CBSE Guess > Papers > Important Questions > Class XII > 2010 > Maths > Mathematics By Mr. Kalpesh
CBSE CLASS XII
Q. 1. Solve the following linear programming problem graphically:
Q. 2. A medical company has factories at two places A and B. From these places, supply is made to each of its three situated at P, Q and R. The monthly requirements of the agencies are respectively 40 , 40 and 50 packets of the medicine while the production capacity of factories A and B are 60 and 70 packets respectively. The transportation cost per packet from the factories to the agencies are given below
| To / From | A | B |
| P | 50 | 40 |
| Q | 40 | 20 |
| R | 30 | 50 |
How many packets from each factory be transported to each agency so that cost of transportation is minimum? Also find the minimum cost?
Q. 3. A man owns a field of area 1000 sq meter. He wants to plant trees in it . He has a sum of Rs. 1400 to purchase young trees. He has the choice of two types of trees .Type A requires 10 sq meter of ground per tree and costs Rs. 20 per tree and type B requires 20 sq meter of ground per tree and costs Rs. 25 per tree. When fully grown, type A produces an average of 20 kg of fruits which can be sold at a profit of Rs. 2 per kg and type B produces an average of 40 kg of fruits which can be sold at a profit of Rs. 1.50 per kg. How many trees of each type should be planted to achieve maximum profit when the trees are fully grown? What is the maximum profit?
Q. 4. A firm is engaged in breeding goats. The goats are fed on various products grown on the farm. They need certain nutrients, named as X, Y and Z. The goats are fed on two products A and B .One unit of product A contain 36 units of X, 3 units of Y and 20 units of Z , while one unit of products B contain 6 units of X , 12 units of Y and 10 units of Z . The minimum requirement of X,Y and Z is 108 units , 36 units and 100 units ,respectively . Product A costs Rs. 20 per unit and product B costs Rs. 40 per unit. How many units of each product must be taken to minimize the cost?
Q. 5. A husband and wife appear in an interview for two vacancies for the same post. The probability of husband’s selection is 
and that of wife’s selection is
. what is the probability that
- Both of them will be selected?
- Only one of them will be selected?
- None of them will be selected?
- At least one of them will be selected?
Q. 6. A laboratory blood test is 99% effective in detecting a certain disease when it is, in fact, present. However, test also yields a false positive result for 0.5% of the healthy person tested (i.e. if a healthy person is tested, then with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?
Q. 7. Show that if a coin is tossed n times, the probability of not more then r heads is 
.
Q. 8. On a multiple choice examination with three possible answers for each of the five questions , what is the probability that a candidate would get four or more correct answer just by guessing ?.
Q. 9. There are 2% defective nuts in a large bulk of nuts. Write probability distribution for getting defective nuts in a random sample of 5 nuts. Find its mean and variance.
Q. 10. How many times must a man toss a fair coin so that the probability of having at least one head is more then 90%?
Paper By Mr. Kalpesh
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