# Mathematics Questions for NDA, CDS & CAPF: Quiz-4

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**Q1. What are the coordinates of the foot of the perpendicular drawn from the point (3, 5, 4) on the plane z = 0?**

(a) (0, 5, 4)

(b) (3, 5, 0)

(c) (3, 0, 4)

(d) (0, 0, 4)

**Q2. Consider the following statements**

**I. The function is discontinuous at x = 3.**

**II. The function is not differentiable at x = 0.**

**Which of the above statement(s) is/are correct?**

(a) Only I

(b) Only II

(c) Both I and II

(d) Neither I nor II

**Q3. What does the equation represent?**

(a) It represents a circle of diameter a

(b) It represents a circle of radius a

(c) It represents a parabola

(d) None of the above

**Q9. If the matrix AB is a zero matrix, then which one of the following is correct?**
(a) A must be equal to zero matrix or B must be equal to zero matrix

(b) A must be equal to zero matrix and B must be equal to zero matrix

(c) It is not necessary that either A is zero matrix or B is zero matrix

(d) None of the above

(a) Only I

(b) Only II

(c) Both I and II

(d) Neither I nor II

Sol. The terms of x and y will remain the same as the two circles are concentric. The new constant Î» = 0 as it passes through (–1, –2). By putting point (–1, –2) in the equation.

(c) It is not necessary that either A is zero matrix or B is zero matrix

(d) None of the above

**Q11. A, B, C and D are four sets such that A ∩ B = C ∩ D = Ï•. Consider the following****I. A ∪ C and B ∪ D are always disjoint.****II. A ∩ C and B ∩ D are always disjoint.****Which of the above statement(s) is/are correct?**(a) Only I

(b) Only II

(c) Both I and II

(d) Neither I nor II

**SOLUTIONS**

**S1. Ans.(b)**

Sol. The foot of perpendicular drawn from (3, 5, 4) on z = 0 is

(x-3)/0=(y-5)/0=(z-4)/1=-4/1

⇒ x = 3, y = 5, z = 0

Hence, (x, y, z) = (3, 5, 0)

**S7. Ans.(b)**Sol. The terms of x and y will remain the same as the two circles are concentric. The new constant Î» = 0 as it passes through (–1, –2). By putting point (–1, –2) in the equation.

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