# NCERT Solutions for Class 12 Maths Exercise 9.3

NCERT Solutions for Class 12 Maths Exercise 9.3 of Differential Equations in English Medium. Download NCERT Textbook Answers for other subjects or CBSE Apps for offline use, which work without internet.

 Class 12: Mathematics Differential Equations Exercise 9.3

## NCERT Solutions for Class 12 Maths Exercise 9.3

Visit to Class 12 Maths main page

### Differential Equations Solutions Exercise 9.3

#### 12 Maths Chapter 9 Exercise 9.3 Solutions

NCERT Solutions for Class 12 Maths Exercise 9.3 of Differential Equations is given below. For other exercises, please visit to 12 Maths Chapter 9 solutions page.      Visit 12 Maths Chapter 9 or Top of the page

##### 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.

###### Some Important Questions
• 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.
• Using method of integration, find the area of the triangle whose vertices are (1, 0), (2, 2) and (3, 1).
• 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.