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CDS Exam Solved Papers - 2011- I Paper III: Mathematics

1. The diagonal of a cube is 4Ö3 cm. What is its volume ?

(a) 1.6 cm³
(b) 32 cm³
(c) 64 cm³
(d) 192 cm³

2. If 2/x +3/y = 9/xy and 4/x+9/y = 21/xy where x ¹ 0 and y ¹ 0, then what is the value of x + y ?

(a) 2
(b) 3
(c) 4
(d) 8

3. Two trains each 200 m long move towards each other on parallel lines with velocities 20 kmph and 30 kmph respectively. What is the time that elapses when they first meet until they have cleared each other ?

(a) 20 s
(b) 24.8 s
(c) 28.8 s
(d) 30 s

4. ‘X’ is twice as old as ‘Y’ 3 years ago, when ‘X’ was as old as ‘Y’ today. If the difference between their ages at present is 3 years, how old is ‘X’ at present ?

(a) 18 years
(b) 12 years
(c) 9 years
(d) 8 years

5. If ` 2,600 is divided among three persons A, B and C in the ratio 1/2 : 1/3 : 1/4 how much does A get ?

(a) Rs. 600
(b) Rs. 800
(c) Rs. 1,000
(d) Rs. 1,200

6. For a positive integer n, define d(n) = the number of positive divisors of n. What is the value of d(d(d(12))) ?

(a) 1
(b) 2
(c) 4
(d) None of the above

7. In a triangle ABC, side AB is extended beyond B, side BC beyond C and side CA beyond A. What is the sum of the three exterior angles ?

(a) 270°
(b) 305°
(c) 360°
(d) 540°

8. PQR is a triangle right-angled at Q. If X and Y are the mid-points of the sides PQ and QR respectively, then which one of the following is not correct ?

(a) RX² + PY² = 5 XY²
(b) RX² + py² = XY² + PR²
(c) 4 (RX² + PY²) = 5 PR²
(d) RX² + PY² = 3 (PQ²+ QR²)

9. A bicycle is running straight towards north. What is the locus of the centre of the front wheel of the bicycle whose diameter is d ?

(a) A line parallel to the path of the wheel of the bicycle at a height d cm
(b) A line parallel to the path of the wheel of the bicycle at a height d/2 cm
(c) A circle of radius d/2 cm
(d) A circle of radius d cm

10. To pass an examination, a candidate needs 40% marks. All questions carry equal marks. A candidate just passed by getting 10 answers correct by attempting 15 of the total questions. How many questions are there in the examination ?

(a) 25
(b) 30
(c) 40
(d) 45

11. Assume the Earth to be a sphere of radius R. What is the radius of the circle of latitude 40-S ?

(a) R cos 40°
(b) R sin 80°
(c) R sin 40°
(d) R tan 40°

12. The centroid of a triangle ABC is 8 cm from the vertex A. What is the length of the median of the triangle through A ?

(a) 20 cm
(b) 16 cm
(c) 12 cm
(d) 10 cm

13. The equation whose roots are twice the roots of the equation x² – 2x + 4 = 0 is x2

(a) x² – 2x + 4 = 0
(b) x² – 2x + 16 = 0
(c) x² – 4x + 8 = 0
(d) x² – 4x + 16 = 0

14. The outer and inner diameters of a circular pipe are 6 cm and 4 cm respectively. If its length is 10 cm, then what is the total surface area in square centimeters ?

(a) 55 p
(b) 110 p
(c) 150 p
(d) None of the above

15. A cylindrical rod of iron whose radius is one-fourth of its height is melted and cast into spherical balls of the same radius as that of the cylinder. What is the number of spherical balls ?

(a) 2
(b) 3
(c) 4
(d) 5

16. These S = {x Î N : x + 3 = 3} is

(a) Null set
(b) Singleton set
(c) Infinite set
(d) None of the above

17. A telegraph post gets broken at a point against a storm and its top touches the ground at a distance 20 in from the base of the post making an angle 30° with the ground. What is the height of the post ?

(a) 40/Ö3 m
(b) 20/Ö3 m
(c) 40/Ö3 m
(d) 30 m

18. The sum of two numbers is 80. If the larger number exceeds four times the smaller by 5, what is the smaller number ?

(a) 5
(b) 15
(c) 20
(d) 25

19. Consider the following numbers

1. 247
2. 203

Which of the above numbers is/are prime?

(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2

20. If x –1/x = 1/3, then what is 9x² + 9/x²equal to ?

(a) 18
(b) 19
(c) 20
(d) 21