third number is

The cost function at production x is defined as \(C(x) = 3x^3 - x + 2\) and sale function at A cost x is defined as \(S(x) = \left(\frac{A}{x^{\frac{1}{3}}}\right)\). Which of the following is true?

If x is a positive number, then which of the following fractions has the greatest value?

Which values of x are satisfied by the inequality \(2x^2 + x - 3 < 0\)?

If the probability that A will live 15 years is \(\left(\frac{7}{8}\right)\) and that B will live 15 years is \(\left(\frac{9}{10}\right)\), then what is the probability that both will live after 15 years?

A shopkeeper sold a TV set for Rs. 17,940, with a discount of 8% and gained 19.6%. If no discount is allowed, then whatwill be his gain per cent?

The number of tangents that can be drawn to two non-intersecting circles is

A number is increased by 10% and then reduced by 10%. After this operation, the number

The average of 11 numbersis 10.9. If the average of the first six numbers is 10.5 and that of the last six numbersis 11.4, then the middle number is

A man sells an article at 5% profit. If he had bought it at 5% less and sold it for Re. 1 less, he would have gained 10%. The costprice of the article is

A starts 3 min after B for a place 4.5 km distant B, on reaching his destination, immediately returns and after walking a km meets A.if A can walk 1 km in 18 minutes, then whatis B's speed ?

A company has 6,435 bars of soap, if the company has sold 20 per cent of its stock, then how many bars of soap did it sell?

A dairyman pays Rs. 6.4 per liter of milk. He adds water and sells the mixture at Rs. 8 per liter, thereby making 37.5% profit. The proportion of water to milk received by the customers is

Wheels of diameters 7 cm and 14 cm start rolling simultaneously from X and Y, which are 1980 cm apart, towards each other in opposit directions. Both of them make same number of revolutions per second. If both of them meet after 10 seconds, the speed of the smaller wheel is

What is the eighth term of the sequence 1, 4, 9, 16, 25, ...........?

A bicycle originally costs Rs 100 and was discounted 10%. After three months it was sold after being discounted 15%. How much was the bicycle sold for?

\(\left(\frac{1}{2}\right) \log_{10} 25 - 2\log_{10} 3 + \log_{10} 18\) equals

A bag contains Rs. 216 in the form of one rupee, 50 paise and 25 paise coins in the ratio of \(2 : 3 : 4\). The number of 50 paise coins is

The length of the longest rod that can be placed in a room which is 12 m long 9 m broad and 8 m high is

Two trains of equal length are running on parallel lines in the same direction at 46 km and 36 km per hr. The faster train passes the slower train in 36 sec. The length of eachtrain is

The remainder when 784is divided by 342 is

In a 800 m race around a stadium having the circumference of 200 m, the top runner meets the last runner on the 5th minute of the race. If the top runner runs at twice the speed of the last runner, what is the time taken by the top runner to finish the race?