If the function $f(x)=\begin{cases}\frac{e^{2\log_e x^2}-1}{x-1}, & x\ne 1\\ a, & x=1\end{cases}$ is continuous at x=1, then the value of a is:

$f(x) = [x]$, where $[\,]$ represents greatest integer function.

(A) For $2 \leq x < 3$, $[x] = 3$

(B) For $2 \leq x < 3$, $[x] = 2$

(C) Right hand derivative of f at $x = 2$ is not defined

(D) Left hand derivative of f at $x = 2$ is zero

(E) $f(x)$ is not differentiable at $x = 2$

Choose the correct answer from the options given below :

If $y = \sqrt{x + \sqrt{x + \sqrt{x + ...\ ...\ ...}}}$, then

If $x = a(\theta+\sin\theta)$, $y = a(1-\cos\theta)$ then $\dfrac{d^2y}{dx^2}$ is equal to:

If a function $f(x) = \begin{cases}\lambda(x^2-2x), & x \le 0\\4x+1, & x>0\end{cases}$ then

If $e^x + e^y = e^{x+y}$, then $\frac{dy}{dx}$ =

If the function $f(x)=\begin{cases} x^2, & x\le c \\ ax+b, & x>c \end{cases}$ is differentiable at $x=c$, then the relation between $b$ and $c$ is: