Instructions

For the following questions answer them individually

Question 51

The distance from B to C is thrice that from A to B. Two trains travel from A to C via B.Ā The speed of train 2 is double that of train 1 while traveling from A to B and theirĀ speeds are interchanged while traveling from B to C. The ratio of the time taken byĀ train 1 to that taken by train 2 in travelling from A to C is

Question 52

John takes twice as much time as Jack to finish a job. Jack and Jim together takeĀ one-thirds of the time to finish the job than John takes working alone. Moreover, inĀ order to finish the job, John takes three days more than that taken by three of themĀ working together. In how many days will Jim finish the job working alone?

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Question 53

Let $$f(x)=x^{2}+ax+b$$ and $$g(x)=f(x+1)-f(x-1)$$. If $$f(x)\geq0$$ for all real x, and $$g(20)=72$$. then the smallest possible value of b is

Question 54

For the same principal amount, the compound interest for two years at 5% perĀ annum exceeds the simple interest for three years at 3% per annum by Rs 1125.Ā Then the principal amount in rupees is

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Question 55

Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C thatĀ passes through points A and B where A is located 4 meters north of O and B is locatedĀ 3 meters east of O. Then, the length of PQ, in meters, is nearest to

Question 56

In a car race, car A beats car B by 45 km. car B beats car C by 50 km. and car A beats car C by 90 km. The distance (in km) over which the race has been conducted is

Question 57

How many 4-digit numbers, each greater than 1000 and each having all four digitsĀ distinct, are there with 7 coming before 3?

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Question 58

The sum of the perimeters of an equilateral triangle and a rectangle is 90cm. The area, T, of the triangle and the area, R, of the rectangle, both in sq cm, satisfying the relationship $$R=T^{2}$$. If the sides of the rectangle are in the ratio 1:3, then the length, in cm, of the longer side of the rectangle, is

Question 59

A sum of money is split among Amal, Sunil and Mita so that the ratio of the sharesĀ of Amal and Sunil is 3:2, while the ratio of the shares of Sunil and Mita is 4:5. If theĀ difference between the largest and the smallest of these three shares is Rs.400,Ā then Sunilās share, in rupees, is

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Question 60

The value of $$\log_{a}({\frac{a}{b}})+\log_{b}({\frac{b}{a}})$$, for $$1<a\leq b$$ cannot be equal to

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