# Mathematics Questions for CDS & CAPF: 11th 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. A train consists of 12 bogies, each bogie is 15 m long. The train crosses a telegraph post in 18 sec. Due to some problem, two bogies were detached. The train now crosses the telegraph post in:**

(a) 15 s

(b) 12 s

(c) 18 s

(d) 20 s

**Q2. On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs. 7. If he sells the pen at 5% gain and the book at 10% gain, then he gains Rs. 13. The actual price of the book is:**

(a) Rs. 100

(b) Rs. 80

(c) Rs. 10

(d) Rs. 400

**Q3. By selling an article at 80% of its marked price, a merchant makes a loss of 12%. What will be the percent profit or loss made by the merchant if he sells the article at 95% of its marked price?**

(a) 5.5% profit

(b) 1% loss

(c) 5% profit

(d) 4.5% profit

**Q5. A social service camp is planned to be conducted for 30 days. Required food is stored and the intended number of students have been admitted. After 20 days, the number of students is increased by 500 because of unforeseen reasons. The camp could then be run for 5 more days only. What is the number of students originally admitted?**

(a) 1000

(b) 750

(c) 500

(d) 250

**Q6. A mechanic purchases a scooter with marked price of Rs. 2600 at successive discounts of 10% and 5%. If he spent Rs. 477 for its repair etc. and sold it for Rs. 2835, then the profit or loss percent in this deal is:**

(a) 5% profit

(b) 5% loss

(c) 7% profit

(d) 7% loss

**Q8. 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.**

(a) 5 cm

(b) 10 cm

(c) 15 cm

(d) 12 cm

**Q9. The base of a right pyramid is an equilateral triangle with side 10cm and vertical height 5cm. Find its surface area (in cm2)?**

(a) 35√2

(b) 44√3

(c) 50√3

(d) 44√2

**Q10. The total surface area of a solid hemisphere is 108 Ï€ cm2, then the volume of the hemisphere is**

(a) 72Ï€ cubic cm

(b) 144Ï€ cubic cm

(c) 108Ï€ cubic cm

(d) 54Ï€ cubic cm

**SOLUTIONS**

**S1. Ans.(a);**

Sol. Length of train =12×15=180 m

Time = 18 sec.

Speed =180/18=10 m/sec

New Distance = 15×10=150 m

Req. time =150/10=15 sec

**S2. Ans.(b);**

Sol. Let the C.P. of pen & book be Rs. x & Rs. y respectively –

0.95x+1.15y=(x+y)+7

0.15y-0.05x=7 ……………..(i)

and

1.05x+1.1y=(x+y)+13

0.05x+0.1y=13 ……………..(ii)

from (i) & (ii)

y=80Rs.

**S3. Ans.(d);**

Sol. Let the cost price of article be x

S.P. of article =0.88x

Marked price =0.88/80×100×x=1.1x

New selling price of article =1.045x

Profit percent =(1.045x-x)/x×100=4.5%

**S5. Ans.(c);**

Sol. Original student =n

After 20 days

For n students food last for 10 days more.

∴ for (n+500) students food last for 5 days

A.T.Q.–

10n=5(n+500)

n=500

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