If the equations $x^2+ax+b=0$ and $x^2+bx+a=0$ $(a \neq b)$ have a common root,then $a+b$ is equal to

If $a, b, c$ and $d$ are real numbers such that $a^2+b^2+c^2+d^2=1$ and $A=\left[\begin{array}{cc}a+i b & c+i d \\ -c+i d & a-i b\end{array}\right]$,then $A^{-1}$ is equal to

If $\log_{7} 2 = m$,then $\log_{49} 28$ is equal to

Match the following:

Column-$I$	Column-$II$
$(1)$ Oxytocin	$(p)$ Stimulates the secretion of thyroid hormone
$(2)$ Vasopressin	$(q)$ Act on the smooth muscles
$(3)$ $FSH$ and androgens	$(r)$ Stimulates resorption of water
$(4)$ $TSH$	$(s)$ Regulate spermatogenesis

When a point source of monochromatic light is placed at a distance of $0.2 \ m$ from a photoelectric cell,the cut-off voltage and saturation current are $0.6 \ V$ and $18 \ mA$ respectively. If the same source is placed at a distance of $0.6 \ m$ from the photoelectric cell,then:

The solution of the differential equation $\frac{dy}{dx} = \frac{xy+y}{xy+x}$ is