|Differential Equations||Exercise 9.5|
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NCERT Solutions for Class 12 Maths Exercise 9.5
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Differential Equations Solutions Exercise 9.5
12 Maths Chapter 9 Exercise 9.5 Solutions
NCERT Solutions for Class 12 Maths Exercise 9.5 of Differential Equations is given below. For other exercises, please visit to 12 Maths Chapter 9 solutions page.
Questions from Board Papers
- Find the area of the triangle whose vertices are (–1, 1), (0, 5) and (3, 2), using integration.
- Find the area of the region bounded by the curves (x – 1)² + y² = 1 and x² + y² = 1, using integration.
- Find the vector and Cartesian equations of the plane passing through the points (2, 5, – 3), (– 2, – 3, 5) and (5, 3, – 3). Also, find the point of intersection of this plane with the line passing through points (3, 1, 5) and (– 1, – 3, – 1).
- There are two boxes I and II. Box I contains 3 red and 6 black balls. Box II contains 5 red and ‘n’ black balls. One of the two boxes, box I and box II is selected at random and a ball is drawn at random. The ball drawn is found to be red. If the probability that this red ball comes out from box II is 3/5, find the value of ‘n’.
Some Important Questions
- 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 and 20 minutes available for cutting and 4 hours available for assembling. The profit is ₹50 each for type A and ₹ 60 each for type B souvenirs. How many souvenirs of each type should the company manufacture in order to maximize profit? Formulate the above LPP and solve it graphically and also find the maximum profit.
- Find the length of the intercept, cut off by the plane 2x + y – z = 5 on the x-axis.
- X and Y are two points with position vectors 3a + b and a – 3b respectively. Write the position vector of a point Z which divides the line segment XY in the ratio 2:1 externally.
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