# Mathematics Questions for CDS & AFCAT: 9th January(Solutions)

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. The ratio of the numbers giving the measures of the circumference and the area of a circle of radius 3 cm is**

(a) 1 : 3

(b) 2 : 3

(c) 2 : 9

(d) 3 : 2

**Q2. If the length and the perimeter of a rectangle are in the ratio 5 : 16, then its length and breadth will be in the ratio**

(a) 5 : 11

(b) 5 : 8

(c) 5 : 4

(d) 5 : 3

**Q3. Î”ABC is similar to Î”PQR. Length of AB is 36 cm and length of the corresponding side PQ is 16 cm. If area of Î”ABC is 1296 sq cm, what is the area of Î”PQR?**

(a) 128 sq cm

(b) 512 sq cm

(c) 64 sq cm

(d) 256 sq cm

**Q4. If cos(11Ï€/6) = x, then the value of x is**

(a) √3/2

(b) 1/2

(c) 2

(d) √3/2

**Q5. Coefficient of x² in (x+5) (3–2x) (4x–2) is**

(a) 24

(b) 32

(c) –24

(d) –32

**Solutions(1-5)**

**Q6. The sum of the ages of a mother and son is 45 yrs, Five years ago the product of their ages was 4 times the mother’s age at that time. The present age of the mother and son, respectively are**

(a) 36 yrs, 9 yrs

(b) 39 yrs, 6 yrs

(c) 42 yrs, 12 yrs

(d) 25 yrs, 10 yrs

**Q7. If we divide 3150 into four parts such that half of the first part, a third of the second part and a fourth of the third part are equal to one-twelfth of the fourth part. Then find the largest part?**

(a) 1800

(b) 1200

(c) 600

(d) None of these

**Q8. Three glasses of capacity 2 L, 5 L and 9 L contain mixture of milk and water with milk concentrations 90%, 80% and 70% respectively. The contents of three glasses are emptied into a large vessel. Find the ratio of milk to water in the resultant mixture**

(a) 52 : 49

(b) 31 : 151

(c) 125 : 51

(d) 121 : 39

**Q9. A car running at 7/11 of its own speed reached a place in 22 hrs. How much time could be saved if the car would run at its own speed?**

(a) 14 hrs

(b) 7 hrs

(c) 8 hrs

(d) 16 hrs

**Q10. Two trains of lengths 80 m and 100 m respectively run on parallel lines of rails. When running in the same direction, the faster train passes the slower one in 18 s but when they are running in opposite directions with the same speeds as earlier, they pass each other in 9 s. Find the speed of faster train**

(a) 5 m/s

(b) 10 m/s

(c) 15 m/s

(d) 20 m/s

**Solutions(6-10)**

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