# NCERT Solutions for Class 12 Maths Chapter 9 Miscellaneous Exercise

NCERT Solutions for Class 12 Maths Chapter 9 Miscellaneous Exercise 9 of Differential Equations in PDF form free English Medium updated for new academic session 2020-21 and following the latest CBSE Syllabus.

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Class: | 12 |

Subject: | Maths |

Chapter 9: | Miscellaneous Exercise |

### 12th Maths Miscellaneous Exercise 9 Solutions

NCERT Solutions for Class 12 Maths Chapter 9 Miscellaneous Exercise 9 of Differential Equations is given below based on latest NCERT Books. For other exercises, please visit to 12 Maths Chapter 9 solutions page. Join the Discussion forum to ask your doubts related to NIOS or CBSE Board.

### Miscellaneous Exercise 9 Solutions in Hindi & English

#### Questions from Board Papers

1. A dietician wishes to mix two types of food in such a way that the vitamin contents of the mixture contains at least 8 units of vitamin A and 10 units of vitamin C. Food I contains 2 units/kg of vitamin A and 1 unit/kg of vitamin C. It costs ₹ 50 per kg to produce food I. Food II contains 1 unit/kg of vitamin A and 2 units/kg of vitamin C and it costs ₹70 per kg to produce food II. Formulate this problem as a LPP to minimise the cost of a mixture that will produce the required diet. Also find the minimum cost.

2. Find the coordinates of the foot of the perpendicular Q drawn from P (3, 2, 1) to the plane 2x – y + z + 1 = 0. Also, find the distance PQ and the image of the point P treating this plane as a mirror.

3. Find the order of the differential equation of the family of circles of radius 3 units.

4. If P(A) = 0·6, P(B) = 0·5 and P(B|A) = 0·4, find P(A U B) and P(A|B).

5. If an operation * on the set of integers Z is defined by a * b = 2a2 + b, then find (i) whether it is a binary or not, and (ii) if a binary, then is it commutative or not.

##### Important Questions for Practice

1. Four cards are drawn one by one with replacement from a well-shuffled deck of playing cards. Find the probability that at least three cards are of diamonds.

2. The probability of two students A and B coming to school on time are 2/7 and 4/7, respectively. Assuming that the events ‘A coming on time’ and ‘B coming on time’ are independent, find the probability of only one of them coming to school on time.

3. Find the equation of the plane passing through the point (–1, 3, 2) and perpendicular to the planes x + 2y + 3z = 5 and 3x + 3y + z = 0.

4. Find the coordinates of the foot Q of the perpendicular drawn from the point P(1, 3, 4) to the plane 2x – y + z + 3 = 0. Find the distance PQ and the image of P treating the plane as a mirror.

5. A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A require 5 minutes each for cutting and 10 minutes each for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. The profit for type A souvenirs is ₹ 100 each and for type B souvenirs, profit is ₹ 120 each. How many souvenirs of each type should the company manufacture in order to maximise the profit? Formulate the problem as a LPP and then solve it graphically.

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