# Mathematics Questions for CDS & CAPF: 29th October

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 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.**

(a) 40%

(b) 41%

(c) 43%

(d) 44%

**Q2. If a: b = 2:3 and b:c = 4:5, find a2:b2:bc,**

(a) 4: 9: 45

(b) 16: 36: 45

(c) 16: 36: 20

(d) 4: 36: 440

**Q3. 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?**

(a) 17 litres

(b) 16 litres

(c) 18 litres

(d) 15 litres

**Q6. In a flying race between Neha, Deepika, Mamta & Prerna, Neha’s plane is twice as fast as Deepika’s plane. When Neha finishes the race, the distance between her plane & Mamta’s plane is D. when Deepika finishes the race, the distance between hers & Prerna’s plane is also D. If Deepika’s plane is 3 times as fast as Mamta’s plane, then how many times faster is Neha’s plane than Prerna’s plane?**

(a) 8

(b) 4

(c) 12

(d) 6

**Q10. The area of circle whose radius is 8cm is trisected by two concentric circles. The ratio of radii of the concentric circles in ascending order is**

(a) 1 : 2 : 3

(b) 2 : 3 : 5

(c) 1∶√2 ∶√3

(d) √2 ∶√3 ∶√5

**SOLUTIONS**

**S1. Ans.(d)**

Sol.

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%

**S2. Ans.(b)**

Sol.

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

**S4. Ans. (c)**

Sol.

Clearly, 55, 132, & 143 are Pythagorean triplets,

5×11, 12×11, 13×11

∴ 5² + 12² = 13²

⇒ x = 4

**S7. Ans.(a)**

Sol.

No. of girls of XIB & XIC + No. of boys of XIA

= 44 + 12 + 12 = 68

Now, total number of student = 68/0.25=272

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