CDS (I) 2019, Elementary Mathematics question paper

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

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Directions for the following two (02) items : Read the following frequency distribution for two series of observations and answer the two items that follow :
Class interval Frequency Series-I Frequency Series-II
10-20 20 4
20-30 15 8
30-40 10 4
40-50 $x$ $2x$
50-60 $y$ $y$
Total 100 100
1 $What is the mean of frequency distribution of Series-I ?$
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2 $What is the mode of the frequency distribution of Series-II ?$
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Directions for the following four (04) items : Read the following information and answer the four items that follow : Let the distribution of number of scooters of companies $X$ and $Y$ sold by 5 showrooms ( $A$ , $B$ , $C$ , $D$ and $E$ ) in a certain year be denoted by $S1$ and the distribution of number of scooters of only company $X$ sold by the five showrooms in the same year be denoted by $S2$ .
Showroom A B C D E Total number of scooters sold
$S1$ (in %) 19 21 15 33 12 6400
$S2$ (in %) 24 18 20 30 8 3000
3 $Y$
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4 $B$
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5 $Y$
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6 $A$
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Directions for the following four (04) items : Read the following information and answer the four items that follow : The data shows that Indian roads are turning deadlier over the years.
Year 2014 2015 2016 2017
Number of bikers killed 40957 46070 52750 48746
Number of pedestrians killed 12330 13894 15746 20457
Number of cyclists killed 4037 3125 2585 3559
7 $What was the average number of pedestrians killed per day in the year 2017 ?$
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8 $What is the approximate percentage change in the pedestrians' fatalities during the period 2014-17 ?$
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9 $What is the average number of bikers killed daily in road accidents in the year 2017 ?$
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10 $What is the average number of cyclists killed daily in road accidents in 2017 ?$
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11 $a$
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12 $x = \dfrac{1+\sqrt{3}}{2}$
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13 $HCF of two numbers is 12. Which one of the following can never be their LCM ?$
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14 $17^{174}$
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15 $The rate of interest on two different schemes is the same and it is 20%. But in one of the schemes, the interest is compounded half yearly and in the other the interest is compounded annually. Equal amounts are invested in the schemes. If the difference of the returns after 2 years is Rs. 482, then what is the principal amount in each scheme ?$
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16 $k$
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17 $X$
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18 $\dfrac{1}{3}$
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19 $x^2 + 5x + 6 = 0$
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20 $A$
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21 $A trader sells two computers at the same price, making a profit of 30% on one and a loss of 30% on the other. What is the net loss or profit percentage on the transaction ?$
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22 $A$
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23 $The train fare and bus fare between two stations is in the ratio 3 : 4. If the train fare increases by 20% and bus fare increases by 30%, then what is the ratio between revised train fare and revised bus fare ?$
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24 $N$
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25 $A stock of food grains is enough for 240 men for 48 days. How long will the same stock last for 160 men ?$
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26 $V$
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27 $x$
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28 $^2$
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29 $Which one of the following is correct in respect of a right angled triangle ?$
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30 $BAC$
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31 $\log_{10}(\cos\theta) + \log_{10}(\sin\theta) + \log_{10}(\tan\theta) + \log_{10}(\cot\theta) + \log_{10}(\sec\theta) + \log_{10}(\operatorname{cosec}\theta)$
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32 $\cos^2 x + \cos x = 1$
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33 $0 < \theta < 90^\circ$
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34 $h$
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35 $\dfrac{\sin 19^\circ}{\cos 71^\circ} + \dfrac{\cos 73^\circ}{\sin 17^\circ}$
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36 $The perimeter of a triangle is 22 cm. Through each vertex of the triangle, a straight line parallel to the opposite side is drawn. What is the perimeter of triangle formed by these lines ?$
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37 $AD$
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38 $AB$
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39 $ABC$
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40 $PQRS$
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41 $x$
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42 $l$
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43 $150^\circ$
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44 $P$
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45 $p$
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46 $An equilateral triangle and a square are constructed using metallic wires of equal length. What is the ratio of area of triangle to that of square ?$
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47 $All the four sides of a parallelogram are of equal length. The diagonals are in the ratio 1 : 2. If the sum of the lengths of the diagonals is 12 cm, then what is the area of the parallelogram ?$
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48 $ABC$
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49 $2 : 3$
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50 $The length and breadth of a rectangle are increased by 20% and 10% respectively. What is the percentage increase in the area of the rectangle ?$
