# Combined Defence Services Exam 2014 Model Questions

Model Questions and Answers for preparing UPSC’s Combined Defence Services [CDS] Examination on October 26, 2014.

Part-B
Mathematics

1. What is the number of integral solutions of the equations HCF(a,b)=5 and a+b=65?
(a) None
(b) Infinitely many
(c) Less than 65
(d) Exactly one

2. The difference of two consecutive tubes:
(a) is odd or even
(b) is never divisible by 2
(c) is always even
(d) None of the above
Answer: (b) is never divisible by 2

3. The product of four consecutive natural numbers plus one is:
(a) A none-square
(b) Always sum of two square numbers
(c) A square
(d) None of the above

4. A positive number, when increased by 10, equals 200 times its reciprocal. What is that number?
(a) 100
(b) 10
(c) 20
(d) 200

5. x3+6x2+11x+6 is divisible by:
(a) (x+1) only
(b) (x+2) only
(c) (x+3) only
(d) All the above

6. The present age of Ravi’s father is four times Ravi’s present age. Five years back he has seven times as old as Ravi was at that time. What is the present age of Ravi’s father?
(a) 84 years
(b) 70 years
(c) 40 years
(d) 35 years

7. The average age of male employee in a firm is 52 years and that of female employee is 42 years. The mean age of all employees is 50 years. The percentage of male and female employees are respectively.
(a) 80% and 20%
(b) 20% and 80%
(c) 50% and 50%
(d) 52% and 48%

8. 15 men complete a work in 16 days. If 24 men are employed then the time require to complete that work will be?
(a) 7 days
(b) 8 days
(c) 10 days
(d) 12 days

9. The expression 2x3+x2-2x-1 is divisible by
(a) x+2
(b) 2x+1
(c) x-2
(d) 2x-1

10. A train takes 9 sec to cross a pole. If the speed of the train is 48 km/h, the length of the train is:
(a) 150m
(b) 120m
(c) 90m
(d) 80m

11. Ravi’s brother is 3 years elder to him. His father was 28 years of age when Sister was born while his mother was 26 years of age when he was born. If his sister was 4 years of age when his brother was born, the ages of Ravi’s father and mother respectively when his brother was born were
(a) 32 years and 23 years
(b) 32 years and 29 years
(c) 35 years and 29 years
(d) 35 years and 33 years
Answer: (a) 32 years and 23 years

12. In solving a problem, one student make a mistake in the coefficient of the first Degree term and obtains -9 and -1 for the roots. Another student makes a mistake in the constant term of the equation and obtains 8 and 2 for the roots. The correct equation was?
(a) x2+10x+9=0
(b) x2-10x+16=0
(c) x2-10x+9=0
(d) None of the above

13. The value of x2-4x+11 can never be less than
(a) 7
(b) 8
(c) 11
(d) 22

14. What should be added to the expression x(x+a)(x+3a) so that the sum may be a perfect square?
(a) 9a2
(b) 4a2
(c) a4
(d) None of the above

15. If n is a whole number greater than 1, then n2(n2-1) is always divisible by:
(a) 12
(b) 24
(c) 48
(d) 60