Mathematics Mock Test - 4


100 Questions MCQ Test CDS ( Combined Defence Services ) Mock Test Series | Mathematics Mock Test - 4


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This mock test of Mathematics Mock Test - 4 for Defence helps you for every Defence entrance exam. This contains 100 Multiple Choice Questions for Defence Mathematics Mock Test - 4 (mcq) to study with solutions a complete question bank. The solved questions answers in this Mathematics Mock Test - 4 quiz give you a good mix of easy questions and tough questions. Defence students definitely take this Mathematics Mock Test - 4 exercise for a better result in the exam. You can find other Mathematics Mock Test - 4 extra questions, long questions & short questions for Defence on EduRev as well by searching above.
QUESTION: 1

If  then the value of x + y + z is

Solution:

QUESTION: 2

If x + y + z = 6 and xy + yz + zx = 11, then the value of x3 + y3 + Z3 - 3xyz is 

Solution:

QUESTION: 3

 is equal to:

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QUESTION: 4

If cosx =  then the value of tan is x/2. cot y/2 is

Solution:

QUESTION: 5

If α + β+ y = π, then the value of sin2 α + sinβ — siny, is equal to  

Solution:

QUESTION: 6

 is equal to 

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QUESTION: 7

The value of  is 

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QUESTION: 8

The value of  is-

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QUESTION: 9

Sum of the digits of a two digit number is 12. When 18 is deduced from the number, the digits change their positions. Find the number. 

Solution:

QUESTION: 10

In an office 80% of the employees are male. Among them 20% are matriculates and remaining are graduates. Among them females 25% are matriculates and the remaining are graduates. If the total numbers of the female employees of the office is 600, how many graduates are in the Office? 

Solution:

QUESTION: 11

The population of a town is 10,000. It increased by 10% during the first year. During the second year, it decreased by 20% and increased by 30% during the third year. What is the population after 3 years? 

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QUESTION: 12

Copper and zinc are in the ratio 2 : 3 in 200 gms of an alloy. The quantity (in grams) of copper to be added to it to make the ratio 3 : 2 is 

Solution:

QUESTION: 13

The average salary per head of all the workers of an office is Rs. 95. The average salary of 15 officers is Rs. 525 and the average salary of the rest is Rs. 85. Find the total numbers of workers? 

Solution:

QUESTION: 14

By selling oranges at 32 a rupee, a man loses 40%. How many for a rupee should he sell in order to gain 20%? 

Solution:

QUESTION: 15

Two trains P and Q start at the same time in the opposite directions from two points and both the trains after crossing a certain point C arrives at Q and P after   and  hours respectively. At what speed is the second train Q running if the first is running at the speed of 8 km/hrs? 

Solution:

QUESTION: 16

A and B can separately do a work in 20 and 15 days respectively. They worked together for 6 days after which B was replaced by C. If the work is finished in next four days, the number of days in which C alone can do the work will be– 

Solution:

QUESTION: 17

The speeds of three students are in the ratio 2 : 3 : 4. The ratio of the time taken by these students to travel the same distance is 

Solution:

QUESTION: 18

Pipe A can fill a tank in 4 hrs. and pipe B can fill it in 6 hrs. If they are opened on alternative hour, in how many hours the half tank will be filled? 

Solution:


A & B filled tank in 2 hours =3+2=5units Total time required to fill half tank i.e 6 units=  hr
 hours.

QUESTION: 19

The simple interest on an amount in 2 years at the rate of 7% per year is equal to the simple interest on Rs. 1750 in 4 years at the rate of 5% per year. Find the principal. 

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QUESTION: 20

At simple interest Rs. 800 becomes Rs. 920 in 3 years. If rate of interest is increased numerically by 3% then the total amount will become– 

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QUESTION: 21

If A : B : C = 2 : 3 : 5, then the ratio of  is 

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QUESTION: 22

Two roads of 2 metre width cuts each other perpendicularly in a park of dimension 72m×48m in the middle. Each road is parallel to each side of the rectangle. What is the area of the remaining part of the field? 

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QUESTION: 23

The area of circle whose radius is 8cm is trisected by two concentric circles. The ratio of radii of the concentric circles in a scending order is 

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QUESTION: 24

There is a wooden cube of side 2 cm. If a cylinder of maximum volume is cut out from that cube, then what will be the volume of remaining part of the wood? 

