In which of the following reactions will cyanide be obtained as a major product?

If in a $\triangle ABC$,$r_3 = r_1 + r_2 + r$,then $\angle A + \angle B$ is equal to (in $^{\circ}$)

During the reaction of permanganate with thiosulphate,the change in oxidation state of manganese occurs by a value of $3$. Identify which of the below media will favour the reaction.

In which of the following pairs,the central atoms have the same number of lone pairs of electrons?

Consider an ionic solid $M X$ with $NaCl$ structure. Construct a new structure $( Z )$ whose unit cell is constructed from the unit cell of $M X$ following the sequential instructions given below. Neglect the charge balance.

$(i)$ Remove all the anions ( $X$ ) except the central one

$(ii)$ Replace all the face centered cations $(M)$ by anions $(X)$

$(iii)$ Remove all the corner cations $(M)$

$(iv)$ Replace the central anion ( $X$ ) with cation $(M)$

The value of $\left(\frac{\text { number of anions }}{\text { number of cations }}\right)$ in $Z$ is. . . . .

An ideal gas expands isothermally from a volume $V_1$ to $V_2$ and is then compressed to the original volume $V_1$ adiabatically. The initial pressure is $P_1$ and the final pressure is $P_3$. If the total work done is $W$,then: