# CDS 2009 Maths Question Paper -2

ORDERING OF SENTENCES

1. What is the geometric means of the observations 125, 729, 1331?
• 495
• 1485
• 2221
• None of these
2. Examples of data are given below:
3. Information on households collected by an investigator by door-to-door visits.
4. Data on the percentage of literates, sex-wise, for the different districts of a state collected from records of the census of India.
• General Information about families, collected by telephonic interviews.

Which one of the following in respect of the above is correct?

• I and II are primary data
• I and III are primary data
• II and III are primary data
• I, II and III are primary data
1. Which one of the following can be obtained from a historgam?
• Mean
• Median
• Mode
• None of these
2. The median of three positive integers, no two of which are equal, is 5. What is the least possible value of arithmetic means of these integers?
• 2
• 3
• 4
• No such least possible value exists
3. Consider the following pairs of numbers:
4. (8, 12) II. (9, 11) III. (6, 24)

Which pairs of number have the same harmonic means?

• I and II
• II and III
• I and III
• I, II and IIII
1. If 27 × (81)2n+3 – 3m = 0, then what is m equal to?
• 2n + 5
• 5n + 6
• 8n + 3
• 8n + 15
2. There are four numbers forming a GP in which the third term is greater than the first by 9 and the second term is greater than the fourth by 18. What is the first term?
• 2
• 3
• – 2
• – 3
3. What is the value of [log13(10)]/[log169(10)]?
• 1/2
• 2
• 1
• log1013
4. A boy travels a distance of 8 km at the rate of 4 km/h, 6 km at the rate of 3 km/h and 4 km at the rate of 2 km/h. What is the average speed for the entire journey?
• 2 km/h
• 3 km/h
• 4 km/h
• 6 km/h
5. Which one of the following is not correct in respect of the sets A and B?
6. If 0 < θ< Φ< 90°, then which one of the following is correct?
• (sin θ+ cos θ)2 > 2
• (sin2 θ+ cos2 Φ) ≤ 2
• (sin2 θ+ cos2 Φ) < 2
• (sin2 θ+ cos2 Φ) > 2
7. For what value of θ is (sin θ+ cosecθ ) = 2.5 where 0 <θ  ≤ 90°?
• 30°
• 45°
• 60°
• 90°
8. The angles of a triangle are in AP and the greatest angle is double the least. What is the ratio of angles in the Indian measure?
• 2 : 3 : 4
• 1 : 2 : 3
• 3 : 3 : 6
• 4 : 5 : 7
9. The length of the shadow of a person s cm tall when the angle of elevation of the sun is α is p cm. It is q cm when the angle of elevation of the sun is β. Which one of the following is correct when β = 3α  ?

1. If cot θ= 2xy/x2-y2,then what is cosθ  equal to?

1. The value of cosec2 θ– 2 + sin2 θis always
• less than zero
• non-negative
• zero
• 1
2. If tan θ=p/q ,then what is p sec θ-q cosec θ/p sec θ+q cosec θ equal to?
• p –q/p+ q
• q2-p2/ q2+p2
• p2– q2/q2+p2
• 1
1. What is the value of sin3 60° cot 30° – 2 sec2 45° + 3 cos 60° tan 45° – tan2 60°?
• 35/8
• – 35/8
• –11/8
• 11/8
2. If 0 < x < 45° and 45° < y < 90°, then which one of the following is correct?
• sin x = sin y
• sin x < sin y
• sin x > xin y
• sin x ≤ sin y
3. The difference of the two angles in degree measure is 1 and their sum in circular measure is also I. What are the angles in circular measure?

• None of the above
4. is satisfied by which one of the following values of θ?
• π/2
• π/3
• π/4
• π/6
5. Consider the following

Which of the statements given above is/are correct?

• I only
• II only
• Both I and II
• Neither I nor II
1. What is the angle subtended at the centre of a circle of radius 8 m after traversing 4π m along its circumference?
• π/3
• π/2
• 2 π/3
• 3 π/4
2. If cot θ= 8/15, then what is the value of  where θis a positive acute angle?
• 1/5
• 2/5
• 3/5
• 4/5
3. In the figure given above, O is the centre of the circle ∠AOD = 106°. What is ∠BCD equal to?
• 53°
• 43°
• 40°
• 37°
1. The quadrilateral formed by joining the mid-points of the sides AB, BC, CD, DA of a quadrilateral ABCD is

• a trapezium but not a parallelogram
• a quadrilateral but not a trapezium
• a parallelogram only
• a rhombus
2. In the figure given above, ABCD is a square in which AO = AX. What is ∠XOB?

• 25°
• 30°
• 45°
1. In the figure AB is parallel to CD and BE is parallel to FH. What is ∠FHE equal to?

• 110°
• 120°
• 125°
• 130°
2. In the figure given above, ∠AOB = 46°; AC and OB intersect each other at right angles. What is the measure of ∠OBC? (O is the centre of the circle)
• 44°
• 46°
• 67°
1. In the figure given above, O is the centre of the circle. The line UTV is a tangent to the circle at T, ∠VTR = 52° and triangle PTR is an isosceles traingle such that TP = TR. What is ∠x + ∠y + s equal to?

• 175°
• 208°
• 218°
• 250°
2. What is the number of points in the plane of a triangle ABC which are at equal distance from the vertices of the triangle?
• 0
• 1
• 2
• 3
3. The bisectors of the angles ABC and BCA of a triangle ABC meet in a point O. What is the angle at O facing the side BC?
• 90° – (A/2)
• 90° + (A/2)
• 90° – A
• 90° + A
4. ABC is a triangle in which AB = AC. Let BC be produced to D. From a point E on the line AC let EF be a straight line such that EF is parallel to AB. Consider the quadrilateral ECDF thus formed. If ∠ABC = 65° and ∠EFD = 80°, then what is ∠FDC equal to
• 43°
• 41°
• 37°
• 35°
5. ABC is a triangle and the perpendicular drawn from A meets BC in D. If AD2 = BD.DC, then which one of the following is correct?
• ABC must be an obtuse angled triangle
• ABC must be an acute angled triangle
• Either ∠B ≥ 45° or ∠C ≥ 45°
• AC2 = AB2 + BC2
6. Consider the following statements:
7. Congruent triangles are similar.
8. Similar trianlges are congruent.
• If the hypotenuse and a side of one right triangle are equal to the hypotenuse and a side of another right triangle respectively, then the two right triangles are congruent.

Which of the statement given above is/are correct?

• I only
• II only
• II and III
• I and III
1. ABC is triangle. X is a point outside the triangle ABC such that CD = CX, where D is the point of intersection of BC and AX; and ∠BAX = ∠XACWhich one of the following is correct?
• Triangles ABD, ACX are similar
• ∠ABD < ∠ÐACD
• AC = CX
2. A point P moves such that its distance from two given points A and B are equal. Then what is the focus of the point P?
• A straight line which is the high right bisector of AB
• A circle with centre at A
• A circle with centre of B
• A straight line passing through either A or B
3. In the figure given above, PT is a tangent to a circle of radius 6 cm. If P is at a distance of 10 cm from the centre O and PB = 5 cm, then what is the length of the chord BC?

