# CAT Model Paper 8 Questions and Answers with Explanation Part 4

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Q: 22. and are complementary angles. What is the value of ?

(A)

(B)

(C)

(D) None of these

Ans: D

Solution:

or,

Q: 23. In the following figure AB, DC and EF are perpendicular to BC. Find the length of

EF in cms if AB and DC are 6 cm and 18 cm respectively

(A) 9

(B) 4.5

(C) 5

(D) 4

Ans: B

Solution

are similar triangles

Hence, … (1)

Again, are similar triangles.

Hence, … (2)

Adding equation (1) and (2) we get,

So,

Q: 24. A, B and C are three towns connected via some two-way roads. A person can go to B from A in ways and B to C in ways. In how many ways can a person go to A from C?

(A)

(B)

(C)

(D) Cannot be determined

Ans: D

Solution:

let՚s assume there are x roads between A and B; z roads between B and C; y roads between C and A.

From A to B a person can go directly or via C, so, the ways are (given)

From B to C a person can go directly or via A, so, the ways are (given)

From C to A, a person can go directly or via B, so, the ways are

We need to find the value of y

If we subtract to given equations we get:

As and z all are integral, then possible values of must be a factor of . So, the possible values of y are and .

If we add them we get must be a factor of 60.

If we take , then we get:

;

If we take y = 5, then we get:

;

Q: 25.

(A)

(B)

(C)

(D)

Ans: B

Solution:

. Now, if we consider , then;

Thus,

will be found at the point of intersection. Thus

Q: 26. The ratio of the base and perpendicular of a right-angled triangle shaped, fine tin foil is . The hypotenuse is . What is the approximate volume of the biggest cone that can be formed by taking the right angle vertex of the foil as the vertex of the cone?

(A)

(B)

(C)

(D)

Ans: B

Solution:

When the slant height of the cone is the perpendicular on the hypotenuse from right angled point, then the volume of cone will be maximum. Let this slant height be L Then Base of the right angled triangle perpendicular Hypotenuse L

Or,

Now, arc of the sector circumference of the base circle of the cone.

Let, the base radius of the cone is r,

Then

Or,

Let height of the cone

Hence,

Volume of the cone

Q: 27. A right-angled trapezoid ABCD with the parallel sides being BC and AD and AB being perpendicular to AD is circumscribed about a circle. and . Calculate the radius of the circle.

(A)

(B)

(C)

(D) None of these

Ans: A

Solution:

Consider the above figure. We know that the line segments drawn from the same point that are tangent to a circle are of equal length. Hence it is easy to see that . We have where r is the radius of the circle. . Therefore . Let be dropped perpendicular to . Hence . Hence applying Pythagoras theorem to triangle CKD we have CK2 solving which we get