Combined Defence Services Exam - I, 2015 - Elementary Mathematics

  1. 1

    What is the remainder when 4^96 is divided by 6?

  1. 2

    If 37/13=2+ (1/(x+(1/(y+1/z)))) where x,y and z are natural numbers what is the value of z

  1. 3

    For what value of k is (x-5) is  a factor of x³-3x²+kx-10?

  1. 4

    What is 5+√10/(5√5-2√20-√32+√50)

  1. 5

    The digits in the units place of the product 81*82*83*...*99 is

  1. 6

    The square root of (0.75)³/(1-0.75)+[0.75 + (0.75)² +1] is

  1. 7

    What is the reaminder obtained when 1421*1423*1425 is divided by 12

  1. 8

    Consider the following equations:

    1.The equation 1990x-173y=11 has no solution in integers for x and y

    2.The equation 3x-12y=7 has no solution in integers for x and y

    Which of the above statements are correct?

  1. 9

    A student was asked to multiply a number by 25.He instead multiplied the number by 52 and got the answer 324 more than correct answer.The number to be multiplied was

  1. 10

    What is the number of possible pairs of (P,Q) if the number 357P25Q is divisible by both 3 and 5?

  1. 11

    The difference between the squares of two consecutive odd integers is always divisible by

  1. 12

    The expression x³q²- x³pt+4x²pt-4x²q²+3xq²-3xpt is divisible by

  1. 13

    The difference between Compound itnerest and simple interest  at the same rate of interest R percent p.a on an amount of Rs 15000 for 2 years is Rs 96.What is ths value of R?

  1. 14

    What is the maximum value of m if the number N=35*45*55*60*124*75 is divisible by 5^m?

  1. 15

    A milkman claims to sell milk at cost price only,but he 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. 16

    There is 60% increase in an amount in 6 years at SI.What will be the CI on Rs 12000 after 3 years at the same rate of interest?

  1. 17

    16 litres of mixture contains milk and water in the ratio 5:3.If 4 litres of milk is added to the mixture,ratio of milk to water in the new mixture will be

  1. 18

    A person could save 10% of his income.But 2 years later,when his income increased by 20%,he could save the same amount only as before.By how much percentage has  his expenditure increased?

  1. 19

    In how much time the SI on  a principal amount be 0.125 times principal amount  at 10% p.a?

  1. 20

    A man rows 32km downstream and 14km upstream and he takes 6 hours to cover each distance.What is the speed of current?

  1. 21

    A car travels the first one-third of a distance with a speed of 10km/hr,the next one-third distancewith a speed of 20km/hr and the last one-third distance with a  speed of 60km/hr.The average speed of the car for the whole journey is

  1. 22

    Two persons A and B start walking simultanoeusly from two places c km apart and walk in the same direction.If A travels at the rate of p km/hr and B travels at the rate of q km/hr ,then A has travelled before he overtakes B at a distance of

  1. 23

    For which value of k does the pair of equations x²-y²=0 and (x-k)²+y²=1 yield a unique positive solution of x?√

  1. 24

    The efficiency of P is twice that of Q,whereas efficiency of P and Q together is three times that of R.If P,Q and R work together on a job,in what ratio should they share their earnings?

  1. 25

    In a flight of 600km ,an aircraft was slowed down due to bad weather.Its average speed for the trip was reduced by 200km/hr and the time of flight increased by 30 minutes.The duration of the flight is

  1. 26

    With uniform speed,a car covers  a distance in 8 hours.Had the speed been increased by 4km/hr,the same distancec could have been covered in 7 hours 30 minutes.What is the distance covered?

  1. 27

    A runs 5/3 times as fast as B.If A gives B a start of 80m,how far the winning post from the starting point be so that A and B might reach it at the same time?

  1. 28

    A thief is noticed by a policeman from a distance of 200m.The thief starts running and the policeman chases him.The thief and the policeman run at the speed of 10km/hr and 11km/hr respectively.What is the distance between them after 6 minutes?

  1. 29

    When a ball bounces,it rises to 2/3rd of the height from which it fell.If the ball is dropped from a height of 36m,how high will it rise at the third bounce?

  1. 30

    A light was seen regularly at an interval of 13 seconds.It was seen for the first time at 1hour 54 minutes 50 seconds and the last time at 3 hours 17 minutes 49 seconds.How many times was the light seen?

  1. 31

    An automobile financer claims to be leding money at S.I but he includes the interest every 6 months for calculating the principal.If he charging at the rate of 10%,effective rate of interest becomes

  1. 32

    What are the possible solutions of the equation x^√x=√[(x^x)]^n,where x and n are positive integers?²

  1. 33

    Let A and B be finite non-empty sets with the number of elements in  A=m and number of elements in B=n.Let m>n.If for some integer k>=1,the number of non-empty subsets of A=2^k+number of non-empty subsets of B,then which one of the following is correct?

