Combined Defence Services Exam - II, 2015 - Elementary Mathematics

  1. 1

    The number of values satisfying (x+100/x)>50,where is  a natural number less than or equal to 100 is

  1. 2

    What is the sum of digits of the least multiple of 13,which when divided by 6,8 and 12 leaves remainder 5.7 and 11 respectively as remainders?

  1. 3

    A milkman claims to sell milk at cost price only.Still he is making a profit of 20% since he has mixed some amount of water in the milk.What is the percentage of milk in the mixture?

  1. 4

    What is √4+(√4-(√4+....)

  1. 5

    The largest natural number which divides every natural number of the form (n³-n)(n-2),where n is a natural number greater than 2 is

  1. 6

    The average of m numbers is n^4 and average of n numbers is m^4.The average of (m+n) numbers² is

  1. 7

    The digit in the units place of the resulting number of the expression (234)^100+(234)^101 is

  1. 8

    If x=√3+√2,then the value of x³+x+(1/x)+(1/x³) is

  1. 9

    The value of (1/1*4)+(1/4*7)+(1/7*10)+...+(1/16*19) is

  1. 10

    Two trains are moving in the same direction at 1.5km/minute and 60km/hr respectively.A man in the faster train observes that it takes 27s to cross the slower train.The length of the slower train is

  1. 11

    A tin of oil was 4/5th full.When 6 bottles of oil was taken out from this tin and 4 bottles of oil were poured into it,it was 3/4 full.Oil of how many bottles can the tin contain?

  1. 12

    A number when divided by 7 leaves a remainder 3 and the resulting quotient when divided by 11 leaves a remainder 6.If the same number weh divided by 11 leaves a remainder m and the resulting quotient when divided by 7 leaves a remainder n.What are the values of m and n respectively?

  1. 13

    Consider the following in respect of the equation y=√(x-1)²/(x-1)

    1.y=1 if x>1

    2.y=-1 if x<1

    3.y exists for all values of x

    Which of the above statements are correct

  1. 14

    If (x+1) is the H.C.F of Ax²+Bx+C and Bx²+Ax+C where A≠B,then the value of C is

  1. 15

    The seven digit number 876p37q is divisible by 225.The values of p and q can be respectively

  1. 16

    If a,b and c satisfy the equation x³-3x²+2x+1=0,then what is the value of 1/a+1/b+1/c

  1. 17

    A and B are two taps which fill a tank individually in 10 minutes and 20 minutes respectively.However,there is a leakage at the bottom,which can empty a filled tank in 40 minutes.If the tank is empty initially,how much time will both taps take to fill the tank with leakage?

  1. 18

    Which one of the following is correct? 

  1. 19

    The value of a single discount on some amount which is equivalent to a series of discounts of 10%,20% and 40% on the same amount is equal to

  1. 20

    If k=x-y+2z where -2<=x<=1,-1<=y<=2 and 3<=z<=6,then which one of the following is correct?

  1. 21

    The number of pairs (x,y) where x,y are integers satisfying the equation 21x+48y=5 is

  1. 22

    Let x and y be positive integers such that x is prime and y is composite.Which of the following statements are correct?

    1.(y-x) can be an even integer

    2.xy can be an even integer

    3.0.5(x+y) can be an even integer

    Select the correct answer using codes

  1. 23

    Let x and y be positive integers such that x>y.The expressions 3x+2y and 2x+3y when divided by 5 leaves remainders 2 and 3 reapectively.What is the remainder when (x-y) is divided by 5?

  1. 24

    In a race,A B and C take part.A beats B by 30m,B beats C by 20m and A beats C by 48m.Which of the following is correct?

    1.The length of the race is 300m.

    2.The speeds of A,B and C are in the ratio 50:45:42

    Select the correct answer using codes

     

  1. 25

    If the roots of the quadratic equation x²-4x-log N=0 are all real,then the minimum value of N is

  1. 26

    A motor boat whose speed is 15km/hr in still water goes 30km downstream and comes back in a total of 4hr and 30 minutes.The speed of the stream is

  1. 27

    If 4 men working 4 hours per day for 4 days complete 4 units of work,then how many units of work will be completed by 2 men working for 2 hours per day in 2 days?

