# 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 English Medium. Download NCERT Textbook Solutions for other subjects or NCERT Solutions Apps for offline use, which work without internet.

 Class 12: Mathematics Differential Equations Miscellaneous Exercise 9

## NCERT Solutions for Class 12 Maths Chapter 9 Miscellaneous Exercise

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### Differential Equations Solutions Miscellaneous Exercise 9

#### 12 Maths Chapter 9 Miscellaneous Exercise 9 Solutions

NCERT Solutions for Class 12 Maths Chapter 9 Miscellaneous Exercise 9 of Differential Equations is given below. For other exercises, please visit to 12 Maths Chapter 9 solutions page.

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##### 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.
6. 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.
7. 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.

###### Some Important Questions
• 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.
• 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.
• 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.