Objective Mathematics Set - IV

1. In order that the function f(x) = (x + 1)cot x is continuous at x = 0, f(0) must be defined as
A. f(0) = 0    B. f(0) = e    C. f(0) = 1/e    D. none of the above

2. The eccentricity of the ellipse 16x2 + 7y2 = 112 is
A. 4/3    B. 7/16    C. 3/Ö7    D. 3/4

3. If z1, z2, z3 are three complex numbers in A.P., then they lie on
A. a circle    B. an ellipse    C. a straight line    D. a parabola

4. The line y = mx + 1 is a tangent to y2 = 4x, first m equals
A. -1    B. 1    C. 2    D. 4

5. If Q = { x : x = 1/y, where y Î N }, then
A. (2/3) Î Q    B. 2 Î Q    C. 0 Î Q    D. 1 Î Q

6. Which of the following functions is periodic?
A. f(x) = x -

• , where
• denotes the largest integer less than or equal to the real number x

B. f(x) = sin (1/x) for x ¹ 0, f(0) = 0
C. f(x) = x cos x
D. none of the above

7. If | 2x + 5 | £ x + 3, then x lies in the interval
A. [5/2, 8/3]    B. [- 5/2, - 2]    C. [- 8/3, - 2]    D. [- 8/3, - 5/2]

8. The centre of a square ABCD is at z1 = 0. The affix of the vertex A is z. Then the affix of the centroid of the triangle ABC is
A. (z1/3) [cos(p/2) ± i sin(p/2)]    B. z1 [cos(p/2) ± i sin(p/2)]
C. (z1/3) (cos p ± i sin p)    D. z1 (cos p ± i sin p)