Mathematics Questions for CDS & CAPF: 15th November

Dear Students, Defence Adda is providing you all with this quiz on Mathematics questions for CDS, AFCAT, CAPF and other Defence Examinations. The questions asked in Mathematics Section of most of the defence examinations are based on the topics from Mathematics of Class 11th and 12th. The questions asked in this section are complex and comparatively difficult but once attempted with high accuracy, can fetch you full marks in this section. Also, practice on a daily basis helps one dive into the core concepts of a subject and thus, help her perform to the best of her ability in the real examinations. So, attempt the daily quizzes being provided by Defence Adda and score to the maximum in the Mathematics Section of all sorts of defence examinations.

Q1. 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.    
(a) 32 kg
(b) 40 kg
(c) 52 kg
(d) 80 kg

Q2. 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).   
(a) 50
(b) 60
(c) 75
(d) 80

Q3. 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 :   
(a) 2000
(b) 4000
(c) 3000
(d) 3750

Q4.Two candles of same height are lighted at the same time. The first burns out in 8 hrs. and the second in 6 hrs. Assume that each candle burns at constant rate, then in how many hours after being lighted, the ratio of the length of  Ist and IInd candle is 2 : 1.    
(a) 3 hr 24 min
(b) 5 hrs 32 min
(c) 4 hr 48 min
(d) 2 hrs

Q5.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 ?    
(a) 20√3
(b) 25√3
(c) 30√3
(d) 15√3

Q6. 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, 1/6th part at 30 km/hr and rest at 15 km/hr. Find the average speed of the entire journey.   
(a) 18 km/hr
(b) 24 km/hr
(c) 48 km/hr
(d) 36 km/hr

Q9. What is the approximate average monthly income of A over the years ?   
(a) Rs. 44,762
(b) Rs. 48,348
(c) Rs. 53,216
(d) Rs. 51,548 

Q10. Two cylinder of length 2.5m and 15m are to be cut into equal pieces without leaving any extra length of cylinder. Find the greatest length of the cylinder pieces of same size which can be cut from these two        
(a) 0.25 m 
(b) 75 m  
(c) 2.5 m
(d) 15 m


S1. Ans.(b); 
Sol.   Quantity of dry fruit (without water) in 100 kg fresh fruit = 32% of 100 = 32 kg
So, req. quantity of dry fruit =(32×100)/80 kg
= 40 kg

S2. Ans.(d);
Sol.       1/A=1/8 
and 1/A-1/B=1/20
or 1/B=1/8-1/20=3/40
B takes 40/3min to empty the tank 
Capacity of tank =40/3×6 kl = 80 kl

S3. Ans.(a);
Let total profit = 100
Profit share of each = A : B : C = 5/14×70+30∶6/14×70∶3/14×70
= 55 : 30 : 15
Difference of profit between A and B + C = 55 – 45 = 10
Total profit =100×20=Rs.2000

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