A double-decker bus carry `(u+l)` passengers, `u` in the upper deck and `l` in the lower deck. Find the number of ways in which the `u+l` passengers can be distributed in the two decks, if `r(lt=l)` particular passengers refuse to go in the upper deck and `s(lt=u)` refuse to sit in the lower deck.

A double-decker bus carry (u+e) passengers, u in the upper deck and e in the lower deck. Find the number of ways in which the u+e passengers can be distributed in the two decks, if r(lt=e) particular passengers refuse to go in the upper deck and s(lt=u) refuse to sit in the lower deck.

Passengers are to travel by a double decked bus which can accommodate 13 in the upper deck and 7 in the lower deck. Find the number of ways that they can be distributed if 5 refuse to sit in the upper deck and 8 refuse to sit in the lower deck.

A double -decker bus has 5 empty seats in the upper deck and 5 empty seats in the lower deck. 10 people board the bus of which 2 are old people and 3 are children. The children refuse to take seats lower deck while old people insist to stay lower deck. How many different sitting arrangements of the people are possible ?

Number of ways in which the letters of the word ‘B U L B U L’ can be arranged in a line in any order is also equal to the:

Le Chatelier's Principle If a system at equilibrium is subjected to a change of any one of the factors such as concentration, pressure or temperature, the system adjusts itself in such a way as to nullify the effect of that change. Change of pressure : If a system consists of gases, then the concentration of all the components can be alterd by changing the pressure. To increase the pressure on the system,the volume has to be decreased proportionally. The total number of mols per unit volume will now be more and the equilibrium will shift in the direction in which there is a decrease in number of moles i,e. towards the direction in which there can be decrease in pressure. Effect of pressure on melting point : There are two types of solids: (a) Solids whose volume decreases on melting e.g., ice,diamond carborundum magnesium nitride and quratz. Solids (higher volume) hArr Liquid (lower volume) The process of melting is facilitated at high pressure, thus, melting point is lowerd. (b) Solids whose volume increase on melting e.g.,Fe,Cu,Ag,Au,etc. Solid (lower volume) hArr Liquid (higher volume) In this case the process of melting become difficult at high pressure, thus melting point becomes high. (c) Solubility of substances : When solid substances are dissolved in water, either heat is evolved (exothermic) or heat is absorbed (endothermic). KCI+aqhArrKCI(aq)-heat In such cases, solubility increase with increase in temperature. Consider the case of KOH, when this is dissolved,heat is evolved. KOH+aqhArrKOH(aq)+heat In such cases, solubility decrease with increase in temperature. (d) Solubility of gases in liquids : When a gas dissolves in liquid,there is decrease in volume. Thus increase of pressure will favour the dissolution of gas in liquid. Au(s) hArr Au(l) Above equsilibrium is favoured at :

A heavy block B is sliding with constant velocity u=5m//s on a horizontal table. The width of the block is L=4m . There is an insect A at distance d=3m from the block as shown in the figure. The insect wants to cross to the oposite side of the table. It begins to crawl at a constant velocity v at the instant shown in the figure. Find the least value of v (in m/s) for which the insect can cross to the other side without getting hit by the block.

Two identical unifrom rods OA and OB each of length l and mass m are connected to each other by a massless pin connection (both the rods can rotate about O which is free to move), that allows free rotation. The assembly is kept on a frictionless horizontal plane. Now two point masses each of mass m moving with speed u perpendicular to the AB and hit the assembly inelastically at points A and B as shown in the figure. Find the angular speed of rods just after the collision

Two identical unifrom rods OA and OB each of length l and mass m are connected to each other by a massless pin connection (both the rods can rotate about O which is free to move), that allows free rotation. The assembly is kept on a frictionless horizontal plane. Now two point masses each of mass m moving with speed u perpendicular to the AB and hit the assembly inelastically at points A and B as shown in the figure. Find the speed of centre of rod AO just after the collision.

Two long concetric cylindrical conductors of radii a and b (b lt a) are maintained at a potential difference V and carry equal and opposite currents l. Show that an electron with a particular velocity u parallel to the axis may travel underivated in the evacuated region between the conductors, and calculate u when a = 50 mm, b = 2.0 mm, V = 50 V and l = 100 A. It is also possible for the electron to travel in a helical path. By regarding such a path as the combination of a circular motion perpendicular to the axis with a steady velocity parallel to the axis, indicate without detailed mathematics how this comes about.

Shows a wire of length l which can slide on a U- shaped rail of negligible resistance. The resistance of the wire is R. The wire is pulled ot the right with a constant speed v. Draw an equivalent circuit diagram representing the induced emf by a battery. Find the current in the wire usingj this diagram.