• 8 cm
• 0 cm
• 4 cm
• 0 cm
4. A solid cone of height 8 cm and base radius 6 cm is melted and recast into identical cones, each of height 2 cm and radius 1 cm. What is the number of cones formed?
• 36
• 72
• 144
• 180
5. In the triangle ABC, AB = 2 cm, BC = 3cm, and AC = 4 cm, D is the middle point of AC. If a square is constructed on the side BD, what is the area of the square?
• 5 cm2
• 5 cm2
• 35 cm2
• None of these
6. From a cylindrical log whose height is equal to its diameter, the greatest possible sphere has been taken out. What is the fraction of the original log which is cut away?
• 1/2
• 1/3
• 1/4
• 2/3
7. If a sphere of radius 10 cm is intersected by a plane at a distance 8 cm from its centre, what is the radius of the curve of intersection of the plane of the plane and the sphere?
• 8 cm
• 6 cm
• 5 cm
• 4 cm
1. A cylindrical can of internal diameter 24 cm contains was. A solid sphere of radius 6 cm is completely immersed to water in the cylinder. The water level increases by
• 25 cm
• 5 cm
• 2 cm
• 3 cm
2. A person rides a bicycle round a circular path of radius SC. The radius of the wheel of the bicycle is 50 cm. The cycle comes to the starting point for the first time in 1 h. What the number of revolutions of the wheel in 15 min?
• 20
• 25
• 30
• 35
1. ABC is a straight right-angled at C. If p is the length of perpendicular from C to AB and a, b, c are the sides, the which one of the following is correct?
• pa = bc
• pb = ca
• pc = ab
• p2 = ab
1. A bucket which is in the form of a frustum of a corner radii 3 and 5 unit and vertical height 6 unit. How may water can the bucket hold?
• 33 πcu unit
• 45 πcu unit
• 48π cu unit
• None of these
1. How many litres of water (approximately) hemispherical container of radius 21 cm hold?
• 4 L
• 8 L
• 194 L
• 388 L
1. PQRS is a diameter of a circle of radius 6 cm as shown in the figure above. The lengths PQ, QR and RS are equal. Semicircles are drawn on PQ and QS as diameters. What is the perimeter of the shaded region?
• 12 πcm
• 14 πcm
• 16 πcm
• 18π cm
1. If the radius of the base and the height of a right circular cone are increased by 20% then what is the approximate percentage increase in volume?
• 60
• 68
• 73
• 75
1. Seven semi-circular areas are removed from the rectangle ABCD as shown in the figure above. In which AB = 2 cm and AD = 0.5 cm. The radius of each semi-circle r, s, t, u, v is half of that of semi-circle p or q. What is the area of the remaining portion?

• (128 – 13 π)/128 cm2
• (125 – 13 π)/125 cm2
• (128 – 15 π)/128 cm2
• None of these
2. A wire is in the form of a circle of radius 42 cm. If it is bent into a square, then what is the side of the square?
• 66 cm
• 42 cm
• 36 cm
• 33 cm
3. How many litres of water flow out of a pipe having an area of cross-section of 5 cm2 in one minute. If the speed of water in the pipe is 30 cm/s?
• 90 L
• 15 L
• 9 L
• 5 L
4. A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. What is the volume of the solid so obtained?
• 50 πcm3
• 100 πcm3
• 125π cm3
• 150 πcm3

5. The ratio of volumes of two cones is 4 : 5 and the ratio of the radii of their bases is 2 : 3. What is the ratio of their vertical heights?
• 5 : 6
• 6 : 5
• 9 : 5
• 5 : 9
6. The paint in certain container is sufficient to paint an area equal to 5.875 m2. How many bricks of dimensions 12.5 cm ×10 × 7.5 cm can be painted out of this container?
• 225
• 180
• 150
• 100
7. If p is an integer then every square integer is of the form
• 2p or (4p –1)
• 4p or (4p – 1)
• 3p or (3p + 1)
• 4p or (4p + 1)
8. What least value must be given to Å so that the number 84705 Å 2 is divisible by 9?
• 0
• 1
• 2
• 3
1. If x = then what is the value of x3 + 3bx – 2a?
• 2a3
• –2a3
• 1
• 0
2. If the roots of the equation are equal, then what is the value of m?
• 1
• ½
• 0
• – ½
3. What is equal to?
• –3/4
• 1/4
• 3/4
• 0
4. For two natural numbers m and n, let g mn denote the greatest common factor of m and n. Consider the following in respect of three natural numbers k, m and n.
5. g m(nk) = g(mn)k
6. g mng nk = g mk

Which of the above is/are correct?

