XII - MATHEMATICS – Practice Exercise -11. Using the properties of determinants, prove that

2. Differentiate with respect to .

3.Show that the isosceles triangle of maximum area that can be inscribed in a given circle is an equilateral triangle.

4. Evaluate

5. Show that the four points ( 0, –1, –1 ), ( 4, 5, 1 ), ( 3, 9, 4 ) and ( –4, 4, 4 ) are coplanar. Also, find the equation of the plane containing then.6. Using the properties of definite integrals, evaluate

7. Evaluate

8. Evaluate

9.

10. In a hostel, 60% read Hindi newspaper, 40% English and 20% both. A student is selected at random. Find : a) the probability that he / she reads neither of them.b) If he / she reads Hindi newspaper, find the probability that he / she reads

English newspaper also ?A girl student comes from abroad and wants to take an admission in a school. What do you suggest, she should go for a hostel or stay as a paying guest

11. Cost of 4 Kgs of onions, 3 Kgs of wheat and 2 Kgs of rice is Rs.60/-; 2 Kgs of onions, 4 Kgs of wheat and 6 Kgs of rice is Rs.90/- and 6 Kgs of onion, 2 Kgs of wheat and 3 Kgs of rice is Rs.70/-. Form a matrix to find the cost of each item by the matrix multiplication.Shop keeper wants to purchase carry bags. What carry bag will you suggest and why ?

12. Solve the differential equation .

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13.14. In a test, an examinee either guesses or copies or knows the answer to a multiple

choice question with four choices. The probability that he makes a guess is and the

probability that he copies the answer is . The probability that his answer is correct,

given that he copied it, is . Find the probability that he knew the answer to the

question given that he correctly answered it. A student used unfair means, to answer the multiple choice question. What value of life he violates?

15. Prove that the relation R on set N x N defined by (a, b ) R ( c, d ) ad ( b + c ) = bc ( a + d ) for all ( a, b ), ( c, d ) N x N is an equivalence relation.

16.

17.

There are two types of fertilisers and . consists of 10% nitrogen and

6% phosphoric acid and consists of 5% nitrogen and 10% phosphoric acid.

After testing the soil conditions, a farmer finds that she needs at least 14 Kg of nitrogen

and 14 Kg of Phosphoric acid for her crop. If costs Rs.6/- per Kg and costs

Rs.5/- per Kg, determine how much of each type of fertiliser should be used so that nutrient requirements are met at a minimum cost. What is the minimum cost ?Farming can be done by using fertilisers or by using organic manure. Which farming would you prefer and why ?

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