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This mock test of Mathematics Mock Test - 5 for Defence helps you for every Defence entrance exam.
This contains 100 Multiple Choice Questions for Defence Mathematics Mock Test - 5 (mcq) to study with solutions a complete question bank.
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QUESTION: 1

Which of the following will divide 11^{1296} -1?

Solution:

QUESTION: 2

If 5 men or 8 women or 12 boys can do a work in 24 days working 8 hrs a days, how many men must be associated with 16 women and 12 boys to do another with 6 times as great in 30 days working 6 hours per day ?

Solution:

QUESTION: 3

8 Cats and 6 dogs cost me Rs. 37500. I sell them for Rs. 44625 making a profit of 10 percent on cat and 25 percent on dogs what is the average cost of each cat?

Solution:

QUESTION: 4

Gold is 14 times as heavy as water and copper is 6 times as heavy as water. In what ratio should to these be mixed to get an alloy 11 times as heavy as water.

Solution:

QUESTION: 5

A dog takes 7 jumps when a fox takes 10 jumps & a lion takes 12 jumps when a fox takes 10 jumps. And distance of 20 jumps of dog, 15 jumps of fox & 5 jumps of lion are equal. Find the ratio of their speeds.

Solution:

QUESTION: 6

When P liter oil is poured into a vessel, the vessel remains K% empty. How Many litres do we need to pour in the vessel so that the vessel is full.

Solution:

QUESTION: 7

In a town 60% of the adult population is male, a% of the adult Males and b% adult females are Educated. The total Number of Educated adult Males and uneducated adult females is equal in number to the total Number of Uneducated adult Males and Educated adult females if a and b are both integers. Which of the following could be the set of values (a, b)?

Solution:

Let total adult population of town = T Adult population that is male = 0.6T Adult population that is female = 0.4T a% of adult male population and b% of adult female population is Educated. Given, educated adult male + uneducated adult female = sum of uneducated adult males + Educated adult females.

QUESTION: 8

A man takes 8 hrs to walk to a certain place and ride back. However, he could have Saved 2 hrs, if he had covered both ways by riding. How long would he take to walk both ways?

Solution:

Both ways walking = One way walking & one day riding time + Gain in time

= 8 + 2 = 10

hours Alternatively

W+R = 8 hours

R+R = 6 hours

⇒ R = 3 hours

& W = 5 hours

∴ W + W = 10 hours.

QUESTION: 9

If the difference between CI and SI on a sum of money for 3 years is Rs. 5103, then what is the sum if the rate of interest in both cases is 15% (in Rs.)

Solution:

QUESTION: 10

55^{√x }+ 132^{√x} = 143^{√x }find x

Solution:

QUESTION: 11

a+b+c=0, then is

Solution:

QUESTION: 12

bc + ac + ab = abc, then, =?

Solution:

Let a = b = c = 3

so,

QUESTION: 13

Solution:

QUESTION: 14

- 2 cot 58° tan 32°- 4 tan 13° tan 37° tan 53° tan 77° tan 45° + 2 cosec^{2} 58° =?

Solution:

QUESTION: 15

(cosecA — sinA)^{2} + (secA — cosA)^{2} — (cotA — tanA)^{2} =?

Solution:

let A = 45^{ο}

^{}

QUESTION: 16

If a man and a boy can build one and a half walls in 1.5 days, then how many walls do 7 men build in 9 days if efficiency of a man and a boy are in ratio 2:1?

Solution:

QUESTION: 17

Rs. 6000 becomes Rs. 7,200 in 2 years at a certain rate of SI, If the rate becomes 1.5 times of itself, the amount (in Rs.) of the same principal in 15 yrs will be.

Solution:

QUESTION: 18

sin10°. Sin30°. Sin50°. Sin70° =?

Solution:

QUESTION: 19

Solution:

QUESTION: 20

Cos^{2}A + cos^{2} (A+120) + cos^{2} (A-120) =?

Solution:

QUESTION: 21

CI of 7th year & 5th years respectively are 961 & 576 Rs. Find the rate of interest ? (in %)

Solution:

QUESTION: 22

If x + y + z = 22 & xy + yz + zx = 35, then what is the value of (x - y)^{2} + (y - z)^{2} + (z-x)^{2}?

Solution:

QUESTION: 23

If , then, a^{4} + b^{4} =?