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QUESTION: 25

If sin θ + sin2 θ + sin3 θ = 1, then cos6  θ - 4 cos4 θ + 8cos2 θ =?

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QUESTION: 26

If cos2 α - sin2 α = tan2 β, then the value of cos2 β - sin2 β is

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QUESTION: 27

If tan  and , then the value of  is  

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QUESTION: 28

Find radius r (in c.m) of the given circle where CH is tangent to circle & HBA is a secant.
  

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QUESTION: 29

If sec α + tan α = 2, then the value of sin α is — (assume that 00 < α < 90°) 

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QUESTION: 30

If a2 + a + 1 = 0, then the value of a6 is

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QUESTION: 31

In the given fig. AB, CD & EF are three towers. The angle of elevation of the top of the tower CD from the top of the tower AB is 60° and that from EF is 30°. If BD = 2√3 m, CD : EF = 5 : 4 & DF = 4 m .Then, find height of tower AB? 
 

Solution:


QUESTION: 32

Find the value of in if the polynomial x3 - mx2 = - 13x + n has (x + 1) and (x - 3) as factors

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QUESTION: 33

If n = 1 √2, find the value of n3 - 

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QUESTION: 34

A shopkeeper only accepts packages in the form of a right circular cylinder. If sum of the height and the diameter of the base does not exceeds 20 cm. then the height (in cm) of a package of maximum volume that would be accepted will be? 

Solution:

QUESTION: 35

A race course is 600 meters long, If A & B run a race then A wins by 10 meters. If B & C run over the same course then B wins by 5 meters. Also, if C &D run the race, then D wins by 15 meters. If A & D run the race, then who would win and by how much? 

Solution:

QUESTION: 36

A sum of Rs. 7,930 is divided into three parts and given on loan at 5% SI to A, B and C for 2 , 3 and 4 years respectively. If amount obtained from all three are equal after their respective periods of loan, then what amount was lent to B? 

Solution:

QUESTION: 37

Find value of sec2 θ -  is  

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QUESTION: 38

Four coins of the same size (radius 1 cm) are placed on a table such that each of them touches the other two. Then the area(in cm²) enclosed by the coins is? 

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QUESTION: 39

PQR is a ∆ with three squares put on the three sides of the ∆. Then ∠a + ∠b + ∠c =?

Solution:

QUESTION: 40

A man and a woman working together can do a certain work in 22 hrs. If their skills for doing the work are in the ratio 5 : 4. Then how many days will woman takes to finish the work? 

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QUESTION: 41

The area of a rhombus is 3675 square cm and one of its diagonals is one-sixth the other in length. Then length(in cm) of its larger diagonals is 

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QUESTION: 42

If α, β are roots of the equation (x - a) (x -b) = c, c ≠ 0, then the roots of the equation (x – α) (x-β) + c = 0 are 

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QUESTION: 43

If the roots of equation of 3ax2 + 2bx + c = 0 are in the ratio 2 : 3 then 

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QUESTION: 44

2x =  and , then the value of  is

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QUESTION: 45

The average marks obtained by 35 students of a class is 85. If the 5 highest marks are removed, the average reduces by one mark. 1st ranker gets 100 marks and 5th ranker gets 15% less then 1st ranker. Find the average marks of 2nd, 3rd and 4th ranker together are what % more than 5th ranker. 

Solution:

QUESTION: 46

In a factory 70% of the workers are above 30 years and of these 60% are males and the rest are females. If there are 840 Females workers above 30 years, the total number of workers in the factory is- 

Solution:

QUESTION: 47

Find the minimum value of 9 sec2 φ + 4 cosecφ =? 

Solution:

QUESTION: 48

Solution:

QUESTION: 49

Two men A and B are 60 km apart and are walking towards each other with the speed of 10 kmph & 5 kmph and a dog is running at 12 kmph from man A towards Man B & then again towards man A and so on until A meets B. Find the distance travelled by the dog?

