If the angle between the circles $x^2+y^2-12x-6y+41=0$ and $x^2+y^2+kx+6y-59=0$ is $45^{\circ}$,then a value of $k$ is

The joint equation of the lines passing through the origin and trisecting the first quadrant is . . . . . .

In the standing wave shown,particles at the positions $A$ and $B$ have a phase difference of

Two concentric hollow spherical shells have radii $r$ and $R$ $(R \gg r)$. $A$ charge $Q$ is distributed on them such that the surface charge densities are equal. The electric potential at the centre is

Which hormone is produced by the placenta?

$A$ source of sound of frequency $640 ~Hz$ is moving at a velocity of $\frac{100}{3} ~m/s$ along a road,and is at an instant $30 ~m$ away from a point $A$ on the road (as shown in figure). $A$ person standing at $O$,$40 ~m$ away from the road,hears sound of apparent frequency $v^{\prime}$. The value of $v^{\prime}$ is (velocity of sound $= 340 ~m/s$). (in $~Hz$)