Question 1 :
Say true or false.If $y=2  \sec  x$, then $\dfrac{dy}{dx} $ is $2 \sec x  \tan x$.
Question 3 :
What is $\displaystyle \lim _{ x\rightarrow 0 }{ \cfrac { \sqrt { 1+x } -1 }{ x }  } $ equal to?
Question 4 :
$\displaystyle \lim_{x\to0}{\displaystyle \frac{x(e^x - 1)}{1 - \cos x}}$ is equal to
Question 5 :
State whether the given statement is True or False.Derivative of $y=2x^5$ with respect to $x$ is $10x^4$.<br/>
Question 6 :
If $y$ is a function of $x$ and $\log { \left( x+y \right) } -2xy=0$ then the value of $y'(0)$ is equal to
Question 8 :
$\displaystyle \frac{d}{dx}\left ( \tan ^{-1}\left ( \frac{a-x}{1+ax} \right ) \right )$ equals if ax > -1
Question 13 :
Obtain the differential equation whose solution is$\displaystyle y=x\sin \left ( x+A \right ),$ A being constant.
Question 15 :
For instantaneous speed, the distance traveled by the object and the time taken are both equal to zero.
Question 21 :
State if the given statement is True or FalseDerivative of $y= \cos  x$ with respect to $x$ is $\sin x$.
Question 23 :
If $\displaystyley=\frac { x }{ a+\displaystyle\frac { x }{ b+\displaystyle\frac { x }{ a+\displaystyle\frac { x }{ b+.....\infty } } } } $, then $\cfrac{dy}{dx} =$<br><br>
Question 24 :
The value of $\displaystyle \lim_{x \rightarrow 2} \frac{\sqrt{1 + \sqrt{2 + x}} - \sqrt 3}{x- 2}$ is
Question 25 :
The value of $\displaystyle \lim_{x \rightarrow -2} \frac{(x^2 - x - 6)^2}{(x + 2)^2}$ is?
Question 26 :
$\displaystyle \frac{d}{dx}[f(x)\cdot g(x)] =f(x) \frac{d}{dx}g(x)+g(x) \frac{d}{dx}f(x)$ is known as _____ rule.
Question 29 :
Consider the differential equation $\frac { d y } { d x } = \cos x$ Then we observe that <br/>
Question 31 :
If $f ( x ) = \dfrac { a ^ { x } } { x ^ { a } }$ then $f ^ { \prime } ( a ) =$
Question 32 :
$\mathop {\lim }\limits_{x \to \infty } \sum\limits_{r = 1}^n {{{\tan }^{ - 1}}} \left( {\frac{{2r}}{{1 - {r^2} + {r^4}}}} \right)$ is equal to
Question 33 :
The velocity of a particle is given by $v = 12 + 3(t + 7t^{2})$. What is the acceleration of the particle?
Question 34 :
Evaluate $\displaystyle \lim_{x \rightarrow -2} \displaystyle \frac{x^2 - 1}{2x + 4}$.
Question 35 :
The value of $\lim_{x \rightarrow 1^{+}} ({x})^{\frac{1}{x}}$, is : (where ${.}$ denotes the fractional part function)
Question 37 :
Let $f(x + y) = f(x) \times f(y)$ for all $x$ and $y$ and $f(7) = 5, f'(0) = 2$ then $f'(7)$ will be 
Question 39 :
$\mathop {\lim }\limits_{x \to 0} \dfrac{{\sin 2x}}{{2{x^2} + x}} = $
Question 40 :
If$\displaystyle f(x)=|\cos x|$ then $f'\left ( \frac{3\pi }{4} \right )$ is equal to-
Question 43 :
$\underset { x\rightarrow 0 }{ \lim } $ <br> $\dfrac { (1-\cos 2x)(3+\cos x) }{ x\tan 4x } $ is equal to
Question 47 :
$\lim _ { x \rightarrow 0 } \dfrac { 2 ^ { x } - 1 } { \sqrt { 1 + x } - 1 }$ equals
Question 49 :
If $y = \sqrt x  + \dfrac{1}{{\sqrt x }}$ , then $\dfrac{{dy}}{{dx}}$ at $x=1$ is