One says, “Give me a hundred, friend ! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you.” Tell me whatistheamount of their (respective) capital ? [From the Bijaganita of Bhaskara II]

Solve it graphically Shruti and Swati each have certain number of pens. Shruti says to Swati, “If you give me 10 of your pens, I will have twice the number of pens left with you. Swati replies, ‘‘If you give me 10 of your pens, I will have the same number of pens as left with you. Find the number of pens with Shruti and Swati separately.

Solve the following riddles,you may yourself construct such riddles. Who am I? Tell me who I am I shall give a pertty clue! You will get me back If you take me out of twenty two!?

classically an electron can be in any orbit around nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, thousand times bigger than its typical size? Thequestion had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as followswith the basic constants of nature e, me, c and see if we can get a quantity with the dimensions of length that is roughly equal to the known size of an atom (~ 10 m).- You will find that the length obtained above is many orders of magnitude smaller than the atomic dimensions. Further, it involves c. But energies of atoms are mostly in non-relativistic domain where c is not expected to play any role. This is what may have suggested Bohr to discard c and look for else h had already made its appearance elsewhere. Bohr lay in recognising that h, m_e , and e will yield the right atomic size. Construct a quantity with the dimension of length from h, me, and e and confirm that its numerical value has indeed the correct order of magnitude.

Classically, an electron can be in any orbit around the nucleus of an atom. Then what determines the typical atomic size? Why is an atom not, say, thousand times bigger than its typical size? The question had greatly puzzled Bohr before he arrived at his famous model of the atom that you have learnt in the text. To simulate what he might well have done before his discovery, let us play as follows with the basic constants of and see if we can get a quantity with the dimensions of length that is roughly equal to the known of an atom (~ 10^ -10 m).- Construct a quantity with the dimensions of length from the fundamental constants e, m_e , and c. Determine its numerical value.

Solve the following riddles,you may yourself construct such riddles. Who am I? I am a special number Take away from me a six! A whole cricket team You will still be able to fix!.

"Give me a living cell of any plant and I will give you a thousand plants of the same type". Is this only a slogan or is it scientifically possible? Write you’re your comments and justify them.

Ashwin went to a shopkeeper who was Mathematcis graduate asked him that "Uncle I want chocolates to distribute among my friends for my birthday but I have no money to pay for it."Shopkeeper says "I giving you two numbers x=1/(3-2sqrt2) and y=1/(3+2sqrt2) . find the values of thier sum, prodcut sum of thier square and sum of thier cubes. then I will give you one of these resulting values as number of chocolates at free of cost: Find all the four values.