# NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.3

NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.3 of Differential Equations in English Medium free download in PDF form updated for new academic session 2020-2021 based on latest NCERT Books 2020-21.

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## NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.3

 Class: 12 Subject: Maths Chapter 9: Exercise 9.3

### 12th Maths Exercise 9.3 Solutions

NCERT Solutions for Class 12 Maths Exercise 9.3 of Differential Equations is given below to download in PDF form updated for new academic session 2020-21. For other exercises, please visit to 12 Maths Chapter 9 solutions main page.

• ### Exercise 9.3 Solutions in Hindi & English

#### Questions from Board Papers

1. A line passes through the point with position vector 2i – j + 4k and is in the direction of the vector i + j – 2k. Find the equation of the line in Cartesian form.
2. If P(not A) = 0·7, P(B) = 0·7 and P(B/A) = 0·5, then find P(A/B).
3. A coin is tossed 5 times. What is the probability of getting (i) 3 heads, (ii) at most 3 heads?
4. Find the probability distribution of X, the number of heads in a simultaneous toss of two coins.
5. Check whether the relation R defined on the set A = {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive.
6. Find the equation of the normal to the curve x2 = 4y which passes through the point (– 1, 4).
7. The scalar product of the vector a = i + j + k with a unit vector along the sum of the vectors b = 2i + 4j – 5k and c = µi + 2j + 3k is equal to 1. Find the value of µ and hence find the unit vector along b + c.

##### Important Questions for Practice

1. Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is 2R/√3. Also find the maximum volume.
2. Using method of integration, find the area of the triangle whose vertices are (1, 0), (2, 2) and (3, 1).
3. A company produces two types of goods, A and B that require gold and silver. Each unit of type A requires 3 g of silver and 1 g of gold while that of type B requires 1 g of silver and 2 g of gold. The company can use at the most 9 g of silver and 8 g of gold. If each unit of type A brings a profit of ₹40 and that of type B ₹ 50, find the number of units of each type that the company should produce to maximize profit. Formulate the above LPP and solve it graphically and also find the maximum profit.

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