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# Mathematics Mock Test - 3

## 100 Questions MCQ Test CDS ( Combined Defence Services ) Mock Test Series | Mathematics Mock Test - 3

Description
This mock test of Mathematics Mock Test - 3 for Defence helps you for every Defence entrance exam. This contains 100 Multiple Choice Questions for Defence Mathematics Mock Test - 3 (mcq) to study with solutions a complete question bank. The solved questions answers in this Mathematics Mock Test - 3 quiz give you a good mix of easy questions and tough questions. Defence students definitely take this Mathematics Mock Test - 3 exercise for a better result in the exam. You can find other Mathematics Mock Test - 3 extra questions, long questions & short questions for Defence on EduRev as well by searching above.
QUESTION: 1

### A certain number when divided by 899 leaves the remainder 65. when the same number is divided by 31, the remainder is:

Solution:

∵ 899 is divided by 31 and leaves 0.
∴ required remainder = remainder by 65/31 = 3

QUESTION: 2

### The average weight of 8 person is increased by 2.5 kg when one of them whose weight is 56 kg is replaced by a new man. The weight of the new man is:

Solution:

The weight of new man = weight of ex person +2.5*8 = 56 + 20 = 76 kg

QUESTION: 3

### Last year my age was a perfect square number .next year it will be a cubic number. What is my present age?

Solution:

Last year my age was a perfect square number = 25
Next year it will be a cubic number = 27
∴my present age = 26 years

QUESTION: 4

4 men can complete a piece of work in 2 days. 4 women can complete the same piece of work in 4 days whereas 5 children can complete the same piece of work in 4 days. If 2 men, 4 women and 10 children work together, in how many days can the work be completed?

Solution:

2 men can do a piece of work in 4 days 4 women can do same piece of work in 4 days 5 children can do same piece of work in 4 days
So, we can say that 2m = 4w =5c
So , 2men and 4 women and 10 children complete the work
Efficiency of children and women convert in man = (2m + 2m +4m) = 8m
4 men complete the work is = 2 days
8 men complete the work is = 1 days

QUESTION: 5

A 280 meter long train moving with an average speed of 108 km/h crosses a platform in 12 seconds. A man crosses the same platform in 10 seconds. What is the speed of the man?

Solution:

Speed of train = 108km/hr=108*5/18 m/sec = 30m/s
If the length of the platform be x meters,
then
x+280/12=30 x+280=360
x=(360-280)=80m
∴speed of man=80/10 = 8m/s

QUESTION: 6

The compound interest on a certain sum of money for 2 years at 10% per annum is Rs. 420. Find the simple interest at the same rate and for the same time.

Solution:

QUESTION: 7

Manoj marked up an article for Rs 15000. Had he offered a discount of 10% on the marked price, he would have earned a profit of 8%. What is the Cost price?

Solution:

M.P=Rs15000
SP after 10% discount= 15000-10%of15000= 15000-1500=Rs13500
Profit on SP= 8%
CP= 13500⁄108 ×100=Rs 12500

QUESTION: 8

A shopkeeper mixed two verities of rice at Rs. 20/kg and Rs. 30/kg in the ratio 2 : 3 and sell the mixture at 10% profit. Find the price per kg at which he sold the mixture?

Solution:

CP of mixture = (20*2+30*3)⁄2+3 = 26
SP of the mixture = 1.1×26=28.6

QUESTION: 9

Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank?

Solution:

Part filled by A in 1 hour = (1/36); Part filled by B in 1 hour = (1/45);
Part filled by (A + B) In 1 hour =(1/36)+(1/45)=(9/180)=(1/20)
Hence, both the pipes together will fill the tank in 20 hours.

QUESTION: 10

In an examination, 34% of the students failed in mathematics and 42% failed in English. If 20% of the students failed in both the subjects, then find the percentage of students who passed in both the subjects.

