# Mathematics Questions for NDA, CDS & CAPF: 14th August

Dear Students, Defence Adda is providing you all with this quiz on Mathematics questions for NDA, CDS, AFCAT, CAPF and other Police 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 Mathematics Section of all sorts of defence examinations.

**Q1. What is the equation of the sphere with unit radius having centre at the origin?**

(a) x² + y² + z² = 0

(b) x² + y² + z² = 1

(c) x² + y² + z² = 2

(d) x² + y² + z² = 3

**Q7. What is the length of the latusrectum of an ellipse 25x² + 16y² = 400?**

(a) 25/2

(b) 25/4

(c) 16/5

(d) 32/5

**Q8. In how many ways 4 boys and 3 girls can be seated in a row, so that they are alternate?**

(a) 108

(b) 144

(c) 96

(d) 72

**Q9. The system of linear equations kx + y + z = 1, x +ky + z = 1 and x + y + kz = 1 has a unique solution under which one of the following conditions?**

(a) k ≠ 1 and k ≠ – 2

(b) k ≠ 1 and k ≠ 2

(c) k ≠ –1 and k ≠ – 2

(d) k ≠ –1 and k ≠ 2

**Q11. Let N denotes the set of natural numbers and A = {n² : n ∈ N} and B = {n³ : n ∈ N}. Which one of the following is correct?**

(a) A ∪ B = N

(b) The complement of (A ∪ B) is an infinite set

(c) A ∪ B Must be a finite set

(d) A ∩ B must be a proper subset of {m^6 : m ∈ N}

**Q12. If A = {1, 2}, B = {2, 3} and C = {3, 4}, then what is the cardinality of (A×B) ∩ (A×C)?**

(a) 8

(b) 6

(c) 2

(d)1

**Q13. A lamp post stands on a horizontal plane. From a point situated at distance 150m from its foot, the angle of elevation of the top is 30°. What is the height of the lamp post?**

(a) 50m

(b) 50√3 m

(c) 50/√3 m

(d) 100 m

**Q15. If a, b and c ∈ R and a + b + c = 0, then the quadratic equation 4ax² + 3bx + 2c = 0 has**

(a) one positive and one negative root

(b) imaginary roots

(c) real roots

(d) None of the above

**Solutions**

**S2. Ans.(d)**

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