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, 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).
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, option B
Q: 22. Find the remainder when 232323………. 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