CDS (I) 2020, Elementary Mathematics question paper

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

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1 $2 \times 3 \times 5 \times 7 \times 11 + 1$
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2 $x$
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3 $(54)^{10}$
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4 $x^{\sqrt{x}} = \sqrt[n]{x^{x}}$
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5 $In a competitive examination, 250 students have registered. Out of these, 50 students have registered for Physics, 75 students for Mathematics and 35 students for both Mathematics and Physics. What is the number of students who have registered neither for Physics nor for Mathematics ?$
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6 $10^{n} - 1$
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7 $2222^{2}$
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8 $m$
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9 $\frac{a}{b} = \frac{1}{3}$
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10 $3^{x} + 3^{x+1} + 3^{x+2}$
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11 $A two-digit number is 9 more than four times of the number obtained by interchanging its digits. If the product of digits in the two-digit number is 8, then what is the number ?$
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12 $\alpha$
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13 $p$
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14 $(x + k)$
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15 $5^{x+1} - 5^{x-1} = 600$
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16 $A number divides 12288, 28200 and 44333 so as to leave the same remainder in each case. What is that number ?$
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17 $x^{2} + 9y^{2} = 6xy$
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18 $m$
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19 $\frac{1}{a^{m-n} - 1} + \frac{1}{a^{n-m} - 1}$
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20 $x = \sqrt{2}$
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21 $\log x = 1.2500$
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22 $f(x)$
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23 $2401x^4 + 196x^2 + 4$
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24 $x$
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25 $P$
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26 $xy$
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27 $X$
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28 $X$
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29 $A train takes two hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. What is its usual speed ?$
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30 $If 6 men and 8 women can do a piece of work in 10 days; and 13 men and 24 women can do the same work in 4 days, then what is the ratio of daily work done by a man to that of a woman ?$
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31 $Students of a class are made to sit in rows of equal number of chairs. If number of students is increased by 2 in each row, then the number of rows decreases by 3. If number of students is increased by 4 in each row, then the number of rows decreases by 5. What is the number of students in the class ?$
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32 $A sum was put at simple interest at certain rate for 2 years. Had it been put at 1% higher rate of interest, it would have fetched Rs. 24 more. What is the sum ?$
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33 $27 : 34$
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34 $3 : 4$
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35 $What is the median of the data 3, 5, 9, 4, 6, 11, 18 ?$
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36 $1 : 2 : 3$
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37 $The maximum marks in a Test are converted from 250 to 50 for the purpose of an Internal Assessment. The highest marks scored were 170 and lowest marks were 70. What is the difference between the maximum and minimum marks scored in the Internal Assessment ?$
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Directions for the following three (03) items : Read the following information and answer the three items that follow : The following data presents count of released convicts who have served prison terms $X$ , those who have received some educational or technical training during their term $Y$ and those who were offered Company placement $Z$ respectively, from six different jails A, B, C, D, E and F, in the year 2010.
$X$ $Y$ $Z$
A 86 45 25
B 1305 903 461
C 2019 940 474
D 1166 869 416
E 954 544 254
F 1198 464 174
38 $Jails with highest and smallest percentage of trained convicts are respectively$
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39 $Jail with highest placement rate of trained convicts is$
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40 $Jails from which more than half of the trained convicts are offered jobs, are$
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41 $The number of three digit numbers (all digits are different) which are divisible by 7 and also divisible by 7 on reversing the order of the digits, is$
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42 $x$
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43 $XYZ$
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44 $X$
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45 $S$
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46 $X$
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47 $What is the least perfect square which is divisible by 3, 4, 5, 6 and 7?$
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48 $In a water tank there are two outlets. It takes 20 minutes to empty the tank if both the outlets are opened. If the first outlet is opened, the tank is emptied in 30 minutes. What is the time taken to empty the tank by second outlet?$
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49 $(x^2 - 1)$
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50 $\left(x^8 + \frac{1}{x^8}\right) = 47$
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51 $A wheel makes 360 revolutions in one minute. What is the number of radians it turns in one second?$
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52 $(25\,\operatorname{cosec}^2 x + \sec^2 x)$
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53 $0 < \theta < 90^\circ$
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54 $\tan 6\theta = \cot 2\theta$
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55 $30^\circ$
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56 $On a plane area there are two vertical towers separated by 100 feet apart. The shorter tower is 40 feet tall. A pole of length 6 feet stands on the line joining the base of two towers so that the tip of the towers and tip of the pole are also on the same line. If the distance of the pole from the shorter tower is 75 feet, then what is the height of the taller tower (approximately)?$
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57 $p$
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58 $\sin^2 6^\circ + \sin^2 12^\circ + \sin^2 18^\circ + \ldots + \sin^2 84^\circ + \sin^2 90^\circ$
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59 $\frac{\cos\theta}{1 + \sin\theta} + \frac{1}{\cot\theta}$
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60 $\frac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} - \frac{\sin\theta + 1}{\cos\theta}$
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61 $(\tan x + \tan y)(1 - \cot x \cot y) + (\cot x + \cot y)(1 - \tan x \tan y)$
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62 $\sqrt{\frac{\sec x - \tan x}{\sec x + \tan x}}$
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63 $\theta$
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64 $\frac{1 - 2\sin^2\theta\cos^2\theta}{\sin^4\theta + \cos^4\theta} + 4$
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65 $\theta$
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66 $\frac{y}{z} + \frac{z}{x}$
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67 $30^\circ$
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68 $ABCD$
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69 $d$
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70 $AB$
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71 $136\pi$
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72 $If area of a circle and a square are same, then what is the ratio of their perimeters ?$
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73 $A circle of diameter 8 cm is placed in such a manner that it touches two perpendicular lines. Then another smaller circle is placed in the gap such that it touches the lines and the circle. What is the diameter of the smaller circle ?$
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74 $The thickness of a cylinder is 1 foot, the inner radius of the cylinder is 3 feet and height is 7 feet. To paint the inner surface it requires one litre of a particular colour. How much quantity of the same colour is required to paint all the surfaces of the cylinder ?$
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75 $A square and a rectangle have equal areas. If one side of the rectangle is of length numerically equal to the square of the length of the side of the square then the other side of the rectangle is$
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76 $4 : 3$
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77 $20^\circ$
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78 $ABCD$
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79 $A$
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80 $1.4$
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81 $x$
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82 $3x, 4\sqrt{y}, 5\sqrt[3]{z}$
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83 $What is the maximum number of circum-circles that a triangle can have ?$
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84 $30^\circ$
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85 $4.8$
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86 $What is the area of the largest square plate cut from a circular disk of radius one unit ?$
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87 $r$
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88 $p$
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89 $ABCD$
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90 $PQRS$
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91 $What is the area of the shaded region in the given figure, if the radius of each of the circles is 2 cm ?$
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92 $In the given figure, what is the area of the shaded region ?$
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93 $\frac{y}{x} = 6$
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94 $ABCD$
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95 $\angle 1 + \angle 2 + \angle 3 + \angle 4 + \angle 5 + \angle 6 + \angle 7 + \angle 8$
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96 $PQ$
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97 $AB$
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98 $ABC$
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99 $What is the approximate area of the shaded region in the figure given?$
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100 $\triangle AOD$
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	$X$	$Y$	$Z$
A	86	45	25
B	1305	903	461
C	2019	940	474
D	1166	869	416
E	954	544	254
F	1198	464	174

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