# Mathematics Questions for CDS & AFCAT: 11th January (SOLUTIONS)

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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

**Q1. The radius of base and curved surface area of a right cylinder ‘r’ units and 4Ï€rh 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 64Ï€ 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 Î”APQ: Î”ABC 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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