Solution:

Failed in mathematics, n(A) = 34 Failed in English, n(B) = 42
n(AUB) = n(A) + n (B) – n (A∩ B )
= 34 + 42- 20 = 56 Failed in either or both subjects are 56
Percentage passed = (100-56)%=44%

QUESTION: 11

If a:b = 2:3 and b:c = 4:5, find a2:b2:bc,

Solution:

a :b = 2:3, b:c = 4:5
a : b: c = 8:12:15
a2:b2:bc = 82:122:15x12
64 :144 :180
16 : 36 : 45

QUESTION: 12

A jar contains a mixture of 2 liquids A and B in the ratio 4:1. When 10litres of the mixture is taken out and 10 litres of liquid B is poured into the jar, the ratio becomes 2:3. How many litres of the liquid A was contained in the jar?

Solution:

∴ Ratio in which first and second mixtures should be added is 1:1.
It implies that the reduced quantity of the first mixture and the second mixture and the quantity of mixture B which is to be added are the same.
∴Total mixture = 10+10 = 20 litres. and liquid A =(20/5)*4 = 16 litres

QUESTION: 13

If x + y + z = 0, then what is  equal to?
[x ≠-y , y≠-z , z≠-x]

Solution:

QUESTION: 14

If x = 99, values of x(x+ 3x + 3) is

Solution:

x(x2+3x+3) = x3+3x2+3x+1-1
= x3+1+3x(x+1) -1
= (x+1)3-1 = (99+1)3 -1
= 1003-1= 1000000 -1 = 999999

QUESTION: 15

The minimum values of 2sin2 θ + 3cos2 θ is :

Solution:

QUESTION: 16

If θ lies in the second quadrant, then  is equal to

Solution:

QUESTION: 17

Two spherical iron shots each of diameter 6 cm are immersed in the water contained in a cylindrical vessel of radius 6 cm. The level of the water in the vessel will be raised by

Solution:

When the two spherical iron shots are immersed in water, it will displace water equal to its volume.
Let the water be raised in the vessel by x cm

QUESTION: 18

If the length of a rectangular plot of land is increased by 5% and the breadth decreased by 10% by how much will its area change?

Solution:

Required change in area

Negative sign show decrease

QUESTION: 19

A quadrilateral ABCD circumscribes a circle and AB = 6cm, CD = 5 cm and AD = 7 cm. The length of the sides BC is

Solution:

AM = AQ
BM = BN
CP = CN
DP = DQ
→ AM + BM + CP + DP =AQ + DQ + BN + CN
AB + CD = AD + BC
6+5=7+BC
BC = 4 cm

QUESTION: 20

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their respective volumes is:

Solution:

QUESTION: 21

In a figure, ∠ABE=30° and ∠CEB=120°. Find ∠BDC=?

Solution:

QUESTION: 22

In a ∆ABC, BC=9 cm, AC=40 cm and AB = 41 cm. If bisector of angle A meets side BC at D then ratio of area of ∆ABD ad ∆ABC is -

Solution:

QUESTION: 23

If , then the value of  is

Solution:

QUESTION: 24

A can complete a work in 12 days, B in 16 days and C in 32 days they start together. A works for 3 days and leaves and B leaves 3 days before the work is finished. In how many days was the work finished?

Solution:

QUESTION: 25

Find the maximum value of 3 sin2 φ + 4 cos2 φ

Solution:

QUESTION: 26

Find the maximum and minimum value of 8 cos⁡A+15 sin⁡A+15

Solution:

QUESTION: 27

Find (a+b); if a =  and b =

Solution:

QUESTION: 28

If x =  and z =  then the value of   is

Solution:

QUESTION: 29

The simple interest on a sum of money is 13/25 of the sum. If number of years is numerically equal to 1/13 of rate percent per quarter. Then number of years for which the sum as invested is

Solution:

QUESTION: 30

A milkman bought 60 liters of milk at 10 Rs. per liter and also bought 40 liters of milk at 20 Rs per liter and mixed it. Then he spent 100 Rupees and made 12 kg cream and 96 liter toned milk. He sold cream at 80 Rs. per kg and toned milk at 10 Rupee per liter find his profit percentage

Solution:

QUESTION: 31

By what fraction selling price (S.P.) must be multiplied to get cost price (C.P.) if the loss is

Solution:

QUESTION: 32

If the arithmetic mean of 3a and 6b is greater than 75 and a is thrice b then the smallest possible integer value of a is

Solution:

QUESTION: 33

Riya, Geeta & Sunita are running on a circular track of radius 49m. Geeta & Sunita run in the opposite direction of Riya. If the speeds of Riya, Geeta & Sunita are 18, 10, 24 m/min respectively. Then find when will they meet together first time & when will they together meet at the starting point?

