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CDS(I) Exam 2017 Elementary Mathematics Previous Year Paper

July 3, 2019
CDS(II) Exam 2017 Elementary Mathematics Previous Year Paper
July 3, 2019

CDSE 1 2017 Mathematics

Q. 1 What is √[ (0.064 x 6.25) ∕ (0.081 x 4.84)] equal to?

A. 10/99

B. 100/99

C. 9

D. 99

Q. 2 If α and β are the roots of the quadratic equation 2x² + 6x + k = 0, where k < 0, then what is the minimum value of α / β + β / α ?

A. 2

B. -2

C. 9

D. -9

Q. 3 (x+4) is a factor of which one of the following expressions?

A. x²-7x+44

B. x²+7x-44

C. x²-7x-44

D. x²+7x+44

Q. 4 Consider the following statements:

If a=b,c with HCF(b,c)= 1, then HCF(c,bd)=HCF(c,d)

If a=b,c with HCF(b,c)= 1, then HCF(a,d)=HCF(c,bd)

A. 1 only

B. 2 only

C. Both 1 and 2

D. Neither 1 or 2

Q. 5 What is the square root of (0.35)²+0.70+1/2.25+0.19?

A. 1

B. 2

C. 3

D. 4

Q. 6 What is the number of digits in 2⁴⁰ expressions (Given that log₁₀ 2 = 0·301)

A. 14

B. 13

C. 12

D. 11

Q. 7 If one ‘root of (a² – 5a + 3) x² + (3a- 1) x + 2 = 0 is twice the other, then what is the value of’a’?

A. 2/3

B. -2/3

C. 1/3

D. -1/3

Q. 8 What is the remainder when the number ( 4444)⁴⁴⁴⁴ is divided by 9 ?

A. 4

B. 6

C. 7

D. 8

Q. 9 If x =[(√(a+b)-√(a-b))/(√(a+b)+√(a-b))] , then what is bx²- 2ax + b equal to (b * 0)?

A. 0

B. 1

C. ab

D. 2ab

Q. 10 What is the value of

A. 0

B. 1

C. 2

D. 3

Q. 11 If x = (t)^ (1/(t -1)) and y = (t)^(t/(t-1)) , t > 0, t ≠ 1, then what is the relation between x and y?

A. y^x = (x)^(1/y)

B. x^(1/y) = y^(1/x)

C. x^y = y^x

D. x^y = y^(1/x)

Q. 12 If A : B = 3 : 4, then what is the value of the expression [(3A²+4B)/(3A-4B²)]

A. 43/55

B. -43/55

C. 47/55

D. cannot be determined

Q. 13 If A= {x : xis a multiple of 7},

B = {x : x is a multiple of 5} and

C = {x: x is a multiple of35}, then which one of the following is a null set ?

A. (A-B) U C

B. (A-B)-C

C. (A∩B)∩C

D. (A∩B)-C

Q. 14 If x = 2 + 2^⅔ + 2^⅓, then what is the value of x³ -6x² + 6x?

A. 3

B. 2

C. 1

D. 0

Q. 15 If √x/y = 24/5 +√y/x and x+y =26 , then what is the value of xy ?

A. 5

B. 15

C. 25

D. 30

Q. 16 What is the solution of the equation x log₁₀(10/3) + log₁₀3 = log₁₀(2 + 3ⁿ) + n ?

A. 10

B. 3

C. 1

D. 0

Q. 17 If α and β are the roots of the equation x2 + px + q = 0, then what is α2 + β2 equal to?

A. p² – 2q

B. q² – 2p

C. p² + 2q

D. q² – q

Q. 18 If a³ = 335 + b³ and a = 5 + b, then what is the value of a + b (given that a > 0 and b > 0)?

A. 7

B. 9

C. 16

D. 49

Q. 19 If 9ⁱ 3ⁿ = 2187 and 2³ⁱ 2²ⁿ – 4ⁱ ⁿ = 0 then what is the value of (i + n) ?

A. 1

B. 3

C. 5

D. 7

Q. 20 The pair of linear equations kx+3y+1 = 0 and 2x+y+3 =0 intersect each other if :

A. k= 6

B. k is not equal to 6

C. k =0

D. k is not equal to 0

Q. 21 The number of prime numbers which are less than 100 is

A. 24

B. 25

C. 26

D. 27

Q. 22 The cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1:2:3:4. If the loss in total value of the diamond was the ₹ 70,000, what was the price of the original diamond?

A. ₹ 1,00,000

B. ₹ 1,40,000

C. ₹ 1,50,000

D. ₹ 1,75,000

Q. 23 In a 100 m race , A runs at speed 5/3 m/s .If A gives a start of 4m to B and still beats him by 12 sec what is the speed of B?

A. 5/4 m/s

B. 7/5 m/s

C. 4/3 m/s

D. 6/5 m/s

Q. 24 If 15 men take 21 days of 8 hours each to do a piece of work, then what is the number of days of 6 hours each that 21 women would take, if 3 women would do as much work as 2 men?

A. 18

B. 20

C. 25

D. 30

Q. 25 What number must be substracted from both the numerator and denominator of the fraction 27/35 so that it becomes 2/3

A. 6

B. 8

C. 9

D. 11

Q. 26 A sum of Rs 8,400 was taken as a loan. This is to be paid in two equal instalments. If the rate of interest is 10% per annum, compounded annually, then the value of each instalment is

A. Rs 4,200

B. Rs 4,480

C. Rs 4,840

D. none of the above

Q. 27 Leela got married 6 years ago .Today her age is 1(1/4) times at the age of her mariage .Her sons age is 1/10 times her age .What is the present age of her son ?

A. 1 year

B. 2 years

C. 3 years

D. 4 years

Q. 28 A and B working together can finish a piece of work in 12 days while B alone can finish it in 30 days. In how many days can A alone finish the work?

A. 18 days

B. 20 days

C. 24 days

D. 25 days

Q. 29 The value of i which satisfy the equation 5¹ ⁺ ⁱ + 5 ¹ ⁻ ⁱ = 26?

A. -1, 1

B. 0, 1

C. 1, 2

D. -1, 0

Q. 30 If 5 men can do a piece of work in 10 days and 12 women can do the same work in 15 days, the number of days required to complete the work by 5 men and 6 women is

A. 7 (1/2 ) days

B. 8 days

C. 9 (1/2 ) days

D. 12 days

Q. 31 A passenger train departs from Delhi at 6 p.m. for Mumbai. At 9 p.m., an express train, whose average speed exceeds that of the passenger train by 15 km/hour leaves Mumbai for Delhi. Two trains meet each other mid-route. At what time do they meet, given that the distance between the cities is 1080 km?

A. 4 p.m.

B. 2 a.m

C. 12 midnight

D. 6 a.m

Q. 32 In a class of 49 students, the ratio of girls to boys is 4 : 3. If 4 girls leave the class, the ratio of girls to boys would be

A. 11:7

B. 8:7

C. 6:5

D. 9:8

Q. 33 If a + b = 5 and ab = 6, then what is the value of a³ + b³ ?

A. 35

B. 40

C. 90

D. 125

Q. 34 Rajendra bought a mobile with 25% discount on the selling price. If the mobile cost him Rs 4,875, what is the original selling price of the mobile?

A. Rs 6,300

B. Rs 6,400

C. Rs 6,500

D. Rs 6,600

Q. 35 A 225 m long train is running at a speed of 30 km/hour. How much time does it take to cross a man running at 3 km/hour in the same direction?

A. 40 seconds

B. 30 seconds

C. 25 seconds

D. 15 seconds

Q. 36 Which one among the following is the largest?

A. 7/9

B. 11/14

C. 3/4

D. 10/13

Q. 37 The difference between the simple and the compound interest on a certain sum of money at 4% per annum in 2 years is Rs 10. What is the sum?

A. Rs 5,000

B. Rs 6,000

C. Rs 6,250

D. Rs 7,500

Q. 38 If a% of a + b% of b = 2% of ab, then what percent of a is b?

A. 50%

B. 75%

C. 100%

D. Cannot be determined

Q. 39 5/9th part of a village are males .If 30% males are married , the percentage of unmarried females in the population is ?

A. 20(2/9)

B. 27(2/9)

C. 27(7/9)

D. 29(2/9)

Q. 40 Sunil wants to spend Rs 200 on two types of sweets, costing Rs 7 and Rs 10 respectively. What is the maximum number of sweets he can get so that no money is left over?

