NCERT Solutions for Class 12 Maths Exercise 9.1 of Differential Equations in English Medium. Visit to NCERT Solutions Apps page to download offline apps, which work without internet.

Class 12: | Mathematics |

Differential Equations | Exercise 9.1 |

## NCERT Solutions for Class 12 Maths Exercise 9.1

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### Differential Equations Solutions Exercise 9.1

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#### 12 Maths Chapter 9 Exercise 9.1 Solutions

NCERT Solutions for Class 12 Maths Exercise 9.1 of Differential Equations is given below. For other exercises, please visit to 12 Maths Chapter 9 solutions page.

##### Questions from Board Papers

- If A and B are square matrices of the same order 3, such that |A| = 2 and AB = 2I, write the value of |B|.
- If a line makes angles 90, 135, 45 with the x, y and z axes respectively, find its direction cosines.
- Find the vector equation of the line which passes through the point (3, 4, 5) and is parallel to the vector 2i + 2j – 3k.
- Form the differential equation representing the family of curves y = e2x (a + bx), where ‘a’ and ‘b’ are arbitrary constants.
- 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.

###### Some Important Questions

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