If $\alpha$ is a non-real root of the equation $x^6-1=0$,then $\frac{\alpha^2+\alpha^3+\alpha^4+\alpha^5}{\alpha+1}$ is equal to

$A$ straight wire of length $20 \ cm$ carrying a current of $\frac{3}{\pi^2} \ A$ is bent in the form of a circle. The magnetic field at the centre of the circle is

At $25 \ ^\circ C,$ the solubility product of $Mg(OH)_2$ is $1.0 \times 10^{-11}.$ At which $pH$ will $Mg^{2+}$ ions start precipitating in the form of $Mg(OH)_2$ from a solution of $0.001 \ M \ Mg^{2+}$ ions?

Which of the following elements does not show allotropy?

The solution of $\frac{dy}{dx} + \frac{1}{3}y = 1$ is

Which of the following orders are correct?
$I$. Thermal stability : $BeSO_4 < MgSO_4 < CaSO_4 < SrSO_4 < BaSO_4$
$II$. Basic nature : $ZnO > BeO > MgO > CaO$
$III$. Solubility in water : $LiOH > NaOH > KOH > RbOH > CsOH$
$IV$. Melting point : $NaCl > KCl > RbCl > CsCl > LiCl$