A. 25

B. 26

C. 27

D. 28

Q. 41 What is the LCM of x³ + 8, x² + 5x + 6 and x³ + 4x² + 4x

A. x(x + 2)² (x + 3) (x² – 2x + 4)

B. x(x – 2)² (x – 3) (x² + 2x + 4)

C. (x + 2)² (x + 3) (x² – 2x + 4)

D. (x – 2)² (x – 3) (x² – 2x + 4)

Q. 42 The HCF of two expressions p and q is 1. What is the reciprocal of their LCM?

A. p + q

B. p – q

C. pq

D. (pq)⁻¹

Q. 43 What is the value of ∛4(12/125)?

A. 1(3/5)

B. 1(2/5)

C. 1(4/5)

D. 2(2/5)

Q. 44 A thief is spotted by a policeman from a distance of 100 m. When the policeman starts the chase, the thief also starts running. If the speed of the thief is 8 km/hour and that of the policeman is 10 km/hour, then how far will the thief have to run before he is overtaken?

A. 200 m

B. 300 m

C. 400 m

D. 500 m

Q. 45 Aman and Alok attempted to solve a quadratic equation. Aman made a mistake in writing down the constant term and ended up in roots (4, 3) . Alok made a mistake in writing down the coefficient of x to get roots (3, 2). The correct roots of the equation are

A. -4, -3

B. 6,1

C. 4. 3

D. -6, -1

Q. 46 Consider the following statements:

1. Of two consecutive integers, one is even.

2. Square of an odd integer is of the form 8n + 1.

Which of the above statements is/are correct?

A. 1 only

B. 2 only

C. Both 1 and 2

D. neither 1 nor 2

Q. 47 The system of equations 2x + 4y = 6 and 4x + 8y = 8 is

A. Consistent with a unique solution

B. Consistent with infinitely many solutions

C. Inconsistent

D. None of the above

Q. 48 (N^p─1 ─1) is a multiple of p, if N is prime to p and p is a

A. Prime number

B. rational number

C. real number

D. composite number

Q. 49 The ratio of two numbers is 1 : 5 and their product is 320. What is the difference between the squares of these two numbers?

A. 1024

B. 1256

C. 1536

D. 1640

Q. 50 25 kg of alloy X is mixed with 125 kg of alloy Y. If the amount of lead and tin in the alloy X is in the ratio 1 : 2 and the amount of lead and tin in the alloy Y is in the ratio 2 : 3, then what is the ratio of lead to tin in the mixture?

A. 1:2

B. 2:3

C. 3:5

D. 7 :11

Q. 51 The mean of 5 numbers is 15. If one more number is included, the mean of the 6 numbers becomes 17. What is the included number?

A. 24

B. 25

C. 26

D. 27

Q. 52 The mean marks obtained by 300 students in a subject are 60. The mean of top 100 students was found to be 80 and the mean of last 100 students was found to be 50. The mean marks of the remaining 100 students are

A. 70

B. 65

C. 60

D. 50

Q. 53 Consider the following distribution:

If the mean of the above distribution is 50, what is the value of f?

A. 24

B. 34

C. 56

D. 96

Q. 54 In a pie diagram, there are four slices with angles 150°, 90°, 60° and 60°. A new pie diagram is formed by deleting one of the slices having angle 60° in the given pie diagram. In the new pie diagram

A. The largest slice has angle 150°

B. The smallest slice has angle 70°

C. The largest slice has angle 180°

D. The smallest slice has angle 90°

Q. 55 In an asymmetrical distribution, if the mean and median of the distribution are 270 and 220 respectively, then the mode of the data is

A. 120

B. 220

C. 280

D. 370

Q. 56 Let a,b,c,d,e,f,g be consecutive even number and j,k,l,m,n be consecutive odd number. What is the average of all the numbers

A. 3(a + n)/2

B. (5l + 7d)/4

C. (a + b + m + n)/4

D. None of the above

Q. 57 An individual purchases three qualities of pencils. The relevant data is given below: It is known that the average price per pencil is Rs 1.25. What is the value of x?

A. Rs 10

B. Rs 30

C. Rs 40

D. Rs 60

Q. 58 Consider the following frequency distribution:

What are the value of f1 and f2 respectively?

A. 10 and 17

B. 17 and 10

C. 11 and 16

D. 16 and 11

Q. 59 If D is the number of degrees and R is the number of radius is an angle θ,then which one of the follwoing is correct ?

