# 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 3/4^{th} 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 5^{th} instalment is