Q.For the equlibrium, A ⇌ 2B + Heat, the number of 'A' molecules increases if
a. volume is increased
b. temperature is increased
c. catalyst is added
d. concerntration of B is decreased

Applying Le Chatelier's principle to each factor in turn: (1) Concentration -- increasing the concentration of a reactant or product shifts equilibrium in the direction that consumes the added species (e.g. adding extra H2 to the Haber equilibrium $N_2(g)+3H_2(g)\rightleftharpoons 2NH_3(g)+\text{Heat}$ shifts it forward, increasing NH3 yield); the value of $K_c$ itself is unaffected. (2) Pressure/volume -- only affects equilibria where the number of gas moles differs between reactants and products; decreasing pressure (increasing volume) shifts equilibrium toward the side with MORE gas moles (e.g. $N_2O_4(g)\rightleftharpoons 2NO_2(g)$ shifts right, deepening its brown colour, when pressure is decreased), while increasing pressure shifts it toward the side with FEWER gas moles; again $K_c$ is unaffected. (3) Temperature -- increasing temperature shifts equilibrium in the endothermic direction (e.g. for the exothermic forward reaction $CO(g)+2H_2(g)\rightleftharpoons CH_3OH(g)+\text{Heat}$, raising temperature shifts equilibrium left, and unlike concentration/pressure changes, this genuinely changes the numerical VALUE of $K_c$, which falls as temperature rises for an exothermic forward reaction). (4) Catalyst -- speeds up both the forward and reverse reactions equally (by lowering the activation energy of each by the same amount), so equilibrium is reached faster but its position and the value of $K_c$ are both completely unaffected. These factors are applied together in the industrial Haber process, which uses an optimum temperature of about 773 K (balancing the exothermic reaction's equilibrium yield against a workable reaction rate) and an optimum pressure of about 250 atm (favouring the mole-reducing forward reaction without making the iron/molybdenum catalyst inefficient) to maximise the practical yield of ammonia.