Solution:

QUESTION: 34

If , then find m - n =?

Solution:

QUESTION: 35

In square ABCD E, F, G, H, I, J, K & L divide the side in three congruent segments. Then area of quadrilateral PQRS will be if AB = 9 cm (in cm²)

Solution:

QUESTION: 36

If a and b are consecutive natural numbers in an increasing order, then which of the following is always true

Solution:

a < b
so,

QUESTION: 37

2 man and 2 boys can do a job in 6 ⅔ days. 3 women and 4 boys can finish the same job in 5 days. Also 4 men and 3 women can finish the same job in 4 days. In how many days can 1 man, 1 woman and 1 boy finish the work at their double efficiency?

Solution:

QUESTION: 38

A circle of radius 4 cm is externally tangent to a circle of radius 9 cm. A line is tangent to both circles and touches them at points A and B. Find the length AB? (in cm)

Solution:

QUESTION: 39

If the average of x and (x≠0) is m, then the average of x3 and  is

Solution:

QUESTION: 40

Moving at 50 kmph, a passenger trains reaches its destination 10 min late. Next day, it increases its speed by 20% and reaches the destination 5 min before the scheduled time. Find the distance between the starting point and destination? (in kms)

Solution:

QUESTION: 41

Compound interest on Rs. 40,000 for 4 years at 10% per annum will be

Solution:

QUESTION: 42

Value of 'a' for which one root of the quadratic equation (a2 - 5a + 3)x2 + (3a - 1)x + 2 = 0 is twice large as the other, is?

Solution:

QUESTION: 43

Value of ‘a’ for which the sum of square of the roots of the equation x² – (a – 2) x – a – 1 = 0 assume the least value?

Solution:

QUESTION: 44

Solution:

QUESTION: 45

If , then =?

Solution:

QUESTION: 46

13 unit radius circles are packed completely inside a square as shown in figure below then find the side of the square?

Solution:

QUESTION: 47

The length of the sides of a ∆ are x, 16 & 31, where x is the shortest side. If the ∆ is not isosceles, what is the minimum possible value of x?

Solution:

QUESTION: 48

The figure shows a right circular cylinder with dia 6 cm & height 9 cm. If point O is the centre of bottom of the cylinder & point ‘A’ lies on circumference of the top circle. Then shortest distance between O & A will be? (in cms)

Solution:

QUESTION: 49

Three solids are in shape of cylinder, hemisphere and cone. The three solids have same base and same height. Volume of the hemisphere is 16√3 π cm^3. What is the ratio of the volumes of cylinder, hemisphere and cone respectively?

Solution:

QUESTION: 50

Solution:

QUESTION: 51

(sin3A + sinA). sinA + (cos3A–cosA) cosA = ?

Solution:

QUESTION: 52

(cos α + cos β)2+ (sin α + sin β)2 = ?

Solution:

QUESTION: 53

A, B & C enter into a partnership by making investment in the ratio 3 : 5 : 7. After a year C invests another Rs 3, 37, 600 while A withdraws Rs 45600. Ratio of investments then change to 24 : 59 : 167. How much did A invest initially? (in Rs)

Solution:

QUESTION: 54

The value of ; when, (θ ≠ φ

Solution:

QUESTION: 55

If x – y = 8, then which of the following must be true?
I. Both x and y are positive
II. if x is positive, y must be negative
III. if x is negative, y must be negative

Solution:

QUESTION: 56

If x + = 1, then the value of

Solution:

QUESTION: 57

The sum of two numbers is 80 and their HCF and LCM are 4 and 364 respectively. The sum of the reciprocals of two numbers

Solution:

QUESTION: 58

A square hole of cross section area 9cm² is drilled through a cube with its length parallel to a side of the cube if an edge of the cube measures 6 cm, what is the total surface area of the body so formed.

