# NCERT Solutions for Class 12 Maths Exercise 9.1

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

Visit to Class 12 Maths main page

### Differential Equations Solutions Exercise 9.1

#### 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
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.

###### Some Important Questions
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?