If the circle $x^2+y^2+6x-2y+k=0$ bisects the circumference of the circle $x^2+y^2+2x-6y-15=0$,then $k=$

If $f(x)=|x|+|\sin x|$ for $x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, then its left hand derivative at $x=0$ is

For a binomial variate $X$ with parameters $n=5$ and $p=\frac{3}{4}$,if $\alpha=\frac{1}{9} P(X \geq 3)$ and $\beta=P(X \leq 2)$,then $256(\beta-\alpha)=$

If the amplitude of $z-2-3i$ is $\frac{\pi}{4}$,then the locus of $z=x+iy$ is:

The solution of $x dx + y dy = x^2 y dy - x y^2 dx$ is

The $IUPAC$ name for the complex $[Co(NH_3)_5(NO_2)]Cl_2$ is