There is a paternity dispute for a child'. Which technique can solve the problem? Discuss the principle involved.

Can a disease be detected before its symtoms appear? Name the principle involved.

Who developed the technique of electrophoresis and the principle on which it is based?

Carefully observe the followig figurue Name atleast three plants for which this technique can be employed for their commercial production.

A food crop which may help in solving the problem of night blindness in developing countries is :

Assertion : The charge on a conductor can be transferred to a hollow spherical conductor irrespective of the potential, to which it gets raised Reason : It is because of the principle of the spherical capacitor.

The normal activity of living carbon-containing matter is found to be about 15 decays per minute for every gram of carbon. This activity arises from the small proportion of radioactive "_6^14C present with the stable carbon isotope "_6^12C . When the organism is dead, its interaction with the atmosphere (which maintains the above equilibrium activity) ceases and its activity begins to drop. From the known half-life (5730 years) of "_6^14C , and the measured activity, the age of the specimen can be approximately estimated. This is the principle of "_6^14C dating used in archaeology. Suppose a specimen from Mohenjodaro gives an activity of 9 decays per minute per gram of carbon. Estimate the approximate age of the Indus-Valley civilisation.

A technology which has found immense use in solving cases of disputed parentage is:

A man rides his motorcylcle at the speed of 50 km/hour. He has to spend Rs.2 per km on petrol. If the rides it as a faster speed of 80 km/hour, the petrol cost increases to Rs.3 per km. he has atmost Rs.120 to spend on petrol and one hour's time, He wishes to find the maximum distance that he can travel Express this problem as a linear programming problem and solve it graphically to find the maximum distance he can travel.

n different toys have to be distributed among n children. Find the number of ways in which these toys can be distributed so that exactly one child gets no toy.

In each of the problems below, show the different stages of mathematical modelling for solving the problems. An ornithologist wants to estimate the number of parrots in a large field. She uses a net to catch some, and catches 32 parrots, which she ringed and sets free. The following week she manages to net 40 parrots, of which 8 are ringed. : What fraction of her second catch is ringed ?