# CAT Model Paper 5 Questions and Answers with Explanation Part 5

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Q: 21.

In the above figure ABC is a triangle and D and E are points on AB and CD respectively such that, s BOC, BOD and COE have areas 15sq cm, 10sq cm and 5sq cm respectively. What is the area of quadrilateral ADOE in sq cm?

(A)

(B)

(C)

(D) Cannot be determined

Ans: B

Solution:

The correct choice is (B).

Joining , we get let area of

Now (Since they have their heights common)

Again

Hence

Or

Arguing similarly, we have,

Solving (1) & (2), we get,

Hence

Hence, option B

Q: 22. Find the remainder when 232323â€¦â€¦â€¦. times (digits) is divided by .

(A)

(B)

(C)

(D)

Ans: (C)

Solution

When is divided by , remainder is .

When is divided by , remainder is .

When is divided by , remainder is

Similarly, when the given number is divided by , remainder will be same as when divided by .

when divided by leaves a remainder .

Hence, option C

Q: 23. What is the minimum value of the square of the difference of the roots of the quadratic equation?

(A)

(B)

(C)

(D) None of these

Ans: A

Solution

Let roots be a, b

. The minimum value of this is .

Hence option A

Q: 24. If which of the following could be the value of

(A)

(B)

(C)

(D) Both

Ans: (D)

Solution

Given

Using componendo-dividendo rule, if then

Simplifying,

From the above equation,

Moreover, Hence,

Hence, option (a) and (b) are true.

Q: 25. is equal to

(I)

(II)

(III)

(A) I and II only

(B) II and III only

(C) I only

(D) I, II and III

Ans: (A)

Solution

(I)

(II)

(III)

Hence, only statement (I) and (II) are equal to