A market research group conducted a survey of 1000 consumers and reported that 720. consumers liked product A and 450 liked product B. What is the least number that must have like both products ?

In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products Aand B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only.

Represent the following situations mathematically: A toys industry produces a certain number of toys in a day. The cost of production of each toy (in rupese) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. We would like to find out the number of toys produced on that day.

Seeing the growing cases of diabetes and depression among young children, Mr. Lugani, the principal of one reputed school organized a seminar in which he invited parents and principals. They all resolved this issue by strictly banning junk food in schools and introducing healthy snacks and drinks like soup, lassi milk, etc. in school canteens. They also decided to make compulsory half an hour of daily physical activities for the students in the morning assembly. After six months, Mr. Lugani conducted the health survey in most of the schools and discovered a tremendous improvement in the health of the students. After reading the above passage, answer the following question : What are the values (at least two) displayed by Mr. Lugani ?

Read the given passage and answers following questions : Zeolites are alumino-silicates that are micro-porous in nature. Zeolites have a honeycomb like structure, which makes them shape-selective catalysts. They have an extended 3D-nelwork of silicates in which some silicon atoms are replaced by aluminium atoms, giving them an Al-O-Si framework. The reactions taking place in zeolites are very sensitive to the pores and cavity size of the zeolites. Zeolites are commonly used in the petrochemical industry. A catalytic reaction which depends upon the pore structure of the catalyst and on the size of the reactant and the product molecules is called shape-selective catalysis. For example, catalysis by zeolites is a shape selective catalysis. The pore size present in the zeolites ranges from 260-740 pm. Thus, molecules having a pore size more than this cannot enter the zeolite and undergo the reaction. What is the pore size of Zeolites ?

True or False Some vitamin like B12 are products of microorganism.

A soft drinks firm has two bottling plants, one located at P and the other located at Q. each plant produces three different soft drinks A, B and C. The capacities of two plants in number of bottles per day, are as follows: A market survey indicates that during the month of April, there will be a demand of 24000 bottles of A, 16000 bottles of B and 48000 bottles of C. The cost of running the two plants P and Q are respectively Rs.6000 and Rs.4000 per day. find graphically, the number of days for which either of the two plants P and Q should be run in the month of April so as to minimize production cost while still meeting the market demand.

Solve the problems, John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.

Represent the following situations mathematically: John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. We would like to find out how many marbles they had to start with.

An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent, is