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?

    • 5°
    • 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°
  • 5°
  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
    • ∠ADB > ∠DXC
  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