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

Think of this puzzle What do you need to find a chosen number from this square? Four of the clues below are true but do nothing to help in finding the number. Four of the clues are necessary for finding it. Here are eight clues to use: a. The number is greater than 9. b. The number is not a multiple of 10. c. The number is a multiple of 7. d. The number is odd. e. The number is not a multiple of 11. f. The number is less than 200. g. Its ones digit is larger than its tens digit. h. Its tens digit is odd. What is the number? Can you sort out the four clues that help and the four clues that do not help in finding it? First follow the clues and strike off the number which comes out from it. Like - from the first clue we come to know that the number is not from 1 to 9. (strike off numbers from 1 to 9). After completing the puzzle, see which clue is important and which is not?

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.

(Street plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East_West direction. All the other streets of the city run parallel to these roads and are 200m apart. There are 5 streets in each direaction. Using 1 cm =200cm, draw a model of teh city on your note book. Represent the roads/streets by single lines. There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North-South directin and another in the East-West direction. Each cross street is rreferred to in the following manner, If the 2 ^(nd) steeet running in teh North-South direction 5 ^(th) in the East-West direction meet at some crossing, then we will call this cross-street (2,5). Using this convection, find: How many cross-streets can be referred at as (4,3)

(Street plan): A city has two main roads which cross each other at the centre of the city. These two roads are along the North-South direction and East_West direction. All the other streets of the city run parallel to these roads and are 200m apart. There are 5 streets in each direaction. Using 1 cm =200cm, draw a model of teh city on your note book. Represent the roads/streets by single lines. There are many cross-streets in your model. A particular cross-street is made by two streets, one running in the North-South directin and another in the East-West direction. Each cross street is rreferred to in the following manner, If the 2 ^(nd) steeet running in teh North-South direction 5 ^(th) in the East-West direction meet at some crossing, then we will call this cross-street (2,5). Using this convection, find: How many cross-streets can be referred to as (3,4)

The boiling point elevation and freezing point depression of solutions have a number of partical applications. Ethylene glycol (CH_(2)OH-CH_(2)OH) is used in automobile radiatiors as an antifreeze because it lowers the freezing point of the coolant. The same substance also helps to prevent the radiator coolant from boiling away by elevating the boiling point. Ethylene glycol has low vapour pressure. We can also use glycerol as an antifreeze. In order for the boiling point elevation to occur, the solute must be non-volatile, but no such restriction applies to freezing point depression. For example, methanol (CH_(3)OH) , a fairly volatile liquid that boils only at 65^(@)C , is sometimes used as an antifreeze in automobile radiators. 124 g each of the two reagents glycol and glycerol are added in 5 kg of water of the radiators in two cars. Which of the following statements is wrong?