Solution:

Total time of travel required for A & B to meet at a point  =  4 hr & dog will travel only for 4 hr (until A & B meet) to cover a distance = 12 × 4 = 48 km 

QUESTION: 50

A skilled, a half skilled and an unskilled labourer work for 6, 8 and 9 days respectively and they together get Rs. 475 for their work. If the ratio of their each day’s work is ½ : ⅓ : ¼, then how much does the skilled labourer get (in rupee) 

Solution:

QUESTION: 51

a2- by- cz = 0, ax- b2 1+ cz = 0 and ax + I - by- c2 = 0 then value of  will be

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QUESTION: 52

If 5x + 4y = 83 and 2x : 3y = 22 : 21 then x -y is equal to 

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QUESTION: 53

If  = 3, then  =? 

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QUESTION: 54

If the average of x and  be 1, then the value of 8x10 + will be.  

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QUESTION: 55

12 men and 16 boys can do a piece of work in 5 days, 13 men and 24 boys can do it in 4 days then how many days will 4 men finish the same work ? 

Solution:

QUESTION: 56

If x : y = 2 : 1, then (5x2 — 13xy + 6y2) is equal to — 

Solution:

QUESTION: 57

In an election a voter can vote for two candidates. Half of the voter gave first vote to A & second vote to B, C & D in ratio 1 : 2 : 3. Half of the remaining voters gave their first vote to B & second vote to C & D in ratio 1 : 2. If rest 480 didn’t vote for anyone, find no of votes A got? 

Solution:

QUESTION: 58

What is the remainder when (123451)6 is divided by 5?

Solution:

QUESTION: 59

Solution:

QUESTION: 60

A shopkeeper allows 15% discount on market price of a Table and thus suffered a loss of 10% on it. If he gives 10% discount and wants to make a profit of 40%, then what would be the ratio of his cost price and new market price? 

Solution:

QUESTION: 61

A regular hexagonal base prism has height 12 cm and side of base is 16 cm. What is the total surface area (in cm²) of the prism? 

Solution:

QUESTION: 62

The ratio of volumes of two cone are x : y and their heights are in the ratio A : B what is the ratio of their diameters 

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QUESTION: 63

If y & are the roots of the eqn., then = ?

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QUESTION: 64

If , then a is 

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QUESTION: 65

An equilateral ∆ inscribed inside a circle which is also inscribed inside an equilateral ∆. Find the ratio of area of larger to smaller triangle.

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QUESTION: 66

If x & y are integers and 2x5Y = 0.00064, what is the value of xy?

Solution:

QUESTION: 67

If , but , then the eqn. having  as its roots is? 

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QUESTION: 68

In the given figure find the sum of ∠’s made at the circumference of the circle. If all the shaded ∆’s are isosceles (with ∠ at circumference being the non-equal angle) & ∠a + ∠b + ∠c + ∠d + ∠e + ∠f = 720°?

Solution:

QUESTION: 69

For the equilateral triangle ABC, D & E are mid points of AO and OB, and DE = 6 units. Find the area (in unit²) of shaded region if AF is the midian and O is incentre.
  

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QUESTION: 70

A well is dug 9 ft deep and the mud which came out is used to build a wall of width 2 ft around the well on the ground. If the height of the wall around the well is 3 ft, then what is the radius (in ft) of the well?

Solution:

QUESTION: 71

A cylinder of radius 7 cm and height 12 cm just fits in another cylinder completely with their axis perpendicular. What is the radius (in cm) of second cylinder? 

Solution:


QUESTION: 72

Ram aims to score an average of 85 percent marks in quarterly and half yearly exams but his average in quarterly is 5 percent less than his target and that in half yearly is 3 percent marks more than his aim. This difference between the total marks scored in both the exams is 48. Total marks aimed by Ram is. 

Solution:

QUESTION: 73

Total Bike production in a state is 294000, out of which 150000 are made by Hero. Out of every 1000 Hero bike, 98 are red in color, but only 5.3% of the total bike production is red, Find the percentage of non-Hero Bike that are red out of total Non-Hero Bikes. 

Solution:

QUESTION: 74

In the given figure, ABC is an equilateral triangle of side a and each circle is of radius ‘r’. Find r in terms of a.
 

Solution:


QUESTION: 75

A and B started a business with Rs. 20000 and Rs. 35000 respectively. They agreed to share the profit in the ratio of their capital. C joins the partnership after 1 year with the condition that A, B and C will share profit equally and pays Rs. 220000 as premium for this, to be shared between A and B. This is to be divided between A and B in the ratio of 

Solution:

QUESTION: 76

Ratio of area of triangle formed by straight lines 2x+3y=4 and 3x-y+5=0 with x-axis and y-axis is 

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QUESTION: 77

The area of an equilateral triangle is   sq cm. Find the length of its side. 

Solution:

QUESTION: 78

The ratio of length of each equal side and the third side of an isosceles triangle is 3 : 4. If the area of the triangle is 18√5 sq units, the third side is 

Solution:

QUESTION: 79

The hands of a clock are 10 cm and 7 cm respectively. The difference between the distance traversed by their extremities in 3 days 5 hours is: 

Solution:

QUESTION: 80

If the ratio between the sum of n terms of two arithmetic progressions is (7n + 1) : (4n + 27), find the ratio of their 11th terms:

Solution:

QUESTION: 81

The sum of the series 0.4 + 0.44 + 0.444 + ….. to n terms is: 

Solution:

QUESTION: 82

In a temple a cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the piller at the rate of Rs. 10 per sq m. 

Solution:

QUESTION: 83

The diameter of a right circular cone is 14 m, while its slant height is 9 m. Find the volume of the cone. 

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QUESTION: 84

The sides of a right angled triangle are equal to three consecutive numbers expressed in centimeters. What can be the area of such a triangle ? 

Solution:

QUESTION: 85

A took 15 s to cross a rectangular field diagonally walking at the rate of 52 m/min and B took the same time to cross the same field along its sides walking at the rate of 68 m/min. Find the area of the field. 

Solution:

QUESTION: 86

On compound interest a certain amount becomes p times in a year, then in how many years it will become q times. 

Solution:

QUESTION: 87

The value of  is 

Solution:

QUESTION: 88

If the work done by (x – 1) men in (x + 1) days is to the work done by (x + 2) men in (x – 1) days is in the ratio of 9 : 10 then x is equal to:

Solution:

QUESTION: 89

The area of a right angled triangle is 24 cm² and one of the sides containing the right angle is 6 cm. The altitude on the hypotenuse is 

Solution:

QUESTION: 90

The pie-graph given below shows the breakup of the cost of construction of a house. If the total cost of construction is `15, 00,000, answers the questions given below:

Out of total cost of construction what amount has been spent on labour and supervision? 

Solution:

Amount spent on lab our and supervision 
= [(90+54)/360]*1500000 = 6, 00,000 

QUESTION: 91

AD is perpendicular to the internal bisector of ∠ABC of ∆ ABC. DE is drawn through D and parallel to BC to meet AC at E. If the length of AC is 10 cm, then the length of AE (in cm) is 

Solution:


QUESTION: 92

In the given cube find the minimum physical distance between A and O where O is mid-point of FG and AB = a

Solution:


QUESTION: 93

Find the area of a regular octagon inscribed in a circle of radius r? 

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QUESTION: 94

A right angle triangle with base and height measuring 15 cm and 20 cm is rotated along its hypotenuse and formed a new structure. Find the volume (in cm³) of the structure 

Solution:


QUESTION: 95

Given area ∆ FHI = 2 unit² & HI = 2 & is perpendicular to line m & BD‖EG‖HI & BC = 4. Also, line l || line m. AC = FC = 2FI & DC = CG then, find ∠BCE?
 

Solution:

QUESTION: 96

A road which is 7 m wide surrounds a circular track whose circumference is 352 m. Find the area of the road. ( Take π=22/7) 

Solution:


QUESTION: 97

The area of an equilateral triangle ABC is 17320.5 cm². With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle. Find the area of the shaded region. [Use π= 3.14 and √3= 1.73205]

Solution:

QUESTION: 98

R and r are the radius of two circles (R > r) If the distance between the centre of two circles be d, then length of direct common tangent of two circles is 

Solution:

QUESTION: 99

In x-y plane, P and Q are two points having co-ordinates (2,0) and (5,4) respectively. Then the numerical value of the area(in unit²) of the circle with radius  is 

Solution:

QUESTION: 100

What is the height of a solid cylinder of radius 5 cm and total surface area is 660 sq. cm? 

Solution:

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