The minimum value of $|z-1|+|z-5|$ is

Which of the following pairs is incorrectly matched?

If $\alpha, \beta$ are the roots of the equation $x^2+bx+c=0$ and $\alpha+h, \beta+h$ are the roots of the equation $x^2+qx+r=0$,then $h$ is equal to

Which of the following is a correctly matched pair?

The displacements of two particles of same mass executing $SHM$ are represented by the equations $x_1 = 4 \sin \left(10 t + \frac{\pi}{6}\right)$ and $x_2 = 5 \cos (\omega t)$. The value of $\omega$ for which the energies of both the particles remain same is (in $\text{ unit}$)

Which of the following substances is obtained from the fungus $Claviceps$ $\text{purpurea}$ (ergot)?