In which of the following situations, does the list of numbers involved make an arithmetic progression, and why ? :- The amount of air present in a cylinder when a vacuum pump removes `1/4` of the air remaining in the cylinder at a time.

In which of the following situations, does the list of numbers involved make an arithmetic progression, and why ? :- The taxi fare after each km when the fare is $ 15 for the first km and $ 8 for each additional km.

In which of the following situations, does the list of numbers involved make an arithmetic progression, and why ? :- The amount of money in the account every year when ? 10000 is deposited at compound interest at 8% per annum.

In which of the following situations, does the list of numbers involved make an arithmetic progression, and why ? :-The cost of digging a well after every metre of digging, when it costs $150 for the first metre and rises by $50 for each subsequent metre.

A sulphate salt of the group 2 element of the periodic table is a white, soft substance, which can be molded into different shapes by making its dough. When this compound is left in open for some time, it becomes a solid mass and cannot be used for molding purposes. Identify the sulphate salt and why does the show such a behaviour? give one reaciton involved.

Radioactive disintegration is a first order reaction and its rate depends only upon the nature of nucleus and does not depend upon external factors like temperature and pressure. The rate of radioactive disintegration (Activity) is represented as -(dN)/(dt)=lambdaN Where lambda= decay constant, N= number of nuclei at time t, N_(0) =intial no. of nuclei. The above equation after integration can be represented as lambda=(2.303)/(t)log((N_(0))/(N)) Calculate the half-life period of a radioactive element which remains only 1//16 of its original amount in 4740 years: a) 1185 years b) 2370 years c) 52.5 years d) none of these