Mathematics Questions for CDS & AFCAT: 11th 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 radius of base and curved surface area of a right cylinder ‘r’ units and 4πrh square units respectively. The height of the cylinder is:
(a) 4h units
(b) h2 units
(c) h units
(d) 2h units

Q2. The diameter of a circle is equal to the side of the square. What is the area of the square if the area of the circle is 64π sq cm?
(a) 128 sq cm
(b) 196 sq cm
(c) 108 sq cm
(d) 256 sq cm

Q3. If tan2A + cot2A + 2 = x, then the value of x isA
(a) tan2A cosec2A
(b) secA cosecA 
(c) sec2A cosec2A
(d) tanA cosecA 

Q4. If xy = 48 and x² + y² = 100, then (x + y) is
(a) 12
(b) 16
(c) 18
(d) 14

Q5. Point P and Q lie on side AB and AC of triangle ABC respectively such that segment PQ is parallel to side BC. If the ratio of areas of ΔAPQ: ΔABC is 25 : 36. Then the ratio of AP : PB is _______. 
(a) 5 : 6 
(b) 1 : 5  
(c) 6 : 5
(d) 5 : 1 

Q6. P and Q can finish a work in 24 and 12 days respectively. In how many days can they complete 50% of the work if they work together? 
(a) 8 days
(b) 2 days 
(c) 4 days 
(d) 16 days

Q7. A Mogra rice trader buys 16 quintals of rice for Rs. 1,280. 18% rice is in lost in transportation. An what rate should he sell to earn 23% profit? 
(a) Rs. 53.33 per quintal
(b) Rs. 98.4 per quintal 
(c) Rs. 122.5 per quintal 
(d) Rs. 120 per quintal

Q8. A, B and C can complete a work in 40, 48 and 60 days respectively. They received Rs. 13200 to complete the work. They begin the work together but B left 2 days before the completion of the work, and C left 5 days before the completion of the work. A has completed the remaining work alone. What is the share of B (in Rs.)  
(a) 4000
(b) 4400
(c) 4500
(d) 4860

Q9. A shopkeeper earns a profit of 25% after selling a book at 20% discount on the marked price. The ratio of marked price to the cost price is  
(a) 23 : 16
(b) 25 : 16 
(c) 23 : 14
(d) 25 : 14

Q10. A man has 3 sons, 2 daughters and a wife. They divided a sum of Rs. 23000 among themselves such that each daughter got 2.5 times the amount received by each son and his wife received 400 less than each son. What is the total amount (in Rs.) received by the 3 sons together?  
(a) 7800
(b) 6900
(c) 6300
(d) 5700

S10. Ans.(a)
Sol. Let the amount received by each son be Rs. x
∴ ATQ,
3x + 2 × 2.5x + (x – 400) = 23000
⇒ 3x + 5x + x – 400 = 23000
⇒ 9x = 23400
⇒ x = 2600
∴ Total amount by 3 sons together = 3 × 2600 = Rs. 7800

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