A. πD= 180 R

B. πD= 90 R

C. πR= 180D

D. πR= 90D

Q. 60 What is the minimum value of 9 tan ²θ + 4 cot ²θ

A. 6

B. 9

C. 12

D. 13

Q. 61 If , for the given value , what is the valur of 4z²(x²+y²) eqaul to ?

A. (x²+y²)³

B. (x²-y²)²

C. (x²-y²)³

D. (x²+y²)²

Q. 62 If cosθ₁+cosθ₂+cosθ₃= 3 then what is the value of sinθ₁+sinθ₂+sinθ₃ equal to ?

A. 0

B. 1

C. 2

D. 3

Q. 63 What is the value of the θ which satisfies cos θ + tan θ = 1?

A. 0°

B. 30°

C. 45°

D. 60°

Q. 64 What is the value of the given eqaution?

A. √2

B. 2√2

C. √2 tan x

D. 0

Q. 65 What is the given value(in the figure) equal to?

A. cos²A – sin² A

B. cosA – sin A

C. 1

D. 2

Q. 66 If 7 sin²x + 3 cos²x = 4, 0 < x < 90° , then what is the value of tan x ?

A. √2

B. 1

C. √3/2

D. 1/√3

Q. 67 An aeroplane flying at a height of 300 m above the ground passes vertically above another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 60° and 45° respectively. What is the height of the lower plane from the ground?

A. 100 √3 m

B. 100/√3 m

C. 50 √3 m

D. 150 (√3+1) m

Q. 68 If x = a cos θ + b sin θ and y = a sin θ – b cos θ, then what is x^2 + y^2 equal to?

A. 2ab

B. a + b

C. a² + b²

D. a² – b²

Q. 69 From the top of a building 90 m high, the angles of depression of the top and the bottom of a tree are 30° and 45° respectively. What is the height of the tree?

A. 30√3 m

B. 90 -30√3 m

C. 90 + 30√3 m

D. 60+ 30√3 m

Q. 70 Which one of the following triples does not represent the sides of a triangle?

A. (3, 4, 5)

B. (4, 7, 10)

C. (3, 6, 8)

D. (2, 3, 6)

Q. 71 If the perimeter of a rectangle is 10 cm and the area is 4 cm2, then its length is

A. 6 cm

B. 5 cm

C. 4.5 cm

D. 4 cm

Q. 72 The angles of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is

A. 20°

B. 40°

C. 50°

D. 60°

Q. 73 A ball of radius 1 cm is put into a cylindrical pipe so that it fits inside the pipe. If the length of the pipe is 14 m, what is the surface area of the pipe?

A. 2200 square cm

B. 4400 square cm

C. 8800 square cm

D. 17600 square cm

Q. 74 The areas of two circular fields are in the ratio 16 : 49. If the radius of the bigger field is 14 m, then what is the radius of the smaller field?

A. 4 m

B. 8 m

C. 9 m

D. 10 m

Q. 75 Let ABCD be a rectangle. Let P, Q, R, S be the mid-points of sides AB, BC, CD, DA respectively. Then the quadrilateral PQRS is a

A. Square

B. Rectangle, but need not be a square

C. Rhombus, but need not be a square

D. Parallelogram, but need not be a rhombus

Q. 76 Let P , Q , R be the mid points of AB, BC and CA of a triangle ABC .If the area of the trianfgle ABC is 5 units , what is the area of traingle PQR ?

A. 5/3 sqaure units

B. 5/2√2 sqaure units

C. 5/4 sqaure units

D. 1 sqaure units

Q. 77 If each of the dimensions of a rectangle is increased by 200%, the area is increased by

A. 300%

B. 400%

C. 600%

D. 800%

Q. 78 Three circles each of radius 3.5 cm touch one another . The area subtended between them is :

A. 6(√3π−2)

B. 6(2π−√3)

C. 49/ 8 (2√3 – π )

D. 49/ 8 (√3 – π )

Q. 79 The area of regular hexagon of side ‘a’ is equal to

A. (√2/3) a² square units

B. (3√3/2) a² square units

C. (1/2) a² square units

D. (√3/2) a² square units

Q. 80 ABCDEF is a regular polygon. Two poles at C and D are standing vertically and subtend angles of elevation 30° and 60° at A respectively. What is the ratio of the height of the pole at C to that of the pole at D?

A. 1 :1

B. 1 :2√3

C. 2√3 : 1

D. 2 : √3

Q. 81 Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm in length. If both the chords are on the same side of the diameter, then the distance between these chords is

A. 5. 5 cm

B. 5 cm

C. 3.5 cm

D. 3 cm

Q. 82 If the radius of a right circular cone is increased by p% without increasing its height, then what is the percentage increase in the volume of the cone?

