CAT 2020 Slot 2 Question Paper

Instructions

For the following questions answer them individually

CAT 2020 Slot 2 - Question 51


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

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CAT 2020 Slot 2 - Question 52


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

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CAT 2020 Slot 2 - 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

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CAT 2020 Slot 2 - Question 54


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

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CAT 2020 Slot 2 - Question 55


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

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CAT 2020 Slot 2 - 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

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CAT 2020 Slot 2 - Question 57


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

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CAT 2020 Slot 2 - 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

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CAT 2020 Slot 2 - Question 59


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

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CAT 2020 Slot 2 - 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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