  1. 28

    By increasing the speed of his car by 15 km/hr,a person covers 300km distance by taking an hour less than before.The original speed of the car was

  1. 29

    If m persons can paint a house in d days,how many days will it take for (m+2) persons to paint the same house?

  1. 30

    If a:b=3:5 and b:c=7:8 ,then 2a:3b:7c is equal to

  1. 31

    Two trains,one is of 121 m in length at the speed of 40km/hr and the other of 99m in length at the speed of 32km/hr are running in opposite directions.In how much time they will be completely  clear from each other from the moment they meet?

  1. 32

    Three athletes run a 4km race.Their speeds are in the ratio 16:15:11.When the winner wins the race,distance between the athlete in the second position to the athlete in the third position is

  1. 33

    The sum of first 47 terms of the series (1/4+1/5-1/6-1/4-1/5+1/6+1/4+1/5-1/6... is

  1. 34

    Which one of the following is correct? 

  1. 35

    20% of a number when added to 20 becomes the  number itself,then the number is

  1. 36

    Consider the followng statements

    1.(1+tan²θ)/(1+cot²θ)=[(1-tanθ)/(1-cotθ)]² is true for all 0<θ<π/2,θ≠π/4

    2.cotθ=1/tanθ is true for θ=45° only

    Which of the above statement is/are correct?

  1. 37

    If x=acosθ and y=bcotθ ,then (ax^-1-by^-1)(ax^-1+by^-1) is equal to 

  1. 38

    cosθ/(1-sinθ) is equal to

  1. 39

    If tan(x+40)°tan(x+20)°tan(3x)°tan(70-x)°tan(50-x)°=1,then the value of x is equal to

  1. 40

    If θ is an acute angle and sinθcosθ=2cos³θ-1.5cosθ,then  what is sinθ equal to 

  1. 41

    Consider the following statements

    1.sin 66° is less than cos 66°

    2.sin 26° is less than cos 26°

    Which of the above statements are correct?

  1. 42

    If a and b are positive,then the relation sinθ=(2a+3b)/3b is

  1. 43

    An aeroplane flying at a height of 3000m passes vertivally above another aeroplane at an instant when angles of elevation of two planes from some point on the ground is 60° and 45° respectively.Then the vertical distance of the two planes is 

  1. 44

    A pole is standing erect on the ground which is horizontal.The tip of the pole is tied tight with a rope of length √12m to a point on the ground.If the rope is making 30° with the horizontal,then the height of the pole is 

  1. 45

    If tanθ+secθ=2,then tanθ is equal to

  1. 46

    A's salary was increased by 40% and then decreased by 20%.On the whole A's salary is increased by

  1. 47

    A number consists of 2 digits.The sum of the digits is 7.If the digits are reversed,the number is increased by 27.The product of the digits of the number is

  1. 48

    In a race of 100m,A beats B by 4m and A beats C by 2m.By how many metres can C beat B in another 100m race assuming C and B run with their respective speeds as in the earlier race?

  1. 49

    In an election,10% of the voters on the voters list did not cast their vote and 60 voters cast their ballot papers blank.There were only two candidates.The winner was supported by 47% of total votes in the voters' list and he got 308 votes more than his rival.The number of voters on the voter list is

  1. 50

    Consider all positive 2 digit numbers each of which when divided by 7 leaves a remainder 3.What is their sum?

  1. 51

    A pipe with square cross-section is supplying water to a cistern which was initially empty.The area of cross-section is 4cm² and nozzle velocity of water is 40m/s.The dimensions of the cistern are 10m *8m*6m.Then the cistern will be full in

  1. 52

    A hollow cylindrical drum has internal diameter of 30cm and a height of 1m.What is the maximum number of cylindrical boxes of diameter 10cm and height 10cm each that can be packed in the drum?

