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This mock test of Mathematics Mock Test - 2 for Defence helps you for every Defence entrance exam.
This contains 100 Multiple Choice Questions for Defence Mathematics Mock Test - 2 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

If 2 boys consume 2x calories every y/2 days. 8 girls consume z/2 calories every y days. How many calories will 12 girls & 12 boys consume in 12 days ?

Solution:

QUESTION: 2

Adjacent sides of the rectangular plot are 20meter and 12meter respectively. A dishonest builder in an attempt to make more profit has encroached 2meter of land on all four sides and then by doing the fencing of the entire plot, he sold it to a customer at Rs 55 sq meter. How much extra money has been made by the builder?

Solution:

QUESTION: 3

In an Election 10% of the voters on the voters’ list did not cast their votes and 60 voters cast their ballot papers blank. there were only two candidates. The winner was supported by 47% of all the votes in the list and he got 308 votes more than his rival the Number of voters on the list was.

Solution:

QUESTION: 4

The ratio of numbers of boys to the number of girls in a school of 432 pupils is 5 : 4. When some new boys & girls are admitted, the no. of boys increases by 12 and the ratio of the boys to girls changes to 7 : 6. Then number of new girls admitted is:

Solution:

let no. of new girls admitted=g

QUESTION: 5

If X^{2.} is a perfect cube, then which of the following statement is always true.

Solution:

Let n = 8, n^{2} = 64 = 4^{3}

so, n is a perfect cube

QUESTION: 6

B was born when A was 4 yrs 7 months old and C was born When B was 3 yrs 4 months old. When C was 5 yrs 2 months old, then their average age was

Solution:

QUESTION: 7

Abhaya sell his office at a loss of 10%, if he had sold it for Rs. 245 more he would have gained 25% profit. What will be his gain or loss present if he sold it Rs. 595?

Solution:

QUESTION: 8

Neha’s weight is 140% of tina’s weight Mina’s weight is 90% of Lina’s weight. Lina’s weight is twice as much as that of Tina. If Neha’s weight is x% of Mina’s weight then x is equal to-

Solution:

QUESTION: 9

Two barges, traveling at 5 & 10 kms per hour, head directly towards each other. They begin at a distance of 20 kms from each other. How far apart are they (in kms) one min before they collide?

Solution:

QUESTION: 10

Arun borrowed a sum of Rs. 4000 at 5% pa SI for Ramu. He returned the amount with interest after 2 yrs. Ramu returns to Arun 3% of the total amount returned. How much did Ramu received overall?

Solution:

QUESTION: 11

Let α & β be the roots of eqn. x^{2} - 6x - 2 = 0. If α_{n} = α^{n} + β^{n} , for n ≥ 1, then value of

Solution:

QUESTION: 12

If a, b, c are distinct +ve real numbers and a^{2} + b^{2} + c^{2} = 1 then ab + bc + ca =?

Solution:

QUESTION: 13

Find value of x, if

Solution:

QUESTION: 14

Solution:

QUESTION: 15

The base of a triangular field is four times its height. If the cost of cultivating the field at Rs. 15.5 per hectare is Rs. 1116, find the base length (in meter) of the triangular field? (1 hectare = 10000 m^{2 })

Solution:

QUESTION: 16

Find the perimeter (in cm) of a regular quadrilateral with a diagonal of length 3√2 cm?

Solution:

QUESTION: 17

Find the cost of Flooring of the heart shaped pool mentioned in the figure if the rate of flooring is Rs 150 per sq meter and depth of the pool is 2 meters?

Solution:

QUESTION: 18

Find the area of the shaded region where PQRSTU is a regular hexagon of side 12 cm, & W is its centroid.

Solution:

QUESTION: 19

Solution:

QUESTION: 20

Solution:

QUESTION: 21

Solution:

QUESTION: 22

Find ∠PQR of the given isosceles ΔAPQ, when PQ = PA & QR = RA?

Solution:

QUESTION: 23

The sum of real roots of equation x^{2} + |x| - 6 = 0 is

Solution:

QUESTION: 24

If 0° < θ < 90° and 2 tan θ = 3 cosec θ, then θ is —

Solution:

QUESTION: 25

If (tan θ + cot θ) = 1, sin θ + cos θ = b with 0° < θ < 90° then relation between a and b is —

Solution:

QUESTION: 26

Given an equilateral ∆ABC inscribing two circles as shown in the figure below. If DE tangent to both the circles. Then find the ratio of perimeters of the two circles.

Solution:

QUESTION: 27

If = then the value of is

Solution:

QUESTION: 28

A Toy consists of a base that is the section of a sphere and a conical top. The volume of the conical top is 30 π sq. units and its height is 10 units. The total height of the toy is 19 unit. Then the volume of the sphere (in cubic units) is.

