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 .
Q 6 Find the AB and AC
(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, 2nd term is 1 and 3rd 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 ?
Q 10 Find the Value of AOC
(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