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

**Combined Defence Services**

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

**1.What is the number of sperhical balls of 2.5 mm diameter that can be obtained by melting a semicircular disc of 8 cm diameterand 2 thickness?**

(a) 6144

(b) 3072

(c) 1536

(d) 768

**2. From a wooden cylindrical block, whose diameter is equal to its height, a sphere of maximum possible volume is carved out. What is the ratio of the volume of the utilised wood to that of the wasted wood?**

(a) 2 : 1

(b) 1 : 2

(c) 2 : 3

(d) 3 : 2

**3. A bag contains 50 paise, 1 rupee and 2 rupee coins in the ratio 2 : 3 : 4. If the total amount is Rs. 240, what is the total number of coins?**

(a) 90

(b) 150

(c) 180

(d) 200

**4. A train started from a station with a certain number of passengers. At the first halt, 1/ 3rd of its passengers got down and 120 passengers got in. At the second half, half of the passengers got down and 100 persons got in. Then, the train left for its destination with 240 passengers. How many passengers were there in the train fit started?**

(a) 540

(b) 480

(c) 360

(d) 240

**5. Let p, q, r be natural numbers. If m is their LCM and n is their HCF, consider the following:
1. mn = pqr iff each p, q, r is prime
2. mn = pqr iff p, q, r are relatively prime in pairs.
Which of the above is/ are correct?**

(a) 1 only

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2

**6. Out of a sum of Rs. 640, a part was lent at 6% simple interest and the other at 9% simple interest. If the interest on the first partafter 3 yr is equal to the interest on the second part after 6 yr. then what is the second part.**

(a) Rs. 120

(b) Rs. 140

(c) Rs. 160

(d) Rs. 180

**7. The LCM of three different numbers is 150. Whichof the following cannot be their HCF?**

(a) 15

(b) 25

(c) 50

(d) 55

**8. Let S be a set of all even integers. If the operations**

1. addition

2. substraction

3. multiplication

4. division

**9. Ram has Rs. 2 lakh, part of which he lent at 15% pa and rest at 12% pa. Yearly interest accured was Rs. 27,600. How much did helend at 15%?**

(a) Rs. 1,20,000

(b) Rs. 1,00,000

(c) Rs. 80,000

(d) Rs. 60,000

**10. A person bought a certain number of books for Rs. 80. If he had bought 4 more books for the sum, each book would have cost Re 1 less. What is the price of each book?**

(a) Rs. 10

(b) Rs. 8

(c) Rs. 5

(d) Rs. 4