# NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1

NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1 of Differential Equations in English and Hindi Medium updated for new academic session 2020-2021. Visit to NCERT Solutions Apps page to download offline apps, which work without internet.

## NCERT Solutions for Class 12 Maths Chapter 9 Exercise 9.1

Class: | 12 |

Subject: | Maths |

Chapter 9: | Exercise 9.1 |

### 12th Maths Exercise 9.1 Solutions

NCERT Solutions for Class 12 Maths Exercise 9.1 of Differential Equations is given below updated for new academic session 2020-2021. For other exercises, please visit to 12 Maths Chapter 9 solutions main page. NCERT Books and offline apps are based on new CBSE Syllabus free to download.

### Exercise 9.1 Solutions in Hindi & English

#### Questions from Board Papers

1. If A and B are square matrices of the same order 3, such that |A| = 2 and AB = 2I, write the value of |B|.

2. If a line makes angles 90, 135, 45 with the x, y and z axes respectively, find its direction cosines.

3. Find the vector equation of the line which passes through the point (3, 4, 5) and is parallel to the vector 2i + 2j – 3k.

4. Form the differential equation representing the family of curves y = e2x (a + bx), where ‘a’ and ‘b’ are arbitrary constants.

5. A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event “number is even” and B be the event “number is marked red”. Find whether the events A and B are independent or not.

##### Important Questions for Practice

1. A die is thrown 6 times. If “getting an odd number” is a “success”, what is the probability of (i) 5 successes? (ii) atmost 5 successes?

2. Find the equation of tangent to the curve y = √(3x – 2) which is parallel to the line 4x – 2y + 5 = 0. Also, write the equation of normal to the curve at the point of contact.

3. Solve the differential equation: x dy – y dx = √(x2 + y2) dx, given that y = 0 when x = 1.

4. If I + j + k, 2i + 5j , 3i + 2j – 3k and i – 6j – k respectively are the position vectors of points A, B, C and D, then find the angle between the straight lines AB and CD. Find whether AB and CD are collinear or not.

5. A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8 m3. If building of tank costs ₹70 per square metre for the base and ₹45 per square metre for the sides, what is the cost of least expensive tank?

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