Cat 2009 Quant Test 53

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Quant Test 53 Directions for Questions from 1 to 2: Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others. Option A: Invest in a public sector bank. It promises a return of +0.10% Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%, while a fall will entail a return of –3% Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of –2.5%, while a fall will entail a return of +2%

1. What strategy will maximize the guaranteed return to Shabnam?

j 100% in option A k l m n j 36% in option B and 64% in option C k l m n j 64% in option B and 36% in option C k l m n j 1/3 in each of the three options k l m n j 30% in option A, 32% in option B and 38% in option C k l m n i Skip this question j k l m n

2. The area confined between the graphs |x| = |y|

and |x| = a is

j k l m n 2a 2

j k l m n 4a 2

j k l m n a2

j k l m n a 2 /2

j None of these k l m n i Skip this question j k l m n Directions for Questions from 3 to 4: Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes to guarantee maximum returns on her investment. She has three options, each of which can be utilized fully or partially in conjunction with others. Option A: Invest in a public sector bank. It promises a return of +0.10% Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a return of +5%, while a fall will entail a return of –3% Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a return of –2.5%, while a fall will entail a return of +2%

3. The maximum guaranteed return to Shabnam is

j 0.25% k l m n j 0.10% k l m n j 0.20% k l m n j 0.15% k l m n j 0.30% k l m n i Skip this question j k l m n

4. A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10?

j -119 k l m n j -159 k l m n j -110 k l m n j -180 k l m n j -105 k l m n i Skip this question j k l m n

5. The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10 n, on the nth day of 2007 (n = 1, 2, ..., 100), and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89 + 0.15n, on the nth day of 2007 (n = 1, 2, ..., 365). On which date in 2007 will the prices of these two varieties of tea be equal?

j May 21 k l m n j April 11 k l m n j May 20 k l m n j April 10 k l m n j June 30 k l m n i Skip this question j k l m n

6. f(x) = log x for any real number x > 0 and g(n) = (n; if n is even) ; (1/n ; if n is odd) for any natural number n. If ‘x’ is a natural number greater than 1 then what is the value of f(f(xg(10) )) – f(f(xg(9) )) + f(f(xg(8) ) – .....– f(f(xg(1) )?

j log 10 k l m n j og (10!) k l m n j log (256/63) k l m n j log (63/256) k l m n j None of these k l m n i Skip this question j k l m n

7. Between the two natural numbers N and 450(both inclusive), there are four numbers that occur in both the series 7, 12, 17, 22, 27, … and 16, 22, 28, 34, 40, …. Find the number of possible values of N.

j 36 k l m n j 24 k l m n j 15 k l m n j 18 k l m n j 30 k l m n i Skip this question j k l m n

8. The team of 11 players is to be selected out of 16 shortlisted aspirants. The team must include exactly one wicketkeeper, at least five bowlers and at least four batsmen. Out of these shortlisted aspirants, two are wicketkeepers, nine are batsmen and the rest are bowlers. In how many ways can the team be selected?

j 108 k l m n j 126 k l m n j 1512 k l m n j 252 k l m n j 192 k l m n i Skip this question j k l m n Directions for Questions from 9 to 10: Answer the questions on the basis of the information given below.

545 containers were shifted by a certain number of men and the job took 5 working days to complete. Everyday after the first day 6 more men were put on the job as a result of which each man had to shift 5 fewer containers than what he shifted on the previous day.

9. How many men worked on the 5th day?

j 12 k l m n j 15 k l m n j 25 k l m n j 27 k l m n j Cannot be determined k l m n i Skip this question j k l m n

10. What was the total number of containers shifted on the 3rd day?

j 144 k l m n j 150 k l m n j 181 k l m n j 169 k l m n j 200 k l m n i Skip this question j k l m n

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