### UPSC CDS (II) Exam Elementary Mathematics Paper

Union Public Service Commission (UPSC) Combined Defence Service Exam (II) Elementary Mathematics 2010 Paper.

1. A mixture contains milk and water in the ratio 5 : 1 On adding 5 litres of water, the ratio of milk and water becomes 5 : 2. What is the quantity of milk in the original mixture?
(a) 5 litres
(b) 25 litres
(c) 27.5 litres
(d) 32.5 litres

2. What is the smallest positive integer which when divided by 4, 5, 8, 9 leaves remainders 3, 4, 7, 8 respectively?
(a) 119
(b) 319
(C) 359
(d) 719

3. What is the value Inf x for which x, x+ 1, x+ 3 are all prime numbers?
(a) 0
(b) 1
(c) 2
(d) 101

4. A person spends 30% of monthly salary on rent, 25% on food, 20% on childrens education and 12% on electricity, and the balance of Rs 1,040 on the remaining items. . What is the monthly salary of the person?
(a) Rs 8,000
(b) Rs 9,000
(c) Rs 9,600
(d) Rs 10,600

5. If px =ry =m and rw =pz =n, then which one of the following is correct?
(a) xw=yz
(b) xz = yw
(c) x + y = w+ z
(d) x – y = w-z

6. A father and his son start at a point A with speeds of 12 kmph and 18 kmph respectively, and reach another point B. lf his son starts 60 minutes after his father at A and reaches B 60 minutes before his father, what is the distance between A and B?
(a) 90 km
(b) 72 km
(c) 36 km
(d) None of the above

7. if the equation
(a2 + b2)x2 -2(ac+bd)x +(c2 +d2) = 0 has equal roots, then which one of the following is correct?
(a) ab=cd
(C) a2+c2 =b2 +d2
(d) ac=bd

8. Two trains of lengths 100 m and 150 m are traveling in opposite directional at speeds of 75 kmph and 50 kmph respectively. What is the time taken by them to cross each other?
(a) 7.4 s
(b) 7·2 s
(c) 7s
(d) 6.8s

9. lf (a-b):(a+b)=1:5, then what is (a2-b2) : (a2 +2) equal to?
(a) 2 : 3
(b) 3 : 2
(c) 5 : 13
(d) 13 : 5

10. If x varies as, the mth power of y, y varies as the nth power of z and x varies as the nth power of z, then which one pf the following is correct?
(a) p=m+n
(b) p=m-n
(c) p=mn
(d) None of the above

11. The ratio between the ages of A and B is 2 : 5. After 8 years, their ages will be in the ratio l: 2. What is the difference between} their present ages?
(a) 20 years
(b) 22 years
(C) 24 years
(d) 25 years