• I only
• II only
• Both I and II
• Neither I nor II
1. What is the value of k for which the system of equations x + 2y – 3 = 0 and 5x + ky + 7 = 0 has no solution?
• – 3/14
• –14/3
• 1/10
• 10
2. If x + y + z = 0 then what is the value of
• 1/x2+y2+z2
• 1
• -1
• 0
1. The length of a line segement AB is 2 unit. It is divided into two parts at the point C such that AC2 = AB × CB. What is the length of CB?
• 3 + √5 unit
• 3 – √5 unit
• 2 – √5 unit
• √3 unit
1. If pq + qr + rp = 0, then what is the value of
• 0
• 1
• -1
• 3
1. If a = 1+x/2-x, the what is 1/a+1+2a+1/a2-1equal to?
• (1+x)(2+x)/2x-1
• (1-x)(2-x)/x-2
• (1+x)(2-x)/2x-1
• (1-x)(2-x)/2x+1
2. The following table shows the percentage of male and female coffee drinkers and non-coffee drinkers in two Towns A and B.

Atributes                       Town A                       Town B

Male Female              Male Female

Coffee drinkers             40%     5%                   25%     15%

Non-coffee drinkers     20%     35%                 30%     30%

If the total population of the Towns A and B are 10000 and 20000 respectively, then what is the total number of female coffee drinkers in both towns?

