The electrode potentials for $Cu^{2+}_{(aq)} + e^- \to Cu^{+}_{(aq)}$ and $Cu^{+}_{(aq)} + e^- \to Cu_{(s)}$ are $+0.15 \ V$ and $+0.50 \ V$ respectively. The value of $E^\circ$ for the reaction $Cu^{2+}_{(aq)} + 2e^- \to Cu_{(s)}$ will be ............ $V$.

If the circle $x^2 + y^2 = a^2$ intersects the hyperbola $xy = c^2$ in four points $P(x_1, y_1), Q(x_2, y_2), R(x_3, y_3), S(x_4, y_4)$,then:

What are the oxidation numbers of nitrogen in $NH_4NO_3$?

Consider the depicted hydrogen $( H )$ in the hydrocarbons given below. The most acidic hydrogen $( H )$ is

$A$ rod of glass $(\mu = 1.5)$ with a square cross-section is bent into the shape shown in the figure. $A$ parallel beam of light falls on the plane flat surface $A$ as shown. If $d$ is the width of a side and $R$ is the radius of the inner circular arc, then for what maximum value of $\frac{d}{R}$ will light entering the glass slab through surface $A$ emerge from the glass through surface $B$?

Which of the following exhibits moderate electrical conductivity?