CDS (I) 2017, Elementary Mathematics question paper

100 questions · 100 marks · 120 minutes · +1 per correct answer, -0.33 per wrong one

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1 $\sqrt{\dfrac{0.064 \times 6.25}{0.081 \times 4.84}}$
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2 $(x + 4)$
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3 $\alpha$
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4 $a = bc$
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5 $\dfrac{(0.35)^2 + 0.70 + 1}{2.25} + 0.19$
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6 $2^{40}$
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7 $(a^2 - 5a + 3) x^2 + (3a - 1) x + 2 = 0$
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8 $(4444)^{4444}$
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9 $x = \dfrac{\sqrt{a + b} - \sqrt{a - b}}{\sqrt{a + b} + \sqrt{a - b}}$
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10 $\dfrac{(443 + 547)^2 + (443 - 547)^2}{443 \times 443 + 547 \times 547}$
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11 $x = t^{\frac{1}{t-1}}$
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12 $A : B = 3 : 4$
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13 $A = \{x : x \text{ is a multiple of } 7\}$
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14 $x = 2 + 2^{2/3} + 2^{1/3}$
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15 $\sqrt{\dfrac{x}{y}} = \dfrac{24}{5} + \sqrt{\dfrac{y}{x}}$
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16 $x \log_{10} \left( \dfrac{10}{3} \right) + \log_{10} 3 = \log_{10} (2 + 3^x) + x$
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17 $\alpha$
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18 $a^3 = 335 + b^3$
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19 $9^x \, 3^y = 2187$
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20 $kx + 3y + 1 = 0$
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21 $The number of prime numbers which are less than 100 is$
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22 $1 : 2 : 3 : 4$
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23 $\dfrac{5}{3}$
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24 $If 15 men take 21 days of 8 hours each to do a piece of work, then what is the number of days of 6 hours each that 21 women would take, if 3 women would do as much work as 2 men ?$
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25 $\dfrac{27}{35}$
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26 $A sum of Rs. 8,400 was taken as a loan. This is to be paid in two equal instalments. If the rate of interest is 10% per annum, compounded annually, then the value of each instalment is$
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27 $1\frac{1}{4}$
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28 $A and B working together can finish a piece of work in 12 days while B alone can finish it in 30 days. In how many days can A alone finish the work ?$
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29 $x$
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30 $If 5 men can do a piece of work in 10 days and 12 women can do the same work in 15 days, the number of days required to complete the work by 5 men and 6 women is$
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31 $A passenger train departs from Delhi at 6 p.m. for Mumbai. At 9 p.m., an express train, whose average speed exceeds that of the passenger train by 15 km/hour leaves Mumbai for Delhi. Two trains meet each other mid-route. At what time do they meet, given that the distance between the cities is 1080 km ?$
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32 $4 : 3$
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33 $a + b = 5$
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34 $Rajendra bought a mobile with 25% discount on the selling price. If the mobile cost him Rs. 4,875, what is the original selling price of the mobile ?$
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35 $A 225 m long train is running at a speed of 30 km/hour. How much time does it take to cross a man running at 3 km/hour in the same direction ?$
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36 $Which one among the following is the largest ?$
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37 $The difference between the simple and the compound interest on a certain sum of money at 4% per annum in 2 years is Rs. 10. What is the sum ?$
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38 $a\%$
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39 $\dfrac{5}{9}$
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40 $Sunil wants to spend Rs. 200 on two types of sweets, costing Rs. 7 and Rs. 10 respectively. What is the maximum number of sweets he can get so that no money is left over ?$
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41 $x^3 + 8$
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42 $p$
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43 $\sqrt[3]{4\frac{12}{125}}$
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44 $A thief is spotted by a policeman from a distance of 100 m. When the policeman starts the chase, the thief also starts running. If the speed of the thief is 8 km/hour and that of the policeman is 10 km/hour, then how far will the thief have to run before he is overtaken ?$
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45 $(4, 3)$
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46 $8n + 1$
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47 $2x + 4y = 6$
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48 $(N^{p-1} - 1)$
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49 $1 : 5$
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50 $1 : 2$
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51 $The mean of 5 numbers is 15. If one more number is included, the mean of the 6 numbers becomes 17. What is the included number ?$
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52 $The mean marks obtained by 300 students in a subject are 60. The mean of top 100 students was found to be 80 and the mean of last 100 students was found to be 50. The mean marks of the remaining 100 students are$
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53 $Consider the following distribution : Class Frequency 0 - 20 17 20 - 40 28 40 - 60 32 60 - 80 f 80 - 100 19 If the mean of the above distribution is 50, what is the value of f ?$
