A company rents three warehouses $$A, B$$ and $$C$$ from which they supply bearings to two customers $$P$$ and $$Q.$$ The profit per piece, the annual demands of the customers and the supplies available from the warehouses are shown below:

As the company is not able to meet the demands, it is proposed to replace warehouse $$C$$ with a warehouse rented at $$D$$ whose supply capacity would be $$5000.$$ The expected profit would be Rs.$$6$$ and Rs.$$5$$ per piece distributed to $$P$$ and $$Q$$ respectively. The rental charges for warehouse $$D$$ is Rs.$$5,000$$ per year. Find the increase in the profit of the company after replacing warehouse $$C$$ by $$D.$$

A small element at the critical section of a component in bi-axial state of stress with the two principal stresses being $$360$$ $$MPa$$ and $$140$$ $$MPa.$$ The maximum working stress according to distortion energy theory is

To make a worm drive reversible, it is necessary to increase

Match the following
List - $${\rm I}$$
(a)$$\,\,\,\,\,$$ Automobile wheel mounting on axle
(b)$$\,\,\,\,\,$$ High speed grinding spindle
(c)$$\,\,\,\,\,$$ $${\rm IC}$$ - Engine connecting rod
(d)$$\,\,\,\,\,$$ Leaf spring eye mounting

List - $${\rm II}$$
1.$$\,\,\,\,\,$$ Magneto bearing
2.$$\,\,\,\,\,$$ Angular contact bearing
3.$$\,\,\,\,\,$$ Taper roller bearing
4.$$\,\,\,\,\,$$ Hydrodynamic journal bearing
5.$$\,\,\,\,\,$$ Sintered metal bearing
6.$$\,\,\,\,\,$$ Teflon/Nylon bush