# CAT Model Paper 4 Questions and Answers with Explanation Part 2

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Q: 5. Find the remainder when the factorial of a two-digit perfect number n is divided by ?

(A)

(B)

(C)

(D)

Ans: D

Solution:

The only digit perfect number is .

When is divided by , remainder is .

Note: when n! is divided by where is prime, the remainder is n.

Hence, the answer will be 28.

Q: 6. In a triangle ABC below, . Points X and Y are chosen on AB and AC such that .

(A)

(B)

(C)

(D)

Ans: B

Solution:

Since AX = AY.

The above equation can reduce to

Substituting and .

Here,

Hence option (B)

Q: 7. What is the number of distinct terms in the expansion of ?

(A)

(B)

(C)

(D) None of these

Ans: B

Solution:

Number of distinct terms would be non-negative integral solutions of the equation

Total number of non-negative integral solutions

Hence, the number will be **300**.

Q: 8. Find the unit digit of

(A)

(B)

(C)

(D)

Ans: B

Solution:

Units digit of first term is 6,

Similarly, 2^{nd} term is 1 and 3^{rd} term is .

Unit digit of product

Hence, the unit digit is 6.

Q: 9. The number of ordered triplets of prime numbers a, b and c such that

(A)

(B)

(C)

(D) Not Possible

Ans: B

Solution:

We know that one of these numbers must be as the sum of numbers is even.

Sum of cubes of two other numbers

So, the numbers are .

They can be arranged in ways.

Q: 10. In the triangle below, and are the angles bisectors of and respectively. Find the value of ?

(A)

(B)

(C)

(D)

Ans: D

Solution:

The point of the intersection of the angle bisector of is O.

Hence, O is the in centre.

Consider Eq. (1)

Consider Eq. (2)

Subtracting Eqn (2) from Eqn (1),

Hence,

Hence, value of