Function $f(x)=[x]$, greatest integer function is

(A) Continuous at $x=2.5$

(B) Continuous at $x=1$

(C) Differentiable at $x=2$

(D) Differentiable at $x=-1.2$

Choose the correct answer from the options given below:

The value of '$\lambda$' for which the function $f(x) = \begin{cases}\frac{1-\cos 4x}{4x^2}, & \text{if } x \neq 0 \\ \lambda, & \text{if } x = 0\end{cases}$ is continuous at $x=0$, is:

If $x = at^2$ and $y = 2at$, then the value of $\frac{d^2y}{dx^2}$ is

( where t is a parameter )

If $y = 3^x + e^x + x^x + x^3$, then the value of $\frac{dy}{dx}$ at $x = 3$ is

If $f(x)=\begin{cases}\frac{\sin(a-b)x}{x}, & x<0\\ 2a+b, & x=0\\ \frac{-\tan 12x}{bx}, & x>0\end{cases}$, $(b>0)$ is continuous at $x=0$, then

If $y=\sqrt[5]{\log_e(5x^2)}$, then $\dfrac{dy}{dx}=$

(Take $\log_e x=\log x$)

If $x = t^2$ and $y = t\sqrt{t}$, then $\dfrac{d^2y}{dx^2}$ at $t = \dfrac{1}{4}$ is :