# CAT Model Paper 5 Questions and Answers with Explanation Part 2

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Q: 8. In a the medians and are to each other. If and . Find the value of

(A)

(B)

(C)

(D)

Ans: A

Solution:

The correct choice is (A) .

PA and QB are the medians and the intersect at G (centroid)

Centroid divides the medians in the ratio

Hence, if

Similarly, If

(Since QB is the median)

(since PA is the median)

Using Pythagoras theorem,

Adding the above equations,

To find the value of PQ, use Pythagoras theorem,

Hence

Hence option A

Q: 9. If , the roots of equation are

(A) Imaginary

(B) both same

(C) real& both negative

(D) real & opposite sign

Ans: D

Solution:

Determinant

is always positive and 8m is also .

So the determinant 0, roots are real.

Product of roots which is negative. Hence the roots are of opposite signs.

Hence option D

Q: 10. Highest power of 5 in a! and b! is 16 and 32 respectively. What is the maximum difference between a and b?

(A)

(B)

(C)

(D)

Ans: B

Solution:

A should be as less as possible. It can be as if a is , the zeroes will be and for 70, zeroes at the end

(b) should be as big as possible. (b) can be , number of zeroes will be .

So difference is .

Hence option B

Q: 11. The distance between two people A and B is km such that A is ahead of B. The speeds of A and B are and respectively. Both start their journey at 9 am moving in the same direction. After 2 hours A changes the direction and starts moving towards B. At what time approximately will they meet?

(A)

(B)

(C)

(D)

Ans: C

Solution:

After hours, A would travel km and B would travel km. So the distance between them now The time taken for them to meet would be distance/relative speed mins approximately. They will meet at 11.17 am.

Hence option C

Q: 12.

(A)

(B)

(C)

(D)

Ans: D

Solution:

The correct choice is (D) .

similarly

similarly so on

we observe that .

Hence option D