Mathematics Question Paper of NDA(National Defence Academy & Naval Academy) Exam (II), 2008

1. Consider the ellipse x²/a² + y²/b²= 1 (b > a). Then, which one of the following is correct?

(a) Real foci do not exist

(b) Foci are (± ae, 0)

(c) Foci are (± be, 0)

(d) Foci are (0, ± be)

Ans: (d)

2. Consider the parabolas S₁ = y² - 4ax = 0 and S₂ = y² - 4bx = 0. S₂ will contain S₁, if

(a) a > b > 0

(b) b > a > O

(c) a > 0, b < 0 but |b| > a

(d) a < 0, b > 0 but b >|a|

Ans: (b)

3. What are the coordinates of the point equidistant from the four points (0, 0, 0),(2, 0, 0), (0,4, 0), (0, 0, 6) ?

(a) (1, 2, 3)    

(b) (2, 3, 1)

(c) (3, 1, 2)    

(d) (1, 3, 2)

Ans: (a)

4. The angle between the lines with direction ratios (1, 0, ± cos a) is 60°. What is the value of a ?

(a) cos^-1 (1/√2)    

(b) cos^-1 (1/√3)

(c) cos^-1 (1/3)    

(d) cos^-1 (1/2)

Ans: (b)

5. The line passing through (1, 2, 3) and having direction ratios given by < 1, 2, 3 > cuts the x-axis at a distance k from origin. What is the value of k ?

(a) 0    

(b) 1

(c) 2    

(d) 3

Ans: (a)

Download Mathematics Paper of NDA Exam II 2008