Instructions

For the following questions answer them individually

Question 51

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?

Question 52

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

Question 54

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

Question 55

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

Question 56

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?

Question 57

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?

Question 58

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

Question 59

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

Question 60

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