  1. 34

    If n is a natural number and n=p1^x1*p2^x2*p3^x3,where p1,p2 and p3 are distinct prime factors,then number of prime factors of n is

  1. 35

    Consider the following statements for the sequence of numbers given below

    11,111,1111,11111,...

    1.Each number can be expressed in the form (4m+3),where m is a natural number

    2.Some numbers are squares

    Which of the above statements are correct?

  1. 36

    The HCF and LCM of two polynomials are (x+y) and (3x^5+5x^4y+2x³y²-3x²y³-5xy^4-2y^5) respectively.If one of the polynomials is x²-y²,then the other polynomial is

  1. 37

    Let p be a prime number other tha 2 or 5.One would like to express the vulgar fraction 1/p in the form of a recurring decimal.Then the decimal will be

  1. 38

    Consider the following statements:

    1.There exists only one prime number p such that (17p+1) is a square.

    2.If x is a product of 10 consecutive prime numbers staring from 2,then (x+1) is also a prime number

    Which of the above statements are correct?

  1. 39

    The sign of quadratic polynomial ax²+bx+c=0 is always positive if

  1. 40

    If A,G and H are the arithmetic,geometric and harmonic means between a and b respectively,then which one of the following relations is correct?

  1. 41

    The geometric mean of 3 positive numbers a,b and c is 3 and the geometric mean of 3  other positive numbers d,e,f is 4.Also,atleast 3 elements in the set {a,b,c,d,e,f} are distinct.Which one of the following inequalities gives the best information about M,the arithmetic mean among 6 numbers?

  1. 42

    There are 5 parties A,B C,D and E in an election.Out of total 100000 votes cast,36000 were cast to party A,24000 to party B,18000 to party C,7000 to party D and rest to party E.What angle will be allocated to party E in a pie chart?

  1. 43

    Out of 532 savings account held in a post office,218 accounts have deposits over Rs 10000 each.Further in 302 accounts,the first or sole depositors are men,of which deposits exceed Rs 10000 in 102 accounts.In how many accounts the first or sole depositors are women and the deposits are upto Rs 10000 only?

  1. 44

    If x+y+z=0 and x³+y³+z³+3xyz is equal to

  1. 45

    If three metalllic spheres of radii 6cm,8cm and 10cm are melted to form a single sphere,then the diameter of the new sphere will be

  1. 46

    If each interior angle of a regular polygon is 135°,then the number of diagonals of polygon is equal to

  1. 47

    The sides of a triangular field are 41m,40m and 9m.The number of rose beds that can be prepared in the field if each rose bed on an average,needs 900sq.m space is

  1. 48

    The ratio of outer and inner perimeters of a circular path is 23:22.If the path is 5m wide,diameter of the inner circle is

  1. 49

    A cylindrical vassel of radius 4m contains water.A solid sphere of radius 3m is lowered into water until it is completely immersed.Water level in the vessel will rise by

  1. 50

    If the height of a right circular cone is increased by 200% and radius of the base is decreased by 50%,then the volume of the cone

  1. 51

    The angles of a triangle are in the ratio 4:1:1.Then the ratio of largest side to the perimeter is

  1. 52

    Let a,b ,c be the sides of a right triangle,where c is the hypotenuse.The radius of the circle which touches the sides of the triangle is

  1. 53

    The area of the largest triangle that can be inscribed in a semi-circle of radius r is²

  1. 54

    AD is a diameter of a circle and AB is a chord.If AD=34cm,AB=30cm,distance of AB from the center of the circle is

  1. 55

    If a star figure is formed by elongating the sides of a regular pentagon,then the measure of each angle at the angular points of the star figure is

  1. 56

    Four equal sized maximum circular plates are cut off from a square paper sheet of area 784sq.cmThe circumference of each plate is

  1. 57

    If tan(A+B)=√3 and tan A=1,then tan(A-B) is equal to

  1. 58

    If the radius of a aphere is increased by 10%,then its volume is increased by

  1. 59

    ABCD is a parallelogram.where AB:AD=2:1.One of the angles of a parallelogram is 60.The two diagonals are in the ratio 

  1. 60

    Consider the following statements

    1.Let D be a point on the side BC of a triangle ABC.If area of a triangle ABD=area of a triangle ACD,then for all points  O on AD,area of triangle ABO=area of triangle ACO

    2.If G is a point of concurrence  of medians of a triangle ABC,then the area of a triangle ABG=area of a triangle BCG=area of a triangle ACG

    Which of the above statement are correct?

  1. 61

    If cos A=tan B,cos B=tan C,cos C=tan A,then sin A is equal to 

  1. 62

    If  (3-tan²A)/(1-3tan²A)=K whre K is a real number,then cosec A(3sin A-4sin³A) is equal to

  1. 63

    The angles of elevation of the top of a tower from two points P and Q at distances m² and n² respectively,from the base and in the same straight line with it are complementary.The height of the tower is

  1. 64

    The angle of elevation of a cloud from a point 200m above the lake is 30° and angle of depression of its reflection in the lake is 60°.

