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 $k$ is equal to

$A$ wire in the form of a square of side '$a$' carries a current $i$. Then the magnetic induction at the centre of the square wire is (Magnetic permeability of free space = $\mu_0$)

An ice ball melts at a rate proportional to the amount of ice present at that instant. Half the quantity of ice melts in $20 \text{ minutes}$. Let $x_0$ be the initial quantity of ice. If after $40 \text{ minutes}$ the amount of ice left is $k x_0$,then the value of $k$ is:

$\int_0^\pi \frac{\theta \sin \theta}{1+\cos ^2 \theta} d \theta$ is equal to

For better survival of the human population,which of the following steps is most important?

The set of solutions of the system of equations
$
\begin{aligned}
x+y & =\frac{2 \pi}{3} \\
\text{and} \quad \cos x+\cos y & =\frac{3}{2},
\end{aligned}
$
where $x, y$ are real,is