If the coefficients $a$ and $b$ of a quadratic expression $x^2+ax+b$ are chosen from the sets $A=\{3,4,5\}$ and $B=\{1,2,3,4\}$ respectively, then the probability that the equation $x^2+ax+b=0$ has real roots is

Three rods $A, B,$ and $C$ of thermal conductivities $K, 2K,$ and $4K$ and equal cross-sectional areas and lengths $2l, l,$ and $l$ respectively are connected as shown in the figure. If the ends of the rods are maintained at temperatures $100\ ^oC, 50\ ^oC,$ and $0\ ^oC$ respectively,then the temperature $\theta$ of the junction is

The major products obtained from the reactions in List$-II$ are the reactants for the named reactions mentioned in List$-I.$ Match each entry in List$-I$ with the appropriate entry in List$-II$ and choose the correct options.

List$-I$	List$-II$
$(P)$ Stephen reaction	$(1)$ Toluene $\xrightarrow{\substack{\text { (i) } CrO _2 Cl _2 / CS _2 \\ \text { (ii) } H _3 O +}}$
$(Q)$ Sandmeyer reaction	$(2)$ Benzoic acid $\xrightarrow{\substack{\text { (i) } PCl _5 \\ \text { (iii) } NH _3 \\ \text { (iii) } P _4 O _{10}, \Delta}}$
$(R)$ Hoffmann bromamide degradation reaction	$(3)$ Nitrobenzene $\xrightarrow{\begin{array}{l}\text { (i) } Fe , HCl \\ \text { (ii) } HCl , NaNO _2 \\ \text { (273-278 K), } H _2 O \end{array}}$
$(S)$ Cannizzaro reaction	$(4)$ Toluene $\xrightarrow{\begin{array}{l}\text { (i) } Cl _2 / hv , H _2 O \\ \text { (ii) } \text {Tollen 's reagent } \\ \text { (iii) } SO _2 Cl _2 \\ \text { (iv) } NH _3\end{array}}$
	$(5)$ Aniline $\xrightarrow{\substack{\text { (i) }\left( CH _3 CO \right)_2 O , \text { Pyridine } \\ \text { (ii) } HN O _3 H _{2} SO _4, 288 K \\ \text { (iii) } aq . NaOH }}$

If the internal energy of an ideal gas decreases by the same amount as the work done by the system,the process is

What is obtained by the electrolysis of carnallite?

Two wires $A$ and $B$ are of lengths $40 \ cm$ and $30 \ cm$. $A$ is bent into a circle of radius $r$ and $B$ into an arc of radius $r$. $A$ current $i_1$ is passed through $A$ and $i_2$ through $B$. To have the same magnetic inductions at the centre,the ratio of $i_1: i_2$ is