The function f(x) = log (x + \(\sqrt{x^2+1}\)) is ___________

(a)

an even function

(b)

an odd function

(c)

a periodic function

(d)

neither an even nor an odd function

If a and b are the roots of the equation x²- kx + 16 = 0 and a²+ b² = 32, then the value of k is

(a)

10

(b)

-8

(c)

-8, 8

(d)

6

The number of real solution of |2x - x²- 3| = 1 is ___________

(a)

0

(b)

2

(c)

3

(d)

4

If ⁿP_r=k x ^n-1P_r-1 what is k:

(a)

r

(b)

n

(c)

n+1

(d)

r+1

Choose the incorrect pair:

(a)

10C₁ - 10C₉

(b)

10C₃ - 10C₇

(c)

10C₄ - 10C₆

(d)

10C₅ - 10C₂

If the sum of n terms of an A. P. be 3n² - n and its common difference is 6, then its first term is ______________

(a)

2

(b)

3

(c)

1

(d)

4

The sum of the series \(\frac { 1 }{ { log }_{ 2 }^{ 4 } } +\frac { 1 }{ { log }_{ 4 }^{ 4 } } +\frac { 1 }{ { log }_{ 8 }^{ 4 } } +.....+\frac { 1 }{ { log }_{ { 2 }^{ n } }^{ 4 } } is\)______________

(a)

\(\frac { n(n+1) }{ 2 } \)

(b)

\(\frac { n(n+1)(2n+1) }{ 2 } \)

(c)

\(\frac { n(n+1) }{ 4 } \)

(d)

none of these

If a is the arithmetic mean and g is the geometric mean of two numbers, then

(a)

a \(\le \) g

(b)

a \(\ge\) g

(c)

a = g

(d)

a > g

The locus of a point which moves such that it maintains equal distances from two fixed points is a ______________

(a)

straight line

(b)

line bisector

(c)

pair of straight lines

(d)

angle bisector

If g(x) = (x² + 2x + 3) f(x) and f(0) = 5 and \(lim_{x \rightarrow 0}{f(x)-5\over x}=4\), then g'(0) is

(a)

20

(b)

14

(c)

18

(d)

12