The equation of the circle concentric with the circle $x^2+y^2-6x+12y+15=0$ and having double its area is

Which of the following statements is incorrect for $Nostoc$ and $Anabaena$?

The graph which represents the variation of mean kinetic energy of molecules with temperature $t^{\circ}C$ is

$x=\cos ^{-1}\left(\frac{1}{\sqrt{1+t^2}}\right), y=\sin ^{-1}\left(\frac{t}{\sqrt{1+t^2}}\right) \Rightarrow \frac{d y}{d x}$ is equal to

An inductor $L$,a resistance $R$ and two identical bulbs $B_1$ and $B_2$ are connected to a battery through a switch $S$ as shown in the figure. The resistance of the coil having inductance $L$ is also $R$. Which of the following statements gives the correct description of the happenings when the switch $S$ is closed?

If $f(x) = \begin{cases} \frac{\sin(1+[x])}{[x]}, & \text{for } [x] \neq 0 \\ 0, & \text{for } [x] = 0 \end{cases}$ where $[x]$ denotes the greatest integer not exceeding $x$,then $\lim_{x \rightarrow 0^{-}} f(x)$ is equal to