CAT Model Paper 5 Questions and Answers with Explanation Part 5

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Q: 21.

Q_21_Find the Area of Quadrilateral ADOE in Sq Cm

In the above figure ABC is a triangle and D and E are points on AB and CD respectively such that, BOC, BOD and COE have areas 15 sq cm, 10 sq cm and 5 sq 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 .

Q_21_1_Area of Quadrilateral ADOE in Sq Cm

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,

Q: 22. Find the remainder when 232323. times (300 digits) is divided by .

(A) 61

(B) 71

(C) 84

(D) 91

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, 84

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

(A) -64

(B) -57

(C) 121

(D) None of these

Ans: A

Solution

Let roots be a, b

. The minimum value of this is

Hence -64

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

(A)

(B)

(C)

(D) Both a and b

Ans: (D)

Solution

Given

Using componendo-dividendo rule, if then

Simplifying,

From the above equation,

Moreover, Hence,

Hence, option and 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