The value of $a$ for which the system of equations $a^3x + (a + 1)^3y + (a + 2)^3z = 0$,$ax + (a + 1)y + (a + 2)z = 0$,$x + y + z = 0$ has a non-zero solution is

The $emf$ (in $V$) of a Daniell cell containing $0.1 \ M$ $ZnSO_4$ and $0.01 \ M$ $CuSO_4$ solutions at their respective electrodes is
$(E_{Cu^{2+} / Cu}^{\circ} = +0.34 \ V; E_{Zn^{2+} / Zn}^{\circ} = -0.76 \ V)$

In which of the following reactions,the concentration of the product is higher than the concentration of reactant at equilibrium? ($K =$ equilibrium constant)

$G-6-P$ dehydrogenase deficiency is associated with haemolysis of:

If $u=\sin ^{-1}\left(\frac{x}{y}\right)+\tan ^{-1}\left(\frac{y}{x}\right)$,then the value of $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}$ is

Two cells $E_1$ and $E_2$ having equal e.m.f '$E$' and internal resistances $r_1$ and $r_2$ $(r_1 > r_2)$ respectively are connected in series. This combination is connected to an external resistance '$R$'. It is observed that the potential difference across the cell $E_1$ becomes zero. The value of $R$ will be