One kind of cake requires 200g of flour and 25g of fat, and another kind of cake requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes.

One kind of cake requires 100 gm of flour and 50 gm of fat and another kind of cake requires 50 gm of flour and 100 gm of fat. Find the maximum number of cakes that can be made from 4 kg of flour and 5 kg of fat. Form a linear programming problem and solve it graphically.

One kind of cake requires 300 gm of flour and 15 gm of fat and another kind of cake requires 150 gm of flour and 30 gm of fat. Find the maximum number of cakes that can be made from 7.5 kg of flour and 600 gm of fat. Form a linear programming problem and solve it graphically.

Every gram of wheat provides 0.1 g of protien and 0.25 g of carbohydrates. The corresponding values for rice are 0.05 g and 0.5 g respectively. Wheat costs Rs 4 per kg and rice Rs 6 per kg. The minimum daily requirements of protien and carbohydrates for an average child are 50 g and 200 g respectively. In what quantities should wheat and rice be mixed in the daily diet so as to provide the maximum daily requirements of protien and carbohydrates at minimum cost? Frame a LPP and solve it graphically.

A magnetic field of 100 G (1 G = 10^-4 T) is required which is uniform in a region of linear dimension about 10 cm and area of cross-section about 10^-3 m^2 . The maximum current-carrying capacity of a given coil of wire is 15 A and the number of turns per unit length that can be wound round a core is at most 1000 turns m^-1 . Suggest some appropriate design particulars of a solenoid for the required purpose. Assume the core is not ferromagnetic.

Gasoline has an enthalpy of combustion 24000 kJ/mol gallon. When gasoline burns in an automobile engine, approximately 30% of the energy released is used to produce mechanical work. The remainder is lost as heat transfer to the engine's cooling system. As a start on estimating how much heat transfer is required, calculate what mass of water could be heated from 25^(@)C to 75^(@)C by the combustion of 1.0 gallon of gasoline in an automobile? (Given : C(H_(2)O)=4.18 J//g^(@)C ) a) 34.45 kg b) 80.383 kg c) 22 kg d) 224 kg

A 10 kW drilling machine is used to drill a bore in a small aluminium block of mass 8.0 kg. How much is the rise in temperature of the block in 2.5 minutes, assuming 50% of power is used up in heating the machine itself or lost to the surroundings. Specific heat of aluminium = 0.91 J g^-1 ^@C^-1

A copper atom consists of copper nucleus surrounded by 29 electrons. The atomic weight of copper is 63.5mol e^(-1) . Let us now take two pieces of copper each weighing 10g. Let us trandfer one elcetron from one piece to another for every 100 atoms in that piece. What will be the Coulomb force between the two pieces after the trandfer of electrons, if they are 1cm apart? Avogadro number= 6xx10^(23) mol e^(-1) , charge on an electron =- 1.6xx10^(-19)C.

1.0 g of a monobassic acid HA in 100 g water lowers the freezing point by 0.155 K. IF 0.75 g, of same acid requires 25 mL of N/5 NaOH solution for complete neutralisation then %, degree of ionization of acid is ( K_(f) of H_(2)O = 1.86 K kg "mol"^(-1) ):