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51 $If the length of the hypotenuse of a right angled triangle is 10 cm, then what is the maximum area of such a right angled triangle ?$
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52 $A square is drawn such that its vertices are lying on a circle of radius 201 mm. What is the ratio of area of circle to that of square ?$
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53 $\text{cm}^2$
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54 $A piece of wire of length 33 cm is bent into an arc of a circle of radius 14 cm. What is the angle subtended by the arc at the centre of the circle ?$
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55 $r$
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56 $x^4 - x^2 + 7x + 5$
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57 $The sides of a triangle are 30 cm, 28 cm and 16 cm respectively. In order to determine its area, the logarithm of which of the quantities are required ?$
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58 $\log_{10} 1995 = 3.3000$
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59 $(x - a)(x - b)(x - c)$
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60 $XYZ$
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61 $A hollow sphere of external and internal diameters 6 cm and 4 cm respectively is melted into a cone of base diameter 8 cm. What is the height of the cone ?$
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62 $1 : 2$
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63 $If one side of a right-angled triangle (with all sides integers) is 15 cm, then what is the maximum perimeter of the triangle ?$
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64 $A thin rod of length 24 feet is cut into rods of equal size and joined so as to form a skeleton cube. What is the area of one of the faces of the largest cube thus constructed ?$
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65 $ABCD$
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66 $Three copper spheres of radii 3 cm, 4 cm and 5 cm are melted to form a large sphere. What is its radius ?$
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67 $\text{cm}^3$
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68 $A bucket is in the form of a truncated cone. The diameters of the base and top of the bucket are 6 cm and 12 cm respectively. If the height of the bucket is 7 cm, what is the capacity of the bucket ?$
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69 $A right circular cone has height 8 cm. If the radius of its base is 6 cm, then what is its total surface area ?$
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70 $Six cubes, each with 12 cm edge are joined end to end. What is the surface area of resulting cuboid ?$
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71 $\frac{26}{5}$
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72 $p$
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73 $Radha and Rani are sisters. Five years back, the age of Radha was three times that of Rani, but one year back the age of Radha was two times that of Rani. What is the age difference between them ?$
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74 $A person carries Rs. 500 and wants to buy apples and oranges out of it. If the cost of one apple is Rs. 5 and the cost of one orange is Rs. 7, then what is the number of ways in which a person can buy both apples and oranges using total amount ?$
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75 $y$
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76 $16 + 6\sqrt{7}$
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77 $7^{25}$
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78 $x$
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79 $X$
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80 $\sqrt{75}$
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81 $A library has an average number of 510 visitors on Sunday and 240 on other days. What is the average number of visitors per day in a month of 30 days beginning with Saturday ?$
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82 $\frac{36}{11} = 3 + \cfrac{1}{x + \cfrac{1}{y + \cfrac{1}{z}}}$
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83 $A person sells two items each at Rs. 990, one at a profit of 10% and another at a loss of 10%. What is the combined percentage of profit or loss for the two items ?$
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84 $It takes 11 hours for a 600 km journey if 120 km is done by train and the rest by car. It takes 40 minutes more if 200 km are covered by train and the rest by car. What is the ratio of speed of the car to that of the train ?$
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85 $x$
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86 $10^n$
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87 $3^{98} - 3^{89}$
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88 $The sum of the squares of four consecutive natural numbers is 294. What is the sum of the numbers ?$
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89 $x^2 + px + q = 0$
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90 $How many pairs of natural numbers are there such that the difference of their squares is 35 ?$
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91 $(b - 6)$
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92 $a = \sqrt{7 + 4\sqrt{3}}$
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93 $\frac{1}{x^2 + 5x + 10}$
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94 $(x + 2)$
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95 $Which one of the following is not correct ?$
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96 $n$
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97 $x^3 + 3x^2 + 3x + 1$
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98 $\frac{(x-y)^3 + (y-z)^3 + (z-x)^3}{9(x-y)(y-z)(z-x)}$
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99 $X = \{a, \{b\}, c\}$
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100 $p$
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Class interval	Frequency Series-I	Frequency Series-II
10-20	20	4
20-30	15	8
30-40	10	4
40-50	$x$	$2x$
50-60	$y$	$y$
Total	100	100

Showroom	A	B	C	D	E	Total number of scooters sold
$S1$ (in %)	19	21	15	33	12	6400
$S2$ (in %)	24	18	20	30	8	3000

Year	2014	2015	2016	2017
Number of bikers killed	40957	46070	52750	48746
Number of pedestrians killed	12330	13894	15746	20457
Number of cyclists killed	4037	3125	2585	3559

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