Consider the pay-off table for two players as given below

(i) Find the saddle point the value of the game.

(ii) Give two equivalent linear programming problems for the above problem.

In a population of lions, the proportionate death rate is 0.55 per year and the proportionate birth rate is 0.45 per year. Formulate a model of the population. Solve the model and discuss its long term behavior. Also, find the equilibrium point of the model

A particle is executing Simple Harmonic Motion of amplitude 6 m and period 3⋅ 5 seconds. Find the maximum velocity of the particle.

A park has a stable population of birds. Prior to this situation, the birds’ population increased from an initial low level. When the population of birds was 1000, the proportionate birth rate was 40% per year and the proportionate death rate was 5% per year. When the population was 3,000, the proportionate birth rate was 30% and the proportionate death rate was 10%. Consider the population model under the following assumptions: 

(i) There is no migration and no exploitation.

(ii) The proportionate birth rate is a decreasing linear function of the population.

(iii) The proportionate death rate is an increasing linear function of the population. Show that

The population grows according to the logistic model.

Find the stable population size.

If the shooting of birds is allowed at the rate of 15% of the population per year, find the new equilibrium population

Write the limitations of the Malthusian model of population growth

The sales of a small factory since 2008 are as follows:

Using 2008 as the zero year, find the least-square trend-line equation.

Write the three-dimensional Gaussian model dispersion for the atmospheric pollution problem. Modify the model under the following assumptions: 

(i) Wind velocity is in only y -direction.

(ii) Mass transfer due to bulk motion in the y -direction overshadows the contributions due to mass diffusion.

(iii) Motion is in steady state.

(iv) Wind speed is constant.

(v) Diffusivities are constant in all the directions

Find the equilibrium price in a perfectly competitive market with the supply function   and the demand function D( p) = − p + .2 Using the static criterion of Walras, determine whether the price is stable or not.

Consider the blood flow in an artery following Poiseuille’s law. If the length of the artery is 3 cm, radius is 3 7 10− × cam and driving force is 3 5×10 dynes/cm2 , then using blood viscosity, µ = 0 ⋅ 027 poise, find the

(i) velocity u( y) and the maximum peak velocity of blood, and

(ii) shear stress at the wall of the artery.

A body is falling free in a vacuum. The fall is necessarily related to the gravitational acceleration g and the height h from which the body is dropped. Use dimensional analysis to show that the velocity V of the falling body satisfies the relation V /  = constant.

Cellular immunity

The genetic code

Carcinogens

Immobilised enzymes

List the different types of antibodies. What are the gross structural features of an antibody molecule? Name any three mechanisms by which these interact with antigens

Explain any three factors which modify the immune response.

Name the steps involved in the biosynthesis of a protein. Describe the first step in detail.

Give one similarity and one dissimilarity between the action of DNA polymerase and RNA polymerase. Describe the transcriptional process

What is the net result of calvin cycle? Explain the action of transketolase enzyme giving structures.

What do you understand by the term committed step? Describe in brief how the committed step in case of glycolysis is regulated