Draw a pyramid from following details and explain in brief. Quantities of organisms are given-Hawks-50, plants-1000.rabbit and mouse-250 + 250, pythons and lizard - 100 + 50 respectively.

The resistances of a platinum resistance thermometer at the ice point, the steam point and the boiling point of sulphur are 2.50, 3.50 and 6.50 Omega respectively. Find the boiling point of sulphur on the platinum scale. The ice point and the steam point measure 0^0 and 100^0 respectively.

A manufacturer produces three products x, y, z which he sells in two markets. Annual sales are indicated below: {:("Market",,"Products",),(I,"10,000","2,000","18,000"),(II,"6,000","20,000","8,000"):} (a) If unit sale prices of x, y and z are Rs. 2.50, Rs. 1.50 and Rs. 1.00, respectively, find the total revenue in each market with the help of matrix algebra. (b) If the unit costs of the above three commodities are Rs. 2.00, Rs. 1.00 and 50 paise respectively. Find the gross profit.

Two godwons A and B have grain capacity of 100 quintals and 50 quintals resepectively. They supply to 3 ration shopts,D, E and F whose requirements are 60,50 and 40 quintals respectively. The cost of transportion per quintal from the godwons to the shops are given in the following table : How should the supplies be transported in order that transportation cost is minimum ? What is the minimum cost ?

Answer the following questions . a. The earth's magnetic field varies from point is space. Does it also change with time ? It so , on what time scate does it change appreciably ? b. The earth's core is known to contain iron. Yet geologists do not regard this as a source of the earth's magnetism why ? c. The charged currents in the outer conducting regions of the earth's core are thought to be responsible for earth's magnetism . What might be the ' battery ' (i.e., the source of energy) to sustain these currents ? d. The earth may have even reversed the direction of its field several times during its history of 4 to 5 billion years. How can geologists know about the earth's field in such distant past ? e. The earth's field departs from its dipole substantially at large distances (greater than about 30,000 km) what agencies may be responsible for this distortion ? f. Interstellar space has an extremely weak magnetic field of the order of 10^(-12) T, Can such a weak field be of any significant consequence ? Explain. [Note : Exercise 2 is meant mainly to arouse your curiosity . Answers to some question above are tentative or unknown . Brief answers wherever possible are given at the end . For details , you should consult a good text on geomagnetism.]

In Fig (a) , the V_(BB) supply can be varied from 0 V to 5.0 V . The Si transistor has beta_(dc) = 250 and R_(B) = 100 kOmega , R_(C) = 1 k Omega , V_(C C) = 5.0 V . Assume that when the transistor is saturated , V_(CE) = 0V and V_(B E) = 0.8 V . Calculate (a) the minimum base current , for which the transistor will reach saturation .