# CAT Model Paper 10 Questions and Answers with Explanation Part 1

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1. The population of a town was 3600 three years back. It is 4800 right now. What is the rate of growth of population, if it has been constant over the years and has been compounding annually?

(A)

(B)

(C)

(D)

Answer: D

Solution:

Conventional approach

Final value Initial value

Thus, rate

Going from answer options

If 10 is the answer

Therefore r is approximately .

2. In how many different ways can the six faces of cube be painted by 6 different colours?

(A) 45

(B) 40

(C) 30

(D)

Answer: C

Solution:

Mark a particular face X. (Later on, we will have to divide whatever answer we get by 6 because all 6 face are identical at this point, and we have chosen one out 6 randomly) .

Put a colour on face X. There are 6 ways to do this.

Put another colour on the face opposite X. There are 5 ways to do this.

Arrange the remaining 4 colours in the remaining four places – there are 3! Ways to do this (circular permutation of 4 colours )

Total

3. Find the no. of non-negative integral solution of: ?

(A) 15

(B)

(C)

(D)

Answer: C

Solution:

Non negative integral solution means

This is also a “similar to different” type of question

Applying 0՚s and 1՚s method.

Total no. of ways

4. Find the complete range of values of “p” for which ?

(A)

(B)

(C)

(D)

Answer: D

Solution:

We can solve this by using common sense

Put . Then .

Thus the inequality is not satisfied for this value

Answer can never be option (a) or (b)

Put .

Then .

Thus, the inequality is not satisfied for this value as well.

Answer is option (d) .

5. What is the maximum value of the function f (x) ?

(A)

(B)

(C)

(D)

Answer: C

Solution:

is a decreasing function, while is an increasing function.

The max of f (x) occurs at the intersection of and .

So, max f (x)

6. Find the remainder when is divided by 10.

(A) 3

(B) 9

(C) 7

(D) 1

Answer: A

Solution

For remainder when a number is divided by 10, we need to check only the last digit.

Last digit 3.

Write .

The first digit in the cycle of (the cycle of 3 is )

Thus

8. The least number which gives a remainder of and 4 when successively divided by respectively is 71. Find x.

(A) 4

(B) 6

(C) 5

(D) 7

Answer: C

Solution:

Solving, we get