Solution:

QUESTION: 29

Amit plans to buy a scooter for his sister for which he saves Rs. 15625 at the start of every year for 3 year. If the rate of CI is 4% pa. then amount at which he plans to buy the scooter is (in Rs.)

Solution:

QUESTION: 30

What is the value of a, if (x -a) is a factor of (x^{3} - a^{2}x + x + 1)?

Solution:

QUESTION: 31

Given ∠D = ∠F = 110° & BD = DC = 1.5 & EF = FG = 1.5 & BC || EG. Then find ∠Y.

Solution:

QUESTION: 32

Three successive discount of 10% , 15% and 20% is equivalent to a single discount

Solution:

QUESTION: 33

Product of two co-prime numbers is 221. Then their LCM is-

Solution:

HCF of two-prime numbers = 1

∴ Product of numbers = their LCM = 221

QUESTION: 34

The Ratio of the No. of boys to that of girls in a school is 5 : 3. If 70% of boys and 80% of the girls are scholarship holders then the percentage of students who do not get scholarship is

Solution:

QUESTION: 35

Two trains starting at the same time from two station 80 km apart and going in opposite direction they meet each other after 20 min. If first train starts 16 minutes late from second train, then they meet after 10 min. Then find the speed of first train?

Solution:

QUESTION: 36

A dishonest dealer defrauds to the extent of 10% in buying and 20% in selling and claims that he earns only 10% profit what will be the gain percent on his outlay.

Solution:

QUESTION: 37

If a^{2} sec^{2} - b^{2} tan^{2} x = c^{2} then the value of (sec^{2} x + tan^{2} x) is equal to (assume b^{2} ≠ a^{2} )

Solution:

QUESTION: 38

A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 5 days and C alone in 25 days then B alone could do the work in.

Solution:

QUESTION: 39

What would be the CI of Rs. 25,000 for 1 ½ years at the rate of 20% per annum compounded half yearly (in Rs.)

Solution:

QUESTION: 40

If AE = CE & FE = ED & FD || AC then AC + x = ?

Solution:

QUESTION: 41

The average height of the girls of a class is 150 cm and the average height of the boys of the class is 5 cm more than the average of the class. If number of girls is 25% less than the number of boys what is the average height of the boys.

Solution:

QUESTION: 42

The daily work of 4 men is equal to that of 6 women or that of 8 youngsters. By employing 14 men, 15 women and 10 youngsters a certain work can be finished in 30 days. If it required to finish it in 10 days and as an additional labour, only men are available, how many of them will be required ?

Solution:

QUESTION: 43

How many zeros will be there at the end of 36!^{36!}?

Solution:

QUESTION: 44

Find the area (in cm^{2}) of the shaded region. It is given that OA = 14cm & OBA is a quarter circle with centre at O & two semi-circles are drawn with dia OB & OA.

Solution:

QUESTION: 45

A man purchases milk for three consecutive years. In the first year, he purchases milk at the rate of Rs 8.5 per liter in second year at the rate of Rs 9 per liter and in the third year at Rs 9.50 per liters. If he purchases milk worth 5814 each year, the average price(in Rs.) of milk per liter for three years is:

Solution:

QUESTION: 46

Volume ( in m^{3}) of a pool which is 20 m long, 5 m breadth & have varying depth of 1 m at one end and 3 m at another end ?

Solution:

QUESTION: 47

Ifx= -5 and y = -2, then the value of x^{3} - 3x^{2} + 3x + 3y + y^{3} + 3y^{2}

Solution:

Required value = (-5)^{3} - 3(-5)^{3} + 3(-5) + 3(-2) + (-2)^{3} + 3(-2)^{2}

= -125 - 75 - 15 - 6 - 8 + 12 = -217

QUESTION: 48

If , then the value of (m^{6} + n^{6}) is

Solution:

QUESTION: 49

If a, b and c are real numbers and a^{2} +b^{2} + c^{2} = 2 (a + b - c)^{-3} then the value of (a+ b - c) is

Solution:

Atq,

a^{2} - 2a + 1 + b^{2} - 2a + 1 + c^{2} + 2c + 1 = 0

(a -1)^{2} + (b - 1)^{2} + (c + 1)^{2} = 0 a=1,b=1,c=-1

Then, (a + b - c) = 1 + 1 - (-1) = 3

QUESTION: 50

If x= , then x^{3} + 3bx is equal to

Solution:

QUESTION: 51

If shaded area is half the area of ∆ABC which is right- angled at B. Find AD = ?

