The function f:R➝R is defined by f(x)=\(\frac { \left( { x }^{ 2 }+cosx \right) \left( 1+{ x }^{ 4 } \right) }{ \left( x-sinx \right) \left( 2x-{ x }^{ 3 } \right) } +{ e }^{ -\left| x \right| }\) is

(a)

an odd function

(b)

neither an odd function nor an even function

(c)

an even function

(d)

both odd function and even function.

Let A = {-2, -1, 0, 1, 2} and f : A ⟶ Z be given by f(x) = x²- 2x - 3 then preimage of 5 is ___________

(a)

-2

(b)

-1

(c)

0

(d)

1

If sin(45 ° + 10°) - sin(45° -10°) = \(\sqrt{2}\)sin x then x is ___________ 

(a)

0^o

(b)

5°

(c)

10°

(d)

15°

The numerical value of tan^-11 + tan^-12 + tan^-13 = _______________

(a)

\(\pi\)

(b)

\(\frac{\pi}{2}\)

(c)

0

(d)

\(\frac{\pi}{4}\)

The n^th term of the sequence \(\frac { 1 }{ 2 } ,\frac { 3 }{ 4 } ,\frac { 7 }{ 8 } ,\frac { 15 }{ 6 } \),......is

(a)

2ⁿ - n - 1

(b)

1 - 2^-n

(c)

2^-n + n - 1

(d)

2^n-1

The Co-efficient of x³ in \(\sqrt { \frac { 1-x }{ 1+x } } ,\left| x \right| <1\ is\ \)______________

(a)

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

(b)

\(\frac { 3 }{ 8 } \)

(c)

\(\frac { -3 }{ 8 } \)

(d)

\(\frac {- 1 }{ 2 } \)

The value of m for which the vectors \(3\hat { i } -6\hat { j } +\hat { k } \) and \(2\hat { i } -4\hat { j } +\lambda \hat { k } \) are parallel is __________ .

(a)

\(\frac { 2 }{ 3 } \)

(b)

\(\frac { 3 }{ 2 } \)

(c)

\(\frac { 5 }{ 2 } \)

(d)

\(\frac { 2 }{ 5 } \)

\(lim_{n \rightarrow \infty}({1\over n^2}+{2\over n^2}+{3\over n^2}+..+{n\over n^2})\) is

(a)

\(1\over 2\)

(b)

0

(c)

1

(d)

\(\infty\)

If pv = 81, then \({dp\over dv}\) at v = 9 is

(a)

1

(b)

-1

(c)

2

(d)

-2

\(\int \frac{\sec ^2 x}{\tan ^2 x-1} d x\) is

(a)

\(2log|{1-tan x\over 1+tan \ x}|+c\)

(b)

\(log|{1+tan x\over 1-tan \ x}|+c\)

(c)

\({1\over2}log|{tan x+1\over tan \ x-1}|+c\)

(d)

\({1\over2}log|{tan x-1\over tan \ x+1}|+c\)