  1. 53

    The speeds of three buses are in the ratio 2:3:4.The time taken for these three buses to travel same distance will be in the ratio

  1. 54

    A square and equilateral triangle have equal perimeter.If the diagonal of the square is 12√2 cm,then the area of the triangle is

  1. 55

    A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute.If the radius of the wheel is 30cm,the speed of the cycle is

  1. 56

    There are 437 fruit plants in an orchard planted in rows.The distance between any two adjacent rows is 2m and the distance between any two adjacent plants is 2m.Each row has the same number of plants.There is 1m clearance on all sides of the orchard.What is the cost of fencing the area at the rate of Rs100 per metre?

  1. 57

    ABCD is a parallelogram with AB and AD as adjacent sides.If <A=60 and AB=2AD,then diagonal BD will be equal to

  1. 58

    The point O is equidistant from three sides of a triangle ABC.Consider the following statements

    1.<OAC+<OCB+<OBA=90

    2.<BOC=2<BAC

    3.The perpendiculars drawn from any point on OA to AB and AC are always equal

    Which of the above statements are correct?

  1. 59

    Consider the following statements

    1.If the height of a cylinder is doubled,the area of the curved surface area is doubled

    2.If the radius of a hemispherical radius is doubled,its total surface area is four-fold

    Which of the above statements is correct?

  1. 60

    A large water tank has the shape of a cube.If 128m³ of water is pumped out,the water level goes down by 2m.Then the maximum capacity of the tank is

  1. 61

    The circumference of a circle is 100cm.The side of a square inscribed inside the circle is

  1. 62

    From the solid gold in the form of a cube of side length 1cm,spherical gold balls each having surface area (π)^(1/3) cm² are to be made.Assuming that there is no loss to the material in the process of making the balls,the maximum number of balls made will be

  1. 63

    Water is filled in a container in such a manner that its volume doubles every 5 minutes.If it takes 30 minutes for the container to be full,in how much time will it be one-fourth full?

  1. 64

    30 metallic cylinders of the same size are melted and cast in the form of cones having the same radius and height as those of the cylinders.

    Consider the following statements

    1.A maximum of 90 cones can be obtained

    2.The curved surface of the cylinder can be flattened in the shape of a rectangle but the curved surface of the cone when flattened has the shape of a triangle

    Which of the above statements are correct?

  1. 65

    An equilateral triangle BOC is drawn inside a square ABCD.If angle AOD=2θ,what is tanθ equal to? 

  1. 66

    The diameter of wheel that makes 452 revolutions to move 2km and 26 decametre is equal to

  1. 67

    If X is any point within a square ABCD and on AX a square AXYZ is described,which of the following is correct?

    1.BX=DZ or BZ=DX

    2.<ABX=<ADZ or <ADX=<ABZ

    Select the correct answer using codes below

  1. 68

    The two adjacent sides of a cyclic quadrilateral are 2cm and 5cm and the angle between them is 60.If the third side is 3cm,then the fourth side of length

  1. 69

    Let A denote set of quadrilaterals having two diagonals equal and bisecting other.Let A denote set of quadrilaterals having two diagonals equal and bisecting other at 90.Then A∩B denotes

  1. 70

    A square is inscribed in a right triangle with legs x and y and has a common right angle with a triangle.The perimeter of a square is give by 

  1. 71

    From a rectangular sheet of sides 18cm and 14cm,a semicircular portion with smaller side as diameter is taken out.Then the area of the remaining sheet will be

  1. 72

    ABCD is a square.If the sides AB and CD are increased by 30%,sides BC and AD are increased by 20%,then the area of the resulting rectangle exceeds area of the square by

  1. 73

    A water tank opened at the top and hemispherical at the bottom and cylindrical above it.The radius is 12m and the capacity is 3312Π m³.The ratio of surface area of spherical and cylindrical portions is

  1. 74

    The areas of three mutually perpendicular faces of a cuboid are x,y,z.If V is the volume ,then xyz is equal to

  1. 75

    Let V be the volume of an inverted cone with vertex at origin and axis of the cone is along the positive y-axis.The cone is filled with water up to half of its height.Then the volume of water is

  1. 76

    Three rectangles R1,R2 and R3 have the same area.Their lengths x1,x2 and x3 respectively are such that x1<x2<x3.If V1,V2,V3 are the volumes of the cylinders formed from rectangles R1,R2,R3 respectively by joinng parallel sides along the breadth,then which one of the following is correct?