Solution:

QUESTION: 52

In ∆ABC, AB = BC &∠ACB = 50°. D is a point on AC such that AD = BD. E is a point on BD such that BE = CD. Find ∠EAD

Solution:

QUESTION: 53

Six equal circles of radius ‘r cm’ are drawn as shown in figure. Find the perimeter (in cm) of triangle.

Solution:

QUESTION: 54

A sphere has been drawn inside the cone of base radius 8 cm and height 6 cm. Find the maximum volume ( in cm^{3}) of sphere inside the given cone.

Solution:

QUESTION: 55

x = y cos^{2π}/3= z cos^{4π}/3' then xy + yz + zx = ?

Solution:

x = -y/2 = -z/2 = k

⇒ xy + yz + zx = -2k^{2} + 4k^{2} - 20 = 0

QUESTION: 56

tan = b/a' then =?

Solution:

QUESTION: 57

If (a + b - 7)^{2} + a^{2} + b^{2} = + 1 + 2b = 2ab + 2a, then the value of a is

Solution:

QUESTION: 58

In given figure. ABCD is a square and E & F are the mid points of AD and BC respectively. Find the ratio of shaded and un-shaded area.

Solution:

QUESTION: 59

If a and b are two odd positive integers, by which of the following integer is (a^{4} - b^{4}) always divisible by

Solution:

a^{4} - b^{4} = (a^{2} + b^{2}) (a + b)(a — b)

Let odd positive integers = 3, 1

(3^{2}+1^{2}) (3 + 1) (3 - 1) = 80 (divisible by 16)

QUESTION: 60

If (a - 2) + = -1 then the value of ( a+ 2)^{2} + is

Solution:

QUESTION: 61

Given that AB || DG || JI, AC=JH=10 cm and CE=EH=5 cm, then find the sum of perimeter of ∆ABC, ∆CDE, ∆EGH & ∆HIJ? (In cm)

Solution:

QUESTION: 62

Two men start walking from A & B, at a distance of 31.5 km towards each other at same time. The Speed of first person is 2 km/h, while the other one starts at 1 km/h and increases his speed every hour by 1/2 km/h. Then after what duration will they meet?

Solution:

QUESTION: 63

The area of an isosceles trapezium is 90 cm^{2 }and the height is 5/9 th of the sum of its parallel sides. If the ratio of the length of the parallel sides is 4 : 5, then the length of a diagonal (in cm) is

Solution:

QUESTION: 64

150 workers were engaged to finish a piece of work in a certain number of days. Four workers dropped on the second day, four more workers dropped on third day and so on. It takes 8 more days to finish the work now, find the number of days in which the work was completed?

Solution:

QUESTION: 65

Solution:

QUESTION: 66

In ∆ ABC with centroid G, if AG = BC & BG = 9 cm & GC = 12 cm. What is the sum of areas of the circle passing through points B, G & C & ∆BGC? (cm^{2})

Solution:

QUESTION: 67

If average of two numbers x and 1/x (were x ≠ 0) is M, what will be the average of

Solution:

QUESTION: 68

Average of 5 consecutive integers is N. What will be the new average when next two integers are also included?

Solution:

QUESTION: 69

If x^{x√x } = (x√x)^{x} then find the value of x

Solution:

QUESTION: 70

In triangle ABC, AD is the median and in triangle ADB, BE is the median. If area of BDE = 20cm^{2} . Find area of ∆ABC.

Solution:

QUESTION: 71

If the curved surface area of a cylinder is 1320 cm^{2} and its base radius is 21 cm, then what is its total surface area?

Solution:

QUESTION: 72

When n is divided by 7, remainder obtained is 3 find the remainder when n^{5} + n^{4} + n^{2} + n^{3} + n + 1 is divided by 7

Solution:

QUESTION: 73

ABC is a triangle. D and E are the mid points of AB and BC and P is any point on AC, if M and N are the mid points of AP and PC, then find DM : EN.

Solution:

QUESTION: 74

If p = sin^{10} x, then which one of the following correct for any value x?

Solution:

QUESTION: 75

A theft occurred in the market and after stealing goods thief ran away. It took 20 minutes for police to arrive at the place where the incident happened and they immediately started chasing him. The thief and policeman run at the rate of 10 kmph and 11 kmph respectively. After certain time police captures the thief. Find out the distance between the thief and police before 12 minutes of the thief’s capture? (Assume that police and thief have followed the same path)

Solution:

QUESTION: 76

Find the remainder when 2222^{5555} + 5555^{2222} is divided by 7

Solution:

Let divide individually

Finally no remainder

QUESTION: 77

In this given figure D, E and F are the mid points of the sides AB, BC and CA respectively and x, y and z are the midpoints of DE, EF and FD respectively. It is given that the area of triangle ABC is 48√3 cm^{2 }and triangle XYZ also inscribes a circle. Find the diameter (in cm) of in-circle of triangle XYZ, if ∆ABC is an equilateral triangle.

