One kind of cake requires 200 g of flour and 25 g of fat and another kind of cake requires 100 g flour and 50g of fat. Find the maximum number of cakes which can be made from 5 kg of flour and 1 kg of fat assuming that there is not shortage of the other ingredients used in making the cakes.

A string of linear mass density 0.5 g cm^-1 and a total length 30 cm is tied to a fixed wall at one end and to a frictionless ring at the other end. The ring can move on a vertical rod. A wave pulse is produced on the string which moves towards the ring at a speed of 20 cm s^-1 . The pulse is symmetric about its maximum which is located at a distance of 20 cm from the end joined to the ring. (a) Assuming that the wave is reflected from the ends without loss of energy, find the time taken by the string to regain its shape. (b) The shape of the string changes periodically with time. Find this time period. (c) What is the tension in the string ?

The pulley shown in figure has a radius of 20 cm and moment of inertial 0.2 kg-m^2. The string going over it is attached at one end to a vertical sprign of spring constant 50 N/m fixed from below and supports a 1 kg mas at other end. The system is released from rest with the spring at its natural length. Find the speed of the block when it has desceds through 10 cm. Take g=10 m/s^2 .

A bakery owner makes two types of cakes A and B. three machines are needed for this pupose. The time in (minutes) required for each type of cake in each machine is given below. Each machines is available for atmost 6 hours per day. Assume that all cakes will be sold out every day. The bakery owner wants to make maximum pforit per day by making Rs. 7.5 from type A and Rs. 5 from type B. a Write the objective function by defining suitable variables. b Write the constraints. c Find the maximum profit graphically.

One end of a metal wire is fixed to a ceiling and a load of 2 kg hangs from the other end. A similar wire is attached to the bottom of the load and another load of 1 kg hangs from this lower wire. Find the longitudinal strain in both wires. Area of cross section of each wire is 0.005 cm^2 and Young modulus of the metal is 2.0xx10^11 Nm^-2. Take g=10ms^-2

Every gram of wheat provides 0.1g of proteins and 0.25g of carbohydrates. The corresponding values of rice are 0.05g and 0.5g respectively. Wheat costs Rs 2 per kg and rice Rs 8. The minimum daily requirements of protein and carbohydrates for an average child are 50g and 200g respectively. In what quantities, should wheat and rice be mixed in the daily diet to provide the minimum daily re-quirement of protein and carbohydrates at minimum cost.

A light rope fixed at one end of a wooden clamp on the ground passes over a tree branch and hangs on the other side. It makes an angle of 30^0 with the ground. A man weighing (60 kg) wants to climb up the rope. The wooden clamp can come out of the ground if an upward force greater than 360 N is applied it. Find the maximum acceleration in the upward direction with which the man can climb safely. Neglect friction at the tree branch. Take g=10 m/s^2

A wire of area of cross section 3.0mm^2 and natural length 50 cm is fixed at one end and a mas of 2.1 kg is hung from the other end. Find the elastic potential energy stored in the wire in steady state. Young modulus of the material of the wire =1.9xx10^11Nm^-2. Take g=10ms^-2