  1. 77

    If the surface area of a cube is 13254cm²,length of the diagonal is

  1. 78

    The area of a trapezium is 336cm².If its parallel sides are in the ratio 5:7 and the perpendicular distance between them is 14cm,then the smaller of the parallel sides are

  1. 79

    How many spherical bullets each of 4cm in diameter can be made out of a cube of lead whose edge is 44cm?

  1. 80

    A river 2.5m deep and 45 m wide is flowing at the speed of  3.6km/hr.The amount of water that runs into the sea per minute is

  1. 81

    AB is a line segment of length 2a,with M as midpoint.Semicircles are drawn on one side with AM,MB and AB as diameter as shown in the above figure.A circle with centre O and radius r is drawn such that this circle touches all the three semi-circles.The value of r is

  1. 82

    From an external point P,tangents PA and PB are drawn to the circles as shown in the above figure.CD is the tangent to the circle at point E.If AP=16cm,then the perimeter of the triangle PCD is equal to

  1. 83

    In the above figure,ABCD is a parallelogram.P is a point on BC such that PB:PC=1:2.DP and AB when both produced meet at Q.If area of triangle BPQ is 20 square unit,the area of triangle DCP is

  1. 84

    Chord CD intersects the diameter of the circle at right angle to the point P in the ratio 1:2.If  diameter of the circle is d,then CD is equal to 

  1. 85

    A circle of radius r is inscribed in a regular polygon with n sides.If the perimeter of the polygon is p,area of the polygon is

  1. 86

    The LCM of 2 numbers is 12 times their HCF.The sum of HCF and LCM is 403.If one of the numbers is 93,then the other number is

  1. 87

    The value of (0.6363...+0.3737...) is

  1. 88

    A sum of Rs 10000 is deposited for 1 year at the rate of interest 10% compounded half-yearly.What will be the interest at the end of 1 year?

  1. 89

    In a mixture of milk and water of volume 30l,the ratio of milk and water is 7:3.The quantity of water to be added to the mixture to make the ratio of milk and water 1:2 is

  1. 90

    The difference of maximum values of the expressions (6+5x-x²) and (y-6-y²) for any values of x and y is

  1. 91

    A clock is startd at noon.By 10 minutes past 5,through what angle the hour hand moves?

  1. 92

    The minimum value of cos²x+cos²y-cos²z is

  1. 93

    The value of 32cot²(π/4)-8sec²(π/3)+8cos³(π/6) is equal to 

  1. 94

    If x=91/216,then the value of 3-(1/(1-x)^1/3) is

  1. 95

    How many right angles triangles can be formed by joining the vertices of a cuboid?

  1. 96

    The average weight of students in a class is 43kg.Four new students are admitted to the class whose weights are 42kg,36.5kg,39kg and 42.5kg.Now the average weight of the students of the class is 42.5 kg.The number of students in the beginning was

  1. 97

    Four years ago,the average age of A and B was 18 years.Now the average age of A,B and C is 24 years.After 8 years,the age of C will be

  1. 98

    If a variable takes discrete values a+4,a-3.5,a-2.5.a-3,a-2,a+0.5,a+5,a-0.5 where a>0,Then the median of the data is

  1. 99

    If each of the n numbers xi=i(i=1,2,3,...n)  is replaced by (i+1)xi,then the new mean is

  1. 100

    The weighted arithmetic mean of first 10 natural numbers whose weights are equal to corresponding numbers is equal to



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