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Mathematics Mock Test - 3 - CDS MCQ


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30 Questions MCQ Test CDS (Combined Defence Services) Mock Test Series 2024 - Mathematics Mock Test - 3

Mathematics Mock Test - 3 for CDS 2024 is part of CDS (Combined Defence Services) Mock Test Series 2024 preparation. The Mathematics Mock Test - 3 questions and answers have been prepared according to the CDS exam syllabus.The Mathematics Mock Test - 3 MCQs are made for CDS 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Mathematics Mock Test - 3 below.
Solutions of Mathematics Mock Test - 3 questions in English are available as part of our CDS (Combined Defence Services) Mock Test Series 2024 for CDS & Mathematics Mock Test - 3 solutions in Hindi for CDS (Combined Defence Services) Mock Test Series 2024 course. Download more important topics, notes, lectures and mock test series for CDS Exam by signing up for free. Attempt Mathematics Mock Test - 3 | 100 questions in 120 minutes | Mock test for CDS preparation | Free important questions MCQ to study CDS (Combined Defence Services) Mock Test Series 2024 for CDS Exam | Download free PDF with solutions
Mathematics Mock Test - 3 - Question 1

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

Detailed Solution for Mathematics Mock Test - 3 - Question 1

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

Mathematics Mock Test - 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: 

Detailed Solution for Mathematics Mock Test - 3 - Question 2

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

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Mathematics Mock Test - 3 - Question 3

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

Detailed Solution for Mathematics Mock Test - 3 - Question 3

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

Mathematics Mock Test - 3 - 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?

Detailed Solution for Mathematics Mock Test - 3 - Question 4

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

Mathematics Mock Test - 3 - 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? 

Detailed Solution for Mathematics Mock Test - 3 - Question 5

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 

Mathematics Mock Test - 3 - 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. 

Detailed Solution for Mathematics Mock Test - 3 - Question 6

Mathematics Mock Test - 3 - 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? 

Detailed Solution for Mathematics Mock Test - 3 - Question 7

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

Mathematics Mock Test - 3 - 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? 

Detailed Solution for Mathematics Mock Test - 3 - Question 8

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

Mathematics Mock Test - 3 - 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? 

Detailed Solution for Mathematics Mock Test - 3 - Question 9

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.

Mathematics Mock Test - 3 - 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. 

Detailed Solution for Mathematics Mock Test - 3 - Question 10

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% 

Mathematics Mock Test - 3 - Question 11

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

Detailed Solution for Mathematics Mock Test - 3 - Question 11

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

Mathematics Mock Test - 3 - 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? 

Detailed Solution for Mathematics Mock Test - 3 - Question 12



∴ 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  

Mathematics Mock Test - 3 - Question 13

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

Detailed Solution for Mathematics Mock Test - 3 - Question 13

Mathematics Mock Test - 3 - Question 14

If x = 99, values of x(x+ 3x + 3) is 

Detailed Solution for Mathematics Mock Test - 3 - Question 14

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 

Mathematics Mock Test - 3 - Question 15

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

Detailed Solution for Mathematics Mock Test - 3 - Question 15

Mathematics Mock Test - 3 - Question 16

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

Detailed Solution for Mathematics Mock Test - 3 - Question 16

Mathematics Mock Test - 3 - 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 

Detailed Solution for Mathematics Mock Test - 3 - Question 17

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 

Mathematics Mock Test - 3 - 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? 

Detailed Solution for Mathematics Mock Test - 3 - Question 18

Required change in area

Negative sign show decrease

Mathematics Mock Test - 3 - 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 

Detailed Solution for Mathematics Mock Test - 3 - Question 19


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 

Mathematics Mock Test - 3 - 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: 

Detailed Solution for Mathematics Mock Test - 3 - Question 20

Mathematics Mock Test - 3 - Question 21

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

Detailed Solution for Mathematics Mock Test - 3 - Question 21

Mathematics Mock Test - 3 - 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 - 

Detailed Solution for Mathematics Mock Test - 3 - Question 22


Mathematics Mock Test - 3 - Question 23

  If , then the value of  is

Detailed Solution for Mathematics Mock Test - 3 - Question 23

Mathematics Mock Test - 3 - 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? 

Detailed Solution for Mathematics Mock Test - 3 - Question 24


Mathematics Mock Test - 3 - Question 25

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

Detailed Solution for Mathematics Mock Test - 3 - Question 25

Mathematics Mock Test - 3 - Question 26

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

Detailed Solution for Mathematics Mock Test - 3 - Question 26

Mathematics Mock Test - 3 - Question 27

Find (a+b); if a =  and b = 

Detailed Solution for Mathematics Mock Test - 3 - Question 27

Mathematics Mock Test - 3 - Question 28

If x =  and z =  then the value of   is 

Detailed Solution for Mathematics Mock Test - 3 - Question 28

Mathematics Mock Test - 3 - 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 

Detailed Solution for Mathematics Mock Test - 3 - Question 29

Mathematics Mock Test - 3 - 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 

Detailed Solution for Mathematics Mock Test - 3 - Question 30

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