Solution:

QUESTION: 78

ABC is a right angle triangle ∠B = 90° and BD is the median. O is the centroid of triangle. Find the length of OB if AB = 9 cm and AC = 41 cm.

Solution:

QUESTION: 79

If three numbers in the ratio 3 : 2 : 5 be such that the sum of the squares is equal to 1862, then which number is the middle one.

Solution:

QUESTION: 80

The average age of eleven players of a cricket team decreases by 2 months when two new players are included in the team replacing two players of age 17 years and 20 yrs. The average age of new players is

Solution:

QUESTION: 81

What is the unit digit of 1! + 2! + 3! + …….49! ?

Solution:

QUESTION: 82

Without stoppage a train travels at an average speed of 75 km per hour and with stoppage it covers same destination at an average speed of 60 km/hr. How many minutes per hour does the train stop?

Solution:

QUESTION: 83

A regular square pyramid has side of its base of 24 cm and height 40 cm is melted and re-casted into 4 regular triangular pyramids of equilateral base of side ‘a’ cm and height 12√3 cm. What is the value of ‘a’ (in cm) ?

Solution:

QUESTION: 84

If (1 – p) is a root of quadratic equation x^{2} + px + (1 - p ) = 0, then sum of the sum of its roots & ‘p’ will be?

Solution:

QUESTION: 85

Measure of a regular polygon’s interior angle is 4 times the measure of its external angle. Find the no. of diagonals of the polygon?

Solution:

QUESTION: 86

Find the area of regular octagon inscribed in a circle of radius ‘5R’.

Solution:

QUESTION: 87

Find the square of ratio of side of a equilateral triangle to the side of a regular octagon, both having equal areas?

Solution:

QUESTION: 88

The ratio of curved surface area and volume of a cylinder is 2 : 7. The ratio of total surface area and volume is 3:7. What is the respective ratio of its base radius and height?

Solution:

QUESTION: 89

A man, his wife & his son works in a park. Man works for 2 days, woman for son for 4 days. Ratio of daily wages of man & woman is 7 : 4 & that of man & child is 7 : 3. If total incomes is Rs. 12000. Find the daily income of man (in Rs.).

Solution:

QUESTION: 90

The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.

Solution:

QUESTION: 91

An oil funnel made of tin sheet consist of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, diameter of the cylindrical portion is 8 cm and diameter of the top of the funnel is 18 cm. Find the area of the tin sheet required to make the funnel.

Solution:

QUESTION: 92

Find the reflection of a point (3, 5) in line x = -2

Solution:

QUESTION: 93

If height, surface area and volume of a regular tetrahedron are x, y and z respectively, then the value of xy/z is

Solution:

QUESTION: 94

Consider an isosceles ∆PQR with PQ = PR = 5 & QR = 6. Where I, O, H denote incenter, circumcenter, & orthocenter, respectively then, area ∆ IOH =?

Solution:

∴ we know that for an isosceles ∆, incenter, circumcenter & orthocenter lie on a St. line

∴ Ar ΔIOH = 0

QUESTION: 95

Square ABCD of side 14 units is shown below. Find the area of dotted region, if blackened region has an area of 14.

Solution:

QUESTION: 96

Ram completes 60% of a task in 15 days and then takes the help of Rahim and Rachel. Rahim is 50% as efficient as Ram is and Rachel is 50% as efficient as Rahim is. In how many more days will they complete the work?

Solution:

Ratio of efficiency of Ram, Rahim and Rachel = 4 : 2 : 1 i.e.

7% of the work in a day completed by Ram, Rahim and Rachel.

So, they will take more days to complete the task

QUESTION: 97

A Number is increased by x % ; to get back to the original Number it is to be reduced by-

Solution:

QUESTION: 98

A & B enter into a partnership. A invested whole of the capital amount of Rs 45000 with the condition that the profit are to be equally divided and that B pays interest on half the capital to A at 10% per annum, but receives Rs 120 per month for carrying on the concern. Find their total yearly profit when B’s income is one half of A’s income (in Rs)

Solution:

QUESTION: 99

If difference between corresponding roots of x^{2} + ax + b = 0 & x^{2} + bx + a = 0 is same & a ≠ b, then

Solution:

QUESTION: 100

a, b and c are distinct +ve integers. Find max value of a × b × c, if a + b + c = 31?

Solution:

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