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# (Paper) CDS: Elementary Mathematics Solved Exam Paper (I): 2007

**Combined Defence Services**

**CDS Elementary Mathematics Solved Exam Paper (I) : 200**7

**1. If the mean of the variable X is M, what is the mean of variable Y = (X – 4)/ 5?**

(a) (M – 4)/ 5

(b) M

(c) M – 5

(d) 5M – 4

**2. A batsman scores 80 runs in his sixth innings and thus increases his average by 5. What is his average after six innings?**

(a) 50

(b) 55

(c) 60

(d) 65

**3.What type of classification is needed to enumerate the female population of India? **

(a) Geographcial

(b) Chronological

(c) Qualitative

d) Quantitative

**4 .What is the geometrical mean of the variate which takes values 210, 201, 102, 20, 12, 10, 2, 1 and 0?**

(a) 3

(b) 2

(c) 1

(d) 0

**5. The vertical height of a right circular cone is twice its diameter and its volume is 36 cm3. What is its vertical height?**

(a) 4 cm

(b) 8 cm

(c) 12 cm

(d) 16 cm

**6. A wax cube of edge 6 cm is melted and formed into three smaller cubes. If the edges of two smaller cubes are 3 cm and 4 cm, what is the edge of the third smaller cube?**

(a) 5 cm

(b) 4.5 cm

(c) 4 cm

(d) 3.5 cm

**7. A right circular cylinder and a right circular cone have equal bases and equal volumes. But the lateral surface area of the right circular cone is 15/ 8 times the lateral surface area of the right circularcylinder. What is the ratio of radius to height of the cylinder?**

(a) 3 : 4

(b) 9 : 4

(c) 15 : 8

(d) 8 : 15

**8.Water i s di st r ibuted to a town 50000 inhabitants from a rectangular reservoir consisting of 3 equal compartments. Each compartment has length and breadth 200 m, 100 m respectively and 12 m depth of water in the beginning. The allowance is 20 litres per head per day. For how many days will the supply of water hold out? **

(a) 240 days

(b) 720 days

(c) 800 days

(d) 900 days

**9. A swimming pool is 24 m long and 15 m broad. When x number of men dive into the pool, the height of the water rises by 1 cm. If the average amount of water displaced by one man is 0.1 m3, then what is the value of x?**

(a) 36

(b) 72

(c) 108

(d) 360

**10. The diameter of a bus wheel is 140 cm. The speed of the bus is 66 km per hour. What is the number of revolutions of the wheel per minute?**

(a) 200

(b) 250

(c) 300

(d) 350