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

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.