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54 $150^\circ$
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55 $In an asymmetrical distribution, if the mean and median of the distribution are 270 and 220 respectively, then the mode of the data is$
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56 $a, b, c, d, e, f, g$
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57 $x$
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58 $f_1$
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59 $\theta$
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60 $9 \tan^2 \theta + 4 \cot^2 \theta$
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61 $x \sin \theta = y \cos \theta = \frac{2z \tan \theta}{1 - \tan^2 \theta}$
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62 $\cos \theta_1 + \cos \theta_2 + \cos \theta_3 = 3$
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63 $\theta$
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64 $\sin x \sqrt{\frac{1}{1 + \cos x} + \frac{1}{1 - \cos x}}$
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65 $\frac{\cos^4 A - \sin^4 A}{\cos^2 A - \sin^2 A}$
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66 $7 \sin^2 x + 3 \cos^2 x = 4$
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67 $60^\circ$
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68 $x = a \cos \theta + b \sin \theta$
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69 $30^\circ$
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70 $Which one of the following triples does not represent the sides of a triangle ?$
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71 $4 \text{ cm}^2$
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72 $The angles of a triangle are in the ratio 2 : 4 : 3. The smallest angle of the triangle is$
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73 $A ball of radius 1 cm is put into a cylindrical pipe so that it fits inside the pipe. If the length of the pipe is 14 m, what is the surface area of the pipe ?$
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74 $The areas of two circular fields are in the ratio 16 : 49. If the radius of the bigger field is 14 m, then what is the radius of the smaller field ?$
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75 $Let ABCD be a rectangle. Let P, Q, R, S be the mid-points of sides AB, BC, CD, DA respectively. Then the quadrilateral PQRS is a$
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76 $Let P, Q, R be the mid-points of sides AB, BC, CA respectively of a triangle ABC. If the area of the triangle ABC is 5 square units, then the area of the triangle PQR is$
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77 $If each of the dimensions of a rectangle is increased by 200%, the area is increased by$
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78 $Three circles each of radius 3.5 cm touch one another. The area subtended between them is$
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79 $The area of a regular hexagon of side 'a' is equal to$
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80 $30^\circ$
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81 $Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm in length. If both the chords are on the same side of the diameter, then the distance between these chords is$
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82 $If the radius of a right circular cone is increased by p% without increasing its height, then what is the percentage increase in the volume of the cone ?$
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83 $121 \text{ cm}^2$
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84 $\angle ADC = \angle BAC$
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85 $If the surface area of a sphere is reduced to one-ninth of the area, its radius reduces to$
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86 $In a trapezium ABCD, AB is parallel to CD and the diagonals intersect each other at O. What is the ratio of OA to OC equal to ?$
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87 $Ice-cream, completely filled in a cylinder of diameter 35 cm and height 32 cm, is to be served by completely filling identical disposable cones of diameter 4 cm and height 7 cm. The maximum number of persons that can be served in this way is$
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88 $The radius of a circle is increased so that its circumference increases by 15%. The area of the circle will increase by$
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89 $ABCD is a rectangle. The diagonals AC and BD intersect at O. If AB = 32 cm and AD = 24 cm, then what is OD equal to ?$
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90 $A field is divided into four regions as shown in the given figure. What is the area of the field in square metres ?$
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91 $In the figure given below, D is the diameter of each circle. What is the diameter of the shaded circle ?$
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92 $In the figure given below, AC is parallel to ED and AB = DE = 5 cm and BC = 7 cm. What is the area ABDE : area BDE : area BCD equal to ?$
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93 $In the figure given below, PQRS is a parallelogram. PA bisects angle P and SA bisects angle S. What is angle PAS equal to ?$
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94 $\angle A = 80^\circ$
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95 $\angle RLM$
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96 $\angle LPR = 35^\circ$
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97 $\angle DAC = \angle DCA$
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98 $\angle DAB = \angle CBA$
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99 $\angle DXA = \angle AYB$
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100 $\alpha$
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Class	Frequency
0 - 20	17
20 - 40	28
40 - 60	32
60 - 80	f
80 - 100	19

Quality	Price per pencil (in Rs.)	Money spent (in Rs.)
A	1.00	50
B	1.50	x
C	2.00	20

x	Frequency	Cumulative frequency
1	8	8
2	10	18
3	$f_1$	29
4	$f_2$	45

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