# CAT Model Paper 10 Questions and Answers with Explanation Part 3

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Question 15:

Find the equation with roots?

(A)

(B)

(C)

(D)

Answer – B

Solution:

Let the equation be

Sum of the product of the roots taken 1 at a time

Sum of the product of the roots taken 2 at a time

Sum of the product of the roots taken 3 at a time

Sum of the product of the roots taken 4 at a time

Sum of the product of the roots taken 5 at a time

16. In the given figure, two circles are inscribed inside two adjoining triangles.

Given: Find TV.

(A) 8

(B) 12

(C) 16

(D) 10

Answer: A

Solution:

Let

Then

Now,

Hence

17. A rectangle is drawn so that none of its sides has a length greater than ‘x’, all lengths lesser than ‘x’ are equally likely. The chance that the rectangle has its diagonal greater than ‘x’ is (in %)?

(A) 29.3%

(B) 21.5%

(C) 66.66%

(D) 33.33%

Answer: B

Solution:

Draw a square of side x and an arc of radius x.

All rectangles with diagonal less than or equal to x will be within or on the quadrant of the circle. The shaded region is the un favourable area.

Hence, required probability

chance.

18. is divisible by which of the following?

(A) 15

(B) 113

(C) 23

(D) More than one of these

Answer: D

Solution:

is of the form where the power is always even because 2n is always even.

That means it is divisible by as well as.

Put , it becomes , which is divisible by and .

The given number is divisible by 15 and 113.

19. Find the rightmost non-zero integer of the expression?

(A) 3

(B) 9

(C) 7

(D) 1

Answer: C

Solution

It can be easily observed than has more number of zeroes as compared to.

Hence, the rightmost non-zero integer will depend on the 1^{st} non-zero digit of , which in turn will depend on the digit of .

343 can written as

In the power cycle of the third digit is 7.

Hence, the last non-zero integer in the expressions is 7.

20. If where and are all positive numbers, then what is the minimum value of?

(A)

(B)

(C)

(D)

Answer: B

Solution:

Using the property of

AM and GM

Using condition, we get

But

Answer