A sweet seller has 420 kaju baths and 130 badam barfis. She wants to stack them in such a way that each stack has the same number and they take up the least area of the tray. What is the number that can be placed in each stack for this purpose ?

In a potato race, a bucket is placed at the starting point, which is 5m from the first potato and the other potatoes are placed 3m apart in a straight line. These are ten potatoes in the line. (see fig) Each competitor starts from the bucket, picks up the nearest potato, runs back with it, dorps it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

In an examination, Yamini has to select 4 questions from each part. There are 6, 7 and 8 questions in Part I, Part II and Part III respectively. What is the number of possible combinations in which she can choose the questions ?

In a potato race a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line (see Fig.) Each competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runsto the bucket to drop it in, and the continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run ?

A packet of plain biscuits costs Rs 6 and that of chocolate bisuits costs Rs 9. A house-wife has Rs 72 and wants to buy at least three packets of plain biscuits and at least four of chocolate biscuits. How many of each type should she buy so that she can have maximum number of packets? Make it as a LPP and solve it graphically.

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in the party, is :