• 8000
• 6000
• 3500
• 2500
1. If (37)x = (0.037)y = 10000, then what is the value of 1/x-1/y?
• 1
• 2
• ½
• ¼
2. If ax = by = cz and abc = 1, then what is xy + yz + zx equal
• xyz
• x + y + z
• 0
• 1
3. When a polynomial is divided by alinear polynomial, then what is the remainder?
• Constant polynomial only
• Zero polynomial only
• Either constant o zero polynomial
• Liner polynomial
4. What is the ratio of sum of squares of roots to the product of the roots of the equation 7x2 + 12x + 18 = 0?
• 6 : 1
• –6 : 7
• – 6 : 1
• – 1 : 6
5. If x = 2 + √3, then what is (x2 + x–2) equal to?
• 12
• 13
• 14
• 15
6. Which one of the following statements is correct?
• Remainder theorem is a special case of factor theorem.
• Factor theorem is a special case of Remainder theorem.
• Factor theorem and Remainder theorem are two indepdent results
• None of the above
7. When x40 + 2 is divided by x4 + 1, what is the remainder?
• 1
• 2
• 3
• 4
8. If the HCF of x3 – 27 and x3 + 4x2 + 12x + k is quadratic polynomial, then what is the value of k?
• 27
• 9
• 3
• – 3
9. A number consists of two digits, whose sum is 10. If 18 is subtracted from the number, digits of the number are reversed. What is the product?
• 15
• 18
• 24
• 32
10. What is the LCM of 3 (a3 – b3) and 11 (a4 – b4)?
• 33(a3 – b3) (a2 + b2) (a + b)
• (a3 – b3) (a2 + b2) (a – b)
• 33 (a – b) (a2 + b2 – ab) (a3 – b3)
• 33 (a3 – b3) (a4 – b4)
11. Students of a class are made to stand in rows. If one student is extra in a row, there would be two rows less. If one student is less is n a row, there would be three rows more. What is the number of students in the class?
• 65
• 55
• 60
• 50
12. A railway ticket for a child costs half the full fare but the reservation charge is the same on half ticket as much as on full ticket. One reserved first class ticket for a journey between two stations is Rs. 362; one full and one half reserved first class tickets cost Rs. 554. What is reservations charge?
• 18
• 22
• 38
• 46
13. Out of a group of swans 7/2 times the square root of the number are swimming in the pool while the two remaining are playing outside the pool. What is the total number of swans?
• 4
• 8
• 12
• 16
14. If the ratio of x to y is 25 times the ratio of y to x, then what is the ratio of x to y?
• 1 : 5
• 5 : 1
• 25 : 1
• 1 : 25
15. A milk vendor bought 28 L of milk at the cost of Rs. 8.50 per litre. After adding some water, he sold the mixture at the same price. If he gains 12.5%, how much water did he add?
• 5 L
• 5 L
• 5 L
• 5 L
16. If m and n are two integers such that m = n2 -n, then (m2 – 2m) is always divisible by
• 9
• 16
• 24
• 48
1. Which one is the largest among the following?
• 725
• 725
• 725
• 725
2. 10% of the inhabitants of a certain city left that city. Later on 10% of the remaining inhabitants of that city again left the city. What is the remaining percentage of population of that city?
• 80%
• 4%
• 6%
• 81%
3. If the rate of interest is 10% per annum and is compounded half yearly, the principal of Rs. 400 in 3/2 yr will amount to
• 463.00
• 463.05
• 463.15
• 463.20
4. The number of workers in the employment guarantee scheme increased by 15 which resulted into an increase of 20%. What are the initial number of workers?
• 60
• 75
• 80
• 90
5. Two men P and Q start from a place walking at 5 km at 6.5 km/h respectively. What is the time they will take to ?? 92 km apart if they walk in opposite directions?
• 2 h
• 4 h
• 6 h
• 8 h
6. In an army camp ration is available for 100 soldier 10 days. After 2 days, 60 soldiers joined. Then for many more days will the remaining ration last?
• 7 days
• 6 days
• 5 days
• 4 days
7. Two trains travel in the same direction at 50 km/h and 32 km/h respectively. A man in the slower train observes that 15 s elapse before the faster train completely passes him. What is the length of the faster train?
• 75 m
• 125 m
• 150 m
• 625/3 m
1. A person walks a distance in 114 days, when he rests 9 h a day. How long will he take to walk twice the distance if he walks twice as fast and rests twice as long each day as before?
• 57 days
• 228 days
• 285 days
• 324 days
2. If x : y = 1 : 3, y : z = 5: k, z : t = 2 : 5 and t : x + 3 :4, then what is the value of k?
• ½
• 1/3
• 2
• 3
3. The number is √0.0001 is
• a rational number less than 0.01
• a rational number
• an irrational number
• neither a rational number nor an irrational number
4. A person P started a business with a capital of Rs. 2525 and another person Q joined P after some months with a capital of Rs. 1200. Out of the total annual profit of Rs. 1644, P’s share was Rs. 1212. When did Q join as partners?
• After 2 months
• After 9 months
• After 4 months
• After 5 months
5. The mess charges for 35 students for 24 days in Rs. 6300. In how many days will the mess charges be Rs. 3375 for 25 students?
• 12
• 15
• 18
• 21
6. If a + b = 2m2, b + c = 6m, a + c = 2, where m is a real number and a ≤ b ≤ c, then which one of the following is correct?
• 0 ≤ m ≤ 1/2
• – 1 ≤ m ≤ 0
• 1/3 ≤ m ≤ 1
• 1 < m ≤ 2
7. What is the least number which when divided by 42, 72 and 84 leaves the remainders 25, 55 and 67 respectively?
• 521
• 512
• 504
• 487
8. A trader sells two cycles at Rs. 1188 each and gains 10% on the first and loses 10% on the second. What is the profit or loss percent on the whole?
• 1% loss
• 1% gain
• No loss no gain
• 2% loss
9. A person borrowed Rs. 7500 at 16% compound interest. How much does he have to pay at the end of 2 yr to clear the loan?
• 9900
• 10092
• 11000
• 11052
10. P and Q can do a job in 2 days: Q and R can do it in 4 days; and P and R in 12/5 days. What is the number of days required for P alone to do the job?
• 5/2
• 3
• 14/5
• 6