    The height of the cloud is

  1. 65

    If tan A+cot A=4 then (tan²)²A+(cot ²)²A is equal to

  1. 66

    If p=√(1-sin x)/(1+sin x) ,q=(1-sinx)/cos x,r=cos x/(1+sin x),then which of the following is correct?

    1.p=q=r

    2.p²=qr

    Select the correct answer

  1. 67

    Consider the following

    1.cos A/(1-tan A) + sin A/(1-cot A)=sin A +cos A

    2.(1-sin A-cos A)²=2(1-sin A)(1+cos A)

    Which of the above identities are correct?

  1. 68

    ABC is a triangle right angled at B and AB:BC=3:4.What is sin A+ sin B+sin C equal to

  1. 69

    The value of cosec²67+sec²57-cot²33-tan²23 is 

  1. 70

    Consider the following statements

    1.There exists atleat one value of x between 0 and ∏/2 which satisfies the equation sin^4x-2sin²x-1=0

    2.sin 1.5 > cos 1.5

    Which of the above statements are correct?

     

  1. 71

    From the top of a tower,angles of depression of two objects P and Q seperated at a distance of 100(3-√3) are 45° and 60° respectively.The height of the tower is

  1. 72

    If sin x +cos x=c then (sin ^6)x+(cos^6)x=²

  1. 73

    Consider the following statements

    1.There exists no value of x such that 1/(1-sinx)=4+2√3,0<x<π/2

    2. sin x=3^sin²x does not hold for any real x

  1. 74

    A triangle ABC is inscribed in a circle.If the sum of squares of sides of a triangle is equal to twice the square of diameter then sin²A+sin²B+sin²C is equal to

  1. 75

    The area of a rhombus with side 13cm and one diagonal 10cm will be

  1. 76

    Two circles,each of radius r,with centres P and Q,are such that each circle passes through the centre of the other circle.Then the area common to the circles is less than one-third of sum of areas of the two circles by 

  1. 77

    A sphere and a cube have the same surface area.The ratio of square of their volumes is π

  1. 78

    The radius of a sphere is equal to radius of the base of a right circular cone,and the volume of sphere is double the volume of cone.The ratio of height of cone to radius of the base is

  1. 79

    Water flows through cylindrical pipe of internal diameter 7cm at the rate of 5m/s.The time,in minutes,the pipe would take to fill an empty rectangular tank 4m*3m*3.1m is

  1. 80

    The total surface area of a right circular cone of height 24cm with a hemisphere of radius 7cm upon its base is π

  1. 81

    The last digit in the expansion of 17^256

  1. 82

    A rectangular block of wood having dimensions 3m*2m*1.75m has to be panted in all its faces.The layer of paint must be 0.1mm thick.Paint comes in cubical boxes having their edges equal to 10cm.The minimum number of boxes of paint to be purchased is

  1. 83

    The sides of a triangle are 25cm,39cm and 56cm.The perpendicular from the opposite vertex on the side of 56cm is

  1. 84

    The diagonals of a trapezium are at right angles,and the slant sides if produced,form an equilateral triangle with the greater of the two parallel sides.If the area of the trapezium is 16 sq.cm,then the distance between parallel sides is

  1. 85

    Three equal circles each of diameter d are drawn on  a plane in such a way that each circle touches the two other circles.A big circle is drawn in such a manner that it touches each of the small circles internally.The area of the big circle is πd²   (√3+2)²

  1. 86

    If the angle between radii of a circle is 130°,then the angle between tangents at the ends of the radii is

  1. 87

    Let OA,OB,OC and OD are rays in the anti-clockwise direction such that <AOB=<COD=100,<BOC=82 and <AOD=78.Consider the following statements.

    1.AOC and BOD are lines

    2.<BOC and <AOD are supplementary

    Which of the above statements are correct?

     

  1. 88

    At 8:30,the hour hand and minute hand of the clock  form an angle of

  1. 89

    The complement angle of 80 is

  1. 90

    Consider the following questions

    1.If the non-parallel sides of a trapezium are equal,then it is cyclic

    2.If the chord of a circle is equal to its radius,then the angle subtended by this chord at a point in major segment is 30

    Which of the above statements are correct?

  1. 91

    Out of the two concentric circles,the diameter of the outer circle is 26cm and the chord MN of length 24 cm is tangent to the inner circle.The radius of the inner circle is

  1. 92

    What is the mean of the distribution?

  1. 93

    What is the median class?

  1. 94

    What is the median of the distribution?

  1. 95

    From a circular piece of cardboard of radius 3 cm,two sectors of 40° each have been cut off.The area of the remaining portion is

  1. 96

    The diagonals of three faces of a cuboid are 13,√281 and 20 linear units.Then the total surface area of the cuboid is

  1. 97

    A rectangular paper of 44cm long and 6cm wide is rolled to from a cylinder of height equal to width of the paper.The radius of base of the cylinder so rolled is

  1. 98

    If a-b=4 and a²+b²=40,where a and b are positive integers,then a³+(b³)² is 

  1. 99

    What is the mode of the distribtuion



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