In a saturated solution of $Mg(OH)_2$,the degree of dissociation of $Mg(OH)_2$ is $\alpha$. Find the concentration $(C)$ of $Mg(OH)_2$ if the concentration of $[OH^{-}]$ is $2$.

Complete hydrolysis of cellulose yields ........

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

In the following circuit,$PN$-junction diodes $D_1, D_2$ and $D_3$ are ideal. For the following potentials of $A$ and $B$,find the correct increasing order of equivalent resistance between $A$ and $B$:
$(i) V_A = -10\,V, V_B = -5\,V$
$(ii) V_A = -5\,V, V_B = -10\,V$
$(iii) V_A = -4\,V, V_B = -12\,V$

At temperature $T \ K$,the $rms$ speed of $CO_2$ gas is $x \ cm/s$. At what temperature (in $Kelvin$) will the $rms$ speed of nitrous oxide $(N_2O)$ be $4x \ cm/s$ (in $T$)?

Which of the following statements is true?