A. p²

B. 2p²

C. p²/100

D. p(2+p²/100)

Q. 83 A copper wire when bent in the form of a square encloses an area of 121 cm². If the same wire is bent in the form of a circle, it encloses an area equal to

A. 121 cm².

B. 144 cm².

C. 154 cm².

D. 168 cm².

Q. 84 ABC is a triangle and D is the point on the side BC .IF BC = 12 cm ,BD= 9 cm and ∠ADC = ∠BAC then the length of AC is equal to

A. 5 cm

B. 6 cm

C. 8 cm

D. 9 cm

Q. 85 If the surface area of a sphere is reduced to one-ninth of the area, its radius reduces to

A. 1/4th

B. 1/3rd

C. 1/5th

D. 1/9th

Q. 86 In a trapezium ABCD, AB is parallel to CD and the diagonals intersect each other at O. What is the ratio of OA to OC equal to?

A. Ratio of OB to OD

B. Ratio of BC to CD

C. Ratio of AD to AB

D. Ratio of AC to BD

Q. 87 Ice-cream, completely filled in a cylinder of diameter 35 cm and height 32 cm, is to be served by completely filling identical disposable cones of diameter 4 cm and height 7 cm. The maximum number of persons that can be served in this way is

A. 950

B. 1000

C. 1050

D. 1100

Q. 88 The radius of a circle is increased so that its circumference increases by 15%. The area of the circle will increase by

A. 31.25%

B. 32.25%

C. 33.25%

D. 34.25%

Q. 89 ABCD is a rectangle. The diagonals AC and BD intersect at O. If AB = 32 cm and AD = 24 cm, then what is OD equal to?

A. 22 cm

B. 20 cm

C. 18 cm

D. 16 cm

Q. 90 A field is divided into four regions as shown in the given figure. What is the area of the field in square metres?

A. a

B. b

C. c

D. d

Q. 91 In the figure given below, D is the diameter of each circle. What is the diameter of the shaded circle?

A. D(√2−1)

B. D(√2+1)

C. D(√2+2)

D. D(2-√2)

Q. 92 In the figure given below, AC is parallel to ED and AB = DE = 5 cm and BC = 7 cm. What is the area ABDE : area BDE : area BCD equal to?

A. 10 : 5 : 7

B. 8 : 4 : 7

C. 2 : 1 : 2

D. 8 : 4 : 5

Q. 93 In the figure given below, PQRS is a parallelogram. PA bisects angle P and SA bisects angle S. What is angle PAS equal to?

A. 60°

B. 75°

C. 90°

D. 100°

Q. 94 In thefigure given below ∠A = 80° and ∠ABC = 60° BD and CD bisect angels B and C resectively .What are the values of X and y respectively /?

A. 10 and 130

B. 10 and 125

C. 20 and 130

D. 20 and 125

Q. 95 In the figure given below , PQR is the non -isoceles right angled triangle , right angled at Q .If LM and QT are parellel and QT = PT , thenwhats is ∠RLM equals to ?

A. ∠PQT

B. ∠LRM

C. ∠RML

D. ∠QPT

Q. 96 In the figure given below, PQ is parellelto Rs and PR is parellel to QS .IF ∠LPR = 35° and ∠UST= 70° ,then what is MTP equal to ?

A. 55°

B. 70°

C. 75°

D. 80°

Q. 97 In the figure given below, ABC is a triangle with AB=BC and D is the interoir point of traingle ABC such that ∠DAC = ∠DCA

Consider the following statements:

1. Triangle ADC is an isosceles triangle.

2. D is the centroid of the triangle ABC.

3. Triangle ABD is congruent to the triangle CBD.

Which of the above statements are correct?

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Q. 98 In the figure given below , M is the mid point of AB and ∠DAB = ∠CBA and ∠AMC = ∠BMD then the traingle ADM is congruent to the traingle BCM by

A. SAS rule

B. SSS rule

C. ASA rule

D. AAA rule

Q. 99 ABCD is a sqaure and x is the mid point of AB and Y is the mid poin of Bc..Consider the following statements .

I.Triangles ADX and BAY are congreunet

II. ∠DXA = ∠AYB

III.DX is inclined to angle 60 deg at AY

IV.DX is perpendicular to AY

Which of the above statements are correct?

A. 2, 3 and 4 only

B. 1, 2 and 4 only

C. 1, 3 and 4 only

D. 1, and \ 2 only

Q. 100 From an aeroplane vertically over a straight horizontal road, the angles of depression of two consecutive kilometer-stones on the opposite sides of the aeroplane are observed to be α and β. The height of the aeroplane above the road is

A. a

B. b

C. c

D. d