Solution:

QUESTION: 24

If x^{a}. x^{b}. x^{c} = 1, then a^{3} + b^{3} + c^{3} =?

Solution:

QUESTION: 25

Solution:

QUESTION: 26

=?

Solution:

QUESTION: 27

Solution:

QUESTION: 28

There were 42 students in a hostel. If the number of students is increased by 7 the expenditure on food increases by 49 per day while the average expenditure is reduced by Re 1. What was the initial expenditure on food per day?

Solution:

QUESTION: 29

The highest score of a batsman in an innings was 2/9 of the total score and the next highest score of another batsman was 2/9 of the remaining total score. These scores differ by 8 runs. What was the total score in the innings?

Solution:

QUESTION: 30

The value of (13+23+33+…+153)-(1+2+3+…+15) is

Solution:

QUESTION: 31

In an examination, 40% marks are required to pass. A obtains 10% less than the number of marks required to pass. B obtains less than A. While C obtained less than the number of marks obtained by A and B together. What percentage of marks did C get?

Solution:

QUESTION: 32

Mohan spends 40% of his salary on food items, 50% of the remaining on transport, 30% of the remaining, after spending on food and transport, he spends on clothes and saves the balance. If he saves Rs 630 every month, what is his monthly salary?

Solution:

QUESTION: 33

In a class with a certain number of students, if one new student weighing 50 kg is added, then the average weight of the class increased by 1 kg. If one more student weighing 50 kg is added, then the average weight of the class increases by 1.5 kg over the original average. What is the original average weight (in kg) of the class?

Solution:

QUESTION: 34

Find the value of (sin5 + cos85)/ (sin5 – cos85)

Solution:

QUESTION: 35

The curved surface area of a cylindrical pillar is 264 sq m and its volume is 924 m^{3}. The ratio of its diameter to its height is

Solution:

QUESTION: 36

Let BE and CF be the two medians of a ABC and G be their point of intersection, also let EF cuts AG at O. Then AO:OG is

Solution:

In the given fig. BE and CF are median of the. ΔABC and meet at point G

AG meet sides BC at D hence AD is also a median

QUESTION: 37

In a fresh fruit, quantity of water by weight is 68 % and in a dried fruit it is 20%. How many kg of dried fruit can be obtained from 100 kg of fresh fruit.

Solution:

Quantity of dry fruit (without water) in 100 kg fresh fruit = 32% of 100 = 32 kg

So, req. quantity of dry fruit kg

= 40 kg

QUESTION: 38

A tap can fill a tank in 8 mins. & another tap can drain 6KL/min. If both the taps are opened together, the tank is filled in 20 min. Find the capacity of the tank (in KL).

Solution:

QUESTION: 39

ABCD is a square & BEC is an equilateral triangle outside the square. DE and AE are produced. Then find the angle DEA.

Solution:

QUESTION: 40

If the base of a prism is a square and height is 15 cm. If total surface area is 608 cm^{2}.Find its volume.

Solution:

QUESTION: 41

A, B and C enter into a partnership with capital contributions of Rs. 25,000, Rs. 30,000 and Rs. 15,000 respectively. A is working partner and gets 30% of profit for managing the business. The remaining profit is distributed according to their capitals. At the end of a year, A gets Rs. 200 more than B & C together, then total profit is :

Solution:

QUESTION: 42

Two circles having radius 9 cm and 4 cm touch each other externally and another circle of radius “c” cm touch both the circles externally and also their direct common tangent. Find the value of “c” .

Solution:

QUESTION: 43

A can do a piece of work in 35 days and B can do it in 28 days. If A after working for 10 days leaves the work and then B comes in and complete the remaining work. In how many days total work will be done.

Solution:

QUESTION: 44

Find the odd one, If A, B and C are vertex of a ∆.

Solution:

QUESTION: 45

Find the 3rd proportional of 0.8 and 0.2

Solution:

0.8 : 0.2 :: 0.2 : x

x = 0.05

QUESTION: 46

The angle of elevation of the top of a tree at a point B due east of the tree is 60° and at a point A due west of the tree is 30°. If the distance between A and B is 100 m. Then the height of tree(in m) is ?

Solution:

4 units → 100m

√3 units → 25√3m

CD = 25√3

QUESTION: 47

A certain distance was travelled in 3 parts. First 1/3 rd part of the journey was travelled at the rate of 20 km/hr, 1/6 th part at 30 km/hr and rest at 15 km/hr. Find the average speed of the entire journey.

