# NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5

NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5 of Differential Equations in English Medium free PDF download updated for new academic session 2020-2021 for those students who are using NCERT Books.

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## NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.5

 Class: 12 Subject: Maths Chapter 9: Exercise 9.5

### 12th Maths Exercise 9.5 Solutions

NCERT Solutions for Class 12 Maths Exercise 9.5 of Differential Equations is given below to download in PDF form free. For other exercises, please visit to 12 Maths Chapter 9 solutions page. Download NCERT Books 2020-2021 and offline apps based on new CBSE Syllabus.

• ### Exercise 9.5 Solutions in Hindi & English

#### Questions from Board Papers

1. Find the area of the triangle whose vertices are (–1, 1), (0, 5) and (3, 2), using integration.
2. Find the area of the region bounded by the curves (x – 1)² + y² = 1 and x² + y² = 1, using integration.
3. 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).
4. 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’.

##### Important Questions for Practice

1. 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.
2. Find the length of the intercept, cut off by the plane 2x + y – z = 5 on the x-axis.
3. 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.            