CAT Model Paper 8 Questions and Answers with Explanation Part 3
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Q: 15. Let f be a function such that
(A) 3
(B) 303
(C) 101
(D) None of these
Ans: D
Solution:
The correct choice is (D).
(1)
Also , putting ,
.(2)
.
Q: 16. A biased coin is tossed n times . Probability of getting heads and 1 tail (in any possible order) is same as the probability of getting all tails. What is the probability of getting a tail in one flip?
(A)
(B)
(C)
(D)
Ans: A
Solution:
Let’s assume probability of getting 1 tail in
So, probability of getting 1 head in 1 toss
So, probability of getting heads and 1 tail in n tosses
So, probability of getting all tails in n tosses
As they are same, we can get:
Q: 17. Two pipes X and Y can fill a tank in 5 and 6 hours respectively whereas two leaks can empty it in 7 and 8 hours respectively. X and Y are opened at 6 am and 6:30 am respectively. Once the tank is full, the leaks also start functioning. What is the approximate total time taken to fill the tank?
(A) 5 hours
(B) 6 hours
(C) 6.5 hours
(D) 5.5 hours
Ans: D
Solution:
Let’s assume the volume of the tank is litres.
Input of X during litres
Litres
Total hourly input of X and litres
X and Y operating together will fill up litres
Time taken to fill up hours
After that, the effective hourly input
Time taken to fill the left over part hours approx.
Total time = . hours.
Q: 18. Two trains A and B start from two points P and Q simultaneously towards Q and P respectively. Difference in their speeds is and A takes 1 hour more than B to cover the distance . When they meet, B covers kms more than A. What is the distance between points P and Q?
(A)
(B)
(C)
(D) Cannot be determined
Ans: B
Solution:
Let the speed of A be “s”. Speed of B is “”. As A takes one hour more,
Speed of
Speed of
Let the distance be (LCM of speeds)
Time taken to meet
B has covered more than when they meet implies
not possible)
Distance
Q: 19. If x is a real number, then find the maximum value of
(A)
(B)
(C)
(D)
Ans: C
Solution:
We know, for two terms,
Hence,
Or.
Or,
Q: 20. “If if n is even, find the value of .”
(A)
(B)
(C)
(D)
Ans: D
Solution:
Hence finally.
Q: 21. Manoranjan borrowed some money from Dipanjan to admit his son in a reputed private school. He agreed to pay the interest free loan of in monthly instalments which increased by a constant amount. After the 20th instalment he found that he had paid 3/4th of the loan. If the entire loan was cleared this way in exactly instalments, find the value of the fifth instalment.
(A)
(B)
(C)
(D)
Ans: B
Solution:
Let the first instalment is p an d increment is q.
Then, according to sum of an A.P.,
So,
Hence 5th instalment is