Solution:

QUESTION: 48

Two trains of same length but different speeds pass a pole in 4 sec and 5 sec respectively. In what time will they cross each-other, if they are moving in same direction.

Solution:

QUESTION: 49

A boat takes 50% more time to cover a certain distance upstream than that downstream. Find the speed of boat, if speed of water is 5 kmph.

Solution:

QUESTION: 50

Three sets of english, mathematics and science books containing 336, 240 and 96 books respectively have to be staked in such a way that all the books are stacked subject wise and height of each stack is same. Find the number of stacks.

Solution:

HCF of 336, 240 & 96 is 48.

No. of stacks = 7 + 5 + 2 = 14 stacks

QUESTION: 51

Simplify :

Solution:

QUESTION: 52

The area of the part enclosed by lines 8x+6y=60 and 3x+4y=12 between x-axis and y-axis is

Solution:

QUESTION: 53

[(2α)(4α)(10α)(11α) + (Kα^{4})] is a perfect square for which value of K:

Solution:

QUESTION: 54

If =1, then the value of is.

Solution:

QUESTION: 55

In the given figure ABCD is a || gm in which AB = CD = 5 cm and BD ⊥ DC such that BD = 6.8 cm. Then, the area of ||gm ABCD = ?

Solution:

QUESTION: 56

If APB and CQD are two parallel lines, then the bisectors of ∠APQ, ∠BPQ, ∠CQP and ∠PQD enclose a

Solution:

QUESTION: 57

The total earnings of A, B and C are Rs. 76000 and they save 30%, 25% and 20% of their incomes respectively. If their savings are in the ratio of 4 : 5 : 6, then the total earnings of A and B is more than the earnings of C by

Solution:

QUESTION: 58

Area of a circle inscribed in a square is 308 cm^{2}. The length of the diagonal of the square is (Take π=22/7)

Solution:

QUESTION: 59

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

Solution:

QUESTION: 60

In the given figure, x= ?

Solution:

QUESTION: 61

If x = 1 + , then the vlue of 2x + is

Solution:

QUESTION: 62

In the figure, ABCD is a parallelogram with AD = α units, DC = 2α units and DE : EC = 1 : 2. CEFG is a rectangle with FE = 3 AE. What is the ratio of the areas of the parallelogram and the rectangle?

Solution:

QUESTION: 63

If , then the value of , where n is a postive integer, is

Solution:

QUESTION: 64

The exterior angle of a regular polygon is one third of its interior angle. The number of sides of polygon is :

Solution:

QUESTION: 65

A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is :

Solution:

QUESTION: 66

From a window (h metres high above the ground) of a house in a street, the angle of elevation and depression of the top and the foot of another house on the opposite side to the street are θ and ∅ respectively.Then, the height of the opposite house is

Solution:

QUESTION: 67

If A (6,4), B (5,–2) and C (7, -2) are vertices of a triangle, then the triangle is?

Solution:

QUESTION: 68

is equal to

Solution:

QUESTION: 69

The number of solutions of the two equations 4x-y=2 and 2x-8y+4=0 is

Solution:

QUESTION: 70

If = and a - b + c ≠ 0, then which one of the following relations is true?

Solution:

QUESTION: 71

The measure of each interior angle of a regular polygon with 8 sides is

Solution:

QUESTION: 72

The total number of zeros at the end (counted from the right) in 500×501×……..×1000 is

Solution:

Each pair of 2 and 5 gives a zero at the end of the product.

No. of twos are abundant, We will find no. of fives present in the given product.

Required no. of zeros = 249-124=125

But 500 is also included

So, no. of zeros =125+2=127

QUESTION: 73

The medians CD and BE of a triangle ABC intersect each other at O. The ratio of area of ∆ODE to that of ∆ABC is equal to

Solution:

QUESTION: 74

Average age of 6 sons of a family is 8 years. Average age of sons together with their parents is 22 years. If the father is older than the mother by 8 years, then the age of mother (in years) is :

Solution:

QUESTION: 75

The H.C.F and the product of two numbers are 15 and 6300 respectively. The number of possible pairs of numbers is:

Solution:

QUESTION: 76

A well of 10m inside diameter is dug 14m deep. Earth taken out from it has been spread all around it to a breadth of 5m to form an embankment. Find the height of embankment(in m)?

Solution:

QUESTION: 77

The angle of elevation of a tower from a distance 50 m from its foot is 30°. The height of the tower is

Solution:

In ΔABC

QUESTION: 78

In an equilateral triangle ABC, P and Q are midpoints of sides AB and AC respectively, such that PQ || BC. If PQ = 5 cm, then find the length of BC.

Solution:

In ΔABC

QUESTION: 79

The base of a right pyramid is an equilateral triangle with side 10cm and vertical height 5cm. Find its surface area (in cm^{2}).?

Solution:

QUESTION: 80

The total surface area of a solid hemisphere is 108 π cm2, then the volume of the hemisphere is

Solution:

QUESTION: 81

A and B enter into a partnership investing Rs 48,000 and Rs 60,000 respectively. After 3 months, A withdraws Rs 8,000 while B invests Rs 6,000 more after 6 months of starting of business. Out of the total amount of profit, if A gets Rs 12,000 as his share at the end of the year, then the total profit is :

Solution:

QUESTION: 82

is equal to

Solution:

QUESTION: 83

The sum of the reciprocals of the ages of two brothers Mahesh Babu and Ravi Teja is five times the difference of the reciprocals of their ages. If the ratio of the product of their ages to the sum of their ages is 14.4 : 1, find their ages.

Solution:

QUESTION: 84

The base of a triangular wall is 7 times its height. If the cost of painting the wall at Rs. 350 per 100 sq m is Rs. 1225, then what is the base length?

Solution:

QUESTION: 85

A triangle with three equal sides has its area equal to 3√3 sq cm. Find its perimeter.

Solution:

QUESTION: 86

What are dimensions (length, breadth and height, respectively) of a cuboid with volume 720 cm3, surface area 484 sq cm and the area of the base 72 sq cm ?

Solution:

QUESTION: 87

The volume of a cube is numerically equal to sum of the length of its edges. What is the total surface area of cube in square units ?

Solution:

QUESTION: 88

If x = then value of is

Solution:

QUESTION: 89

For what value of triple of n, is the arithmetic mean of a and b.

Solution:

QUESTION: 90

Solution of equation is

Solution:

QUESTION: 91

Find the area of quadrilateral PQRS (cm^{2}) ?

(AP = 6 cm, PS = 4 cm, SB = 2 cm, BR = 6cm, CR = 4 cm, AQ =8 cm, QC = 4 cm)

Solution:

QUESTION: 92

Two similar circles are inscribed in a right angled triangle with sides 24 cm and 32 cm as shown in figure. Find the area of the shaded region.

Solution:

QUESTION: 93

In the below given figure, PQR is a right angled triangle. QS is the altitude on hypotenuse PR. Circles are inscribed within the triangle PSQ and QSR. A and B are the centres of circle. What is the distance (in cm) between A and B?

Solution:

QUESTION: 94

In the given figure, AB is the chord of a circle with center O. AB is extended to C such that BC = OB. The straight line CO produced to meet the circle at D. If ∠ADC = y^{ο} ∠AOD = X^{ο} & relation between x & y is, x = ky^{ο} then roots of equation A^{3} + KA - KA^{2} - K/3 = 0 are

Solution:

QUESTION: 95

The interior angles of a polygon are in AP. The smallest angle is 120° and the common difference is 5°. Find the number of sides of the polygon.

Solution:

QUESTION: 96

A sphere with centre O is situated at the top of a pole as shown in the figure. An observer on the ground is at a distance of 100 m from the foot of the pole. The angles of elevation from the observer to the points P and Q on the sphere are 30° and 60° respectively. Then the radius (in m) of the sphere is

Solution:

QUESTION: 97

Two circles C_{1} and C_{2} having radius 36 cm and 25 cm touch each other externally. Another circle whose radius is ‘c’ cm touches both the circles and also their common tangent then find the radius of a smaller circle?

Solution:

QUESTION: 98

In the given figure OAB is quadrant. OC = CA, CD is the bisector of angle OCB. DE is parallel to OA. Then find the angle DBE?

Solution:

QUESTION: 99

If the base of a pyramid is a square of side 28 cm each and height of the pyramid is 10.5 cm, then find the total surface area of the pyramid?

Solution:

QUESTION: 100

The angle of elevation of the top of a building from a point A due south of the tower is α and from B due to east of the tower is β. If AB = d, then the height of building is

Solution:

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