### 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 p^{x} =r^{y} =m and r^{w} =p^{z} =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

(a^{2} + b^{2})x^{2} -2(ac+bd)x +(c^{2} +d^{2}) = 0 has equal roots, then which one of the following is correct?

(a) ab=cd

(b) ad =bc

(C) a^{2}+c^{2} =b^{2} +d^{2}

(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 (a^{2}-b^{2}) : (a^{2} +^{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

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