The range of the function \({1\over 1-2sinx}\) is

(a)

\((-∞,-1)\cup\left( {1\over 3},\infty\right)\)

(b)

\(\left( -1,{1\over 3}\right)\)

(c)

\(\left[ -1,{1\over 3}\right]\)

(d)

\((-∞,-1]\cup [\frac { 1 }{ 3 } ,∞)\)

cos p = \(\frac { 1 }{ 7 } \) and cos Q = \(\frac { 13 }{ 14 } \) where P, Q are angles, then P-Q is _______________

(a)

\(\frac { \pi }{ 6 } \)

(b)

\(\frac { \pi }{ 3 } \)

(c)

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

(d)

\(\frac { 5\pi }{ 12 } \)

The coefficient of a⁵ in the expansion of (3a + 5b)⁵ is ______________

(a)

1

(b)

243

(c)

6750

(d)

9375

If(1, 3) (2,1) (9, 4) are collinear then a is ______________

(a)

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

(b)

2

(c)

0

(d)

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

The function \(f\left( x \right) =\tan { x } \) is discontinuous on the set

(a)

\(\left\{ n\pi :\quad n\in z \right\} \)

(b)

\(\left\{ 2n\pi :\quad n\in z \right\} \)

(c)

\(\left\{ (2n+1)\frac { \pi }{ 2 } ,\quad n\in z \right\} \)

(d)

\(\left\{ n\frac { \pi }{ 2 } ,\quad n\in z \right\} \)

The rate of change of area A of a circle of radius r is

(a)

\(2\pi r\)

(b)

\(2\pi r\frac { dr }{ dt } \)

(c)

\(\pi { r }^{ 2 }\frac { dr }{ dt } \)

(d)

\(\pi \frac { dr }{ dt } \)

If f(x) = x² - 3x, then the points at which f(x) = f '(x) are

(a)

both positive integers

(b)

both negative integers

(c)

both irrational

(d)

one rational and another irrational

If f(x) = x + 2, then f '(f(x)) at x = 4 is

(a)

8

(b)

1

(c)

4

(d)

5

Choose the correct or the most suitable answer from the given four alternatives.
If f(x) is an odd function, then  f^'(x) is an ______ function

(a)

even

(b)

odd

(c)

even or odd

(d)

neither even nor odd

\(\int \frac{e^x\left(x^2 \tan ^{-1} x+\tan ^{-1} x+1\right)}{x^2+1} d x\) is

(a)

e^x tan^-1(x+1)+c

(b)

tan^-1(e^x)+c

(c)

\(e^x{(tan^{-1}x)^2\over 2}+c\)

(d)

e^x tan^-1 x+c