Solution:

Required surface area = 6 x 62 + (3 X 6)4- 9 X 2 = 270 cm2

QUESTION: 59

Of the two trains the length of one is 150 m more than the other. When they travel in opposite direction they cross each other in 25 sec. When they travel in same direction then the faster train crosses the slower train in 5 min. and the speed of slower train is 11 km/min then find the speed of the faster train?

Solution:

QUESTION: 60

Six straight, zigzagging lines are drawn inside a rectangle. The drawing starts at the top left vertex and ends at the top right vertex. What is the minimum possible sum of the lengths of these 6 segments?

Solution:

Make six copies of the 1 by 8 rectangle and place them next to each as shown below, so they make a 6 by 8 rectangle. The minimum distance from the top left vertex to the bottom right vertex is a straight line, so minimum sum will be 10.

QUESTION: 61

Measure of regular polygon’s interior angle is 4 times its exterior angle. Then no. of diagonals the polygon can have?

Solution:

QUESTION: 62

A cube is inscribed in a hemisphere of radius R. Such that four of its vertices lie on the base of the hemisphere and the other four touch the hemispherical surface of the half sphere. What is the volume of the cube?

Solution:

QUESTION: 63

If  = 3, then the value of x is

Solution:

QUESTION: 64

First ten multiple of 1, 2………..10 are taken. What is the average of all these 100 numbers?

Solution:

QUESTION: 65

How many zeroes are there at the end of the number obtained from 999!

Solution:

QUESTION: 66

The ratio of total surface area and volume of a sphere is 1 : 7. This sphere is melted to form small spheres of equal size. The radius of each small sphere is 1/6th the radius of the large sphere. What is the sum (in unit²) of total surface areas of all small spheres?

Solution:

QUESTION: 67

If a > b, then by what percentage,  is less than its Reciprocal?

Solution:

QUESTION: 68

If  , then what is the value of 'a'?

Solution:

QUESTION: 69

a + b = 10 &  - 13 = -  -11, Then 3ab + 4a2 + 5b2 =?

Solution:

QUESTION: 70

If x = 7- 4√3, then √x + =?

Solution:

QUESTION: 71

If α4 + 1 = , then, α4 + b4 =?

Solution:

QUESTION: 72

Adjacent sides of a rectangular field are 20 cm and 12 cm if the cost of fencing is 30 Rs. Per meter and the flooring cost is 60 Rs./sq. meter. Then find the total cost of flooring and fencing?

Solution:

QUESTION: 73

In ∆ABC, AC = CD, &∠CAB - ∠ABC = 30°. Find ∠BAD.

Solution:

QUESTION: 74

In fig circle with centre at B touches a bigger circle with centre A internally& also a circle with centre C externally as shown these circles are tangent to each other. If AB = 6cm, AC = 5cm & BC = 9cm. Find AX =?

Solution:

QUESTION: 75

In ∆ABC, AB = 6cm, BC = 8cm, & CA = 10cm. If I is the in-center of the ∆ then find length of IA?

Solution:

QUESTION: 76

Find the area (in cm²) of the shaded region. Given OP = 12cm.

Solution:

QUESTION: 77

In triangle, ∆ABC PQ & WV ∥ BC & PQRXYZ & RWVUTS are two regular hexagons. Then find Area of two regular hexagon if Area ∆ ABC = 36√3 cm².

Solution:

QUESTION: 78

If ac + bc + ab = abc, then the value of  is

Solution:

QUESTION: 79

Volume of a sphere, a cube, a tetrahedron and an octahedron is same. Find for which of the following structures, it will have the minimum surface area

Solution:

Sphere will have minimum surface area.

