# NCERT Solutions for Class 11 Maths Chapter 10

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines in English and Hindi Medium for CBSE first term exam, DOWNLOAD in PDF file format to use it offline updated for new academic session 2021-2022.

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### NCERT Solutions for Class 11 Maths Chapter 10 in PDF

Class: | 11 |

Subject: | Maths |

Chapter 10: | Straight Lines |

### 11th Maths Chapter 10 Solutions

NCERT Solutions for Class 11 Maths Chapter 10 Straight Lines is given below to free download in PDF form. NCERT Solutions and Offline Apps are updated for new session 2021-22 following CBSE Syllabus 2021-2022.

#### Important Questions on Straight Lines

1. On shifting the origin to (p, q), the coordinates of point (2, –1) changes to (5, 2). Find p and q. [Answer: p = -3, q = – 3]

2. Determine the equation of line through a point (–4, –3) and parallel to x-axis. [Answer: y + 3 = 0]

3. If the image of the point (3, 8) in the line px + 3y – 7 = 0 is the point (–1, –4), then find the value of p. [Answer: p = 1]

4. Find the distance of the point (3, 2) from the straight line whose slope is 5 and is passing through the point of intersection of lines x + 2y = 5 and x – 3y + 5 = 0. [Answer: 10/√26]

5. The line 2x – 3y = 4 is the perpendicular bisector of the line segment AB. If coordinates of A are (–3, 1) find coordinates of B. [Answer: (1, -5)]

##### Questions for Practice

1. If a vertex of a triangle is (1, 1) and the midpoints of two sides through this vertex are (–1, 2) and (3, 2). Then find the centroid of the triangle. [Answer: (1, 7/3)]

2. The points (1, 3) and (5, 1) are two opposite vertices of a rectangle. The other two vertices lie on line y = 2x + c. Find c and remaining two vertices. [Answer: c = – 4, (2, 0), (4, 4)]

3. If two sides of a square are along 5x – 12y + 26 = 0 and 5x – 12y – 65 = 0 then find its area. [Answer: 49 square units]

4. In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line x + y = 4? [Answer: 1:2]

5. Find the equation of a line with slope –1 and whose perpendicular distance from the origin is equal to 5. [Answer: x + y + 5√2 = 0 and x + y – 5√2 = 0]

###### Questions with Answers for Final Exams

1. If a vertex of a square is at (1, –1) and one of its side lie along the line 3x – 4y – 17 = 0 then find the area of the square. [Answer: 4 square units]

2. Find the area of the triangle formed by the lines y = x, y = 2x, y = 3x + 4. [Answer: 4 square units]

3. Find the coordinates of the orthocentre of a triangle whose vertices are (–1, 3) (2, –1) and (0, 0). [Orthocentre is the point of concurrency of three altitudes]. [Answer: (-4, -3)]

4. What is the value of y so that line through (3, y) and (2, 7) is parallel to the line through (–1, 4) and (0, 6)? [Answer: y = 9]

5. Find the equation of the lines which cut-off intercepts on the axes whose sum and product are 1 and –6 respectively. [Answer: 2x – 3y – 6 = 0 and – 3x + 2y – 6 = 0]

###### Try These

1. Find the equation of a straight line which passes through the point of intersection of 3x + 4y – 1 = 0 and 2x – 5y + 7 = 0 and which is perpendicular to 4x – 2y + 7 = 0. [Answer: x + 2y = 1]

2. If the image of the point (2, 1) in a line is (4, 3) then find the equation of line. [Answer: x + y – 5 = 0]

### Important Questions on 11th Maths Chapter 10

##### Write the equations for the x and y-axes.

The y-coordinate of every point on the x-axis is 0.

Therefore, the equation of the x-axis is y = 0.

The x-coordinate of every point on the y-axis is 0.

Therefore, the equation of the y-axis is y = 0.

##### Find the equation of the line which intersects the x-axis at a distance of 3 units to the left of origin with slope –2.

It is known that if a line with slope m makes x-intercept d, then the equation of the line is given as y = m(x – d)

For the line intersecting the x-axis at a distance of 3 units to the left of the origin, d = –3.

The slope of the line is given as m = –2

Thus, the required equation of the given line is y = –2 [x – (–3)] y = –2x – 6 i.e., 2x + y + 6 = 0

##### Find the value of p so that the three lines 3x + y – 2 = 0, px + 2y – 3 = 0 and 2x – y – 3 = 0 may intersect at one point.

The equations of the given lines are

3x + y – 2 = 0 …………………… (1)

px + 2y – 3 = 0 ………………… (2)

2x – y – 3 = 0 …………………… (3)

On solving equations (1) and (3), we obtain

x = 1 and y = –1

Since these three lines may intersect at one point, the point of intersection of lines (1) and (3) will also satisfy line (2).

p (1) + 2 (–1) – 3 = 0

p – 2 – 3 = 0

p = 5

Thus, the required value of p is 5.

##### How many exercises are there in class 11 Maths Chapter 10?

There are four exercises in class 11 Maths Chapter 10.

- In the first exercise (Ex 10.1), there are 14 questions and five examples (examples 1, 2, 3, 4, 5).
- In the second exercise (Ex 10.2), there are 20 questions and seven examples (examples 6, 7, 8, 9, 10, 11, 12).
- In the third exercise (Ex 10.3), there are 18 questions and seven examples (examples 13, 14, 15, 16, 17, 18, 19).
- In the last exercise (Miscellaneous), there are 24 questions and 6 examples (examples 20, 21, 22, 23, 24, 25).
- So, there are in all 25 examples and 76 questions in class 11 Maths Chapter 10.

##### Which problems of chapter 10 of class 11th Maths are important and can come in the exams?

Problems of chapter 10 of class 11th Maths that are most important and can come in the exams are:

1. Questions 3, 5, 7, 9, 10, 11, 13, and 14 of exercise 10.1.

2. Questions 4, 8, 9, 11, 14, 15, 17, 18, and 19 of exercise 10.2.

3. Questions 1, 5, 6, 8, 12, 14, 16, 17, and 18 of exercise 10.3.

4. Questions 1, 2, 3, 6, 8, 9, 11, 12, 15, 16, 18, 19, 20, 21, 22, and 24 of miscellaneous exercise on chapter 10.

5. Examples 1, 3, 6, 9, 13, 14, 15, 21, 22, 24, and 25.

##### Are there any books other than NCERT from which students can practice extra questions of chapter 10 of class 11th Maths?

Yes, R.L. Arora, R.D. Sharma, R.S. Aggarwal , etc are some books other than NCERT from which students can