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, 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 .
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