QUESTION: 80

A right circular cone of base radius 12 cm is cut at the height of 8 cm and made into a frustum. Then find the volume (in cm3) of original cone if the radius of smaller cone is cut is 8 cm.

Solution:

QUESTION: 81

What is the unit digit of ?

Solution:

32 is an even number which is having a power of the form 4n. so it will give 6 as the unit digit.

QUESTION: 82

Ratio of sides of ∆ having ∠’s. 30°, 60° and 90° is

Solution:

QUESTION: 83

In the given fig. 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 ∠ACD = y° & ∠AOD = x°, & relation between x & y is, x = Ky° then roots of equation A³ + KA – KA² – K⁄3 = 0 are

Solution:

QUESTION: 84

A frustum of Pyramid having square base with upper side 9 cm and the larger side 15 cm has a height of 4 cm Then the lateral surface area of frustum will be

Solution:

QUESTION: 85

The area of the shaded region in the figure given below is (if center of circle A and C are collinear and B, C and D are collinear)

Solution:

QUESTION: 86

The height of the cone is 60 cm. A small cone is cut off at the top by a plane parallel to its base. If its volume is 1/27 of the volume of the cone, at what height, above the base, is the section made?

Solution:

QUESTION: 87

In given figure, AG is parallel to CD & AG = 2/7 CD. Point B on AC is such that BC =2/7 AC. If line BG meets AD at F & the line through C is parallel to BG meets AD at E, Find FG/EC.

Solution:

QUESTION: 88

OB & OD are radius of circle with centre O, while BD is not the diameter of circle. C & A are two points on circle. BA & CD, when produced meet at E. If ∠DOC = 60° &∠ABD = 30° &∠OCA = 17° then find ∠AED.

Solution:

QUESTION: 89

In fig CD = BF = 10 cm &∠CED = ∠BAF = 30°. Find BC(in cm) = ?

Solution:

QUESTION: 90

In the equilateral triangle ABC, AD = DE = BE, D and E lies on the AB. If each side of the triangle be 12 cm, then area of the shaded region is (in cm²)

Solution:

QUESTION: 91

In given fig. Find length of AB(in cm).

Solution:

QUESTION: 92

Kamlesh halwai sells rasgullas at Rs. 120 per kg. A rasgulla is made up of Sugar, Maida & Milk in the ratio 5 : 2 : 3. The ratio of prices of sugar, maida & milk is 1 : 5 : 5. Thus he gains 33 1/3% profit. Find the amount invested in sugar per kg of rasgulla?

Solution:

QUESTION: 93

A cricketer, whose bowling average is 24.85 runs per wicket, takes 5 wickets for 52 runs and thereby decreases his average by 0.85. The number of wickets taken by him till the last match was:

Solution:

QUESTION: 94

If a, b ∈ [0,100], then find the no. of ordered pairs satisfying a2 + b2 = (a + b)2

Solution:

QUESTION: 95

Ravi, an architect in his quest to make something new, decided to plant green lawn on both sides of the rectangular house BCEF, one full of flowers and another full of special herbs. If the total area of the green lawn is 18√3 sq. meter then find the area of living area (in m²). (ABCDEF is a regular hexagon)

Solution:

QUESTION: 96

In the given figure, ABCDEF is a regular hexagon of side 12 cm. P, Q and R are the mid points of the sides AB, CD and EF respectively. What is the area (in cm²) of triangle PQR ?

Solution:

QUESTION: 97

If , then find the value of   is-

Solution:

QUESTION: 98

is equal to-

Solution:

QUESTION: 99

Veer earned a profit of Rs. 640 by selling some Books at the rate of Rs. 5 per book and incurred a loss of Rs. 320 if he sells same number of Book at the rate of Rs. 2 per book. How many books did Veer have?

Solution:

Let no. of books Veer had = n
Then total selling price of books selling at Rs 5 per book = 5n
And total selling price of books selling at Rs 2 per book = 2n
Cost price = 5n – 640 = 2n + 320
3n = 960
n = 320

QUESTION: 100

Fiind real value of x for

Solution: