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# (Paper) CDS: Elementary Mathematics Solved Exam Paper (I): 2006

**Combined Defence Services**

**CDS Elementary Mathematics Solved Exam Paper (I) : 2006**

**Directions: The following four (4) items consist of two statements, one labelled as the ‘Assertion (A)’ and the other as ‘Reason (R)’. You are to examine these two statements carefully and select the answers to these items using the codes given below: **

**Codes:
(a) Both A and R are individually true and R is the correct explanation of A
(b) Both A and R are individually true but R is not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true**

**1. The mean, median and mode of given data of scores are 21, 23 and 22 respectively. If 3 is added to each score, what are the new valuesof mean, median and mode, respectively.
(a) 21, 23, 22 (b) 24, 26, 25
(c) 24, 23, 22 (d) None of these**

**2. The mean grade of a section of 20 students is 66% and that of another sect ion of 15 students is 70%. What is the combined mean grade?
(a) 66.7% (b) 67.7%
(c) 68.7% (d) 69.7%**

**3. For finding the average speed of a person, w hi ch one of the fol low ing i s most appropriate?
(a) Arithmetic mean (b) Harmonic mean
(c) Median (d) Mode**

**4. If the selling price of 4n items equals the cost pr ice of 5n items, w hat i s the pr of it percentage?
(a) 20 (b) 24
(c) 25 (d) 30**

**5. An arc of 60° in one circle is double the arc in a second circle whose radius is three times that of the first circle. What is the degree measure of the arc of the second circle?
(a) 30°
(b) 20°
(c) 10°
(d) 1°**

**6. What is the value of the expression log tan 10° + log tan 20° + log tan 30° + log tan 40° + log tan 50° + log tan 60° + log tan 70° tan 80°?
(a) 4
(b) 1
(c) 0
(d) –1**

**7. Sanjay sold a bicycle to Salman at 46% profit. Salman, spent Rs. 40 on repairs and sold it to Sunil for Rs. 1500. In this deal, Salman made neither profit nor loss. What is the cost price for Sanjay?
(a) Rs. 900
(b) Rs. 960
(c) Rs. 1000
(d) Rs. 1060**

**8. In the month of January, Sachin’s income and expenses were Rs. 15000 and Rs. 9000,respectively. His monthly expenses vary directly as the square of his monthly income.
What is his income when it just equals his expenses?
(a) Rs. 20600
(b) Rs. 25000
(c) Rs. 27600
(d) Rs. 28600**

**9. In a college, 500 students study mathematics and 400 students study economics. If 300 students study both the subjects, then what is the total number of students enrolled in the two subjects?
(a) 600
(b) 800
(c) 900
(d) 1200**

**10. A two-digit number is given. If this number is added to a number obtained by reversing the digits of the given number, then the sum is always divisble by which one of the following numbers?
(a) 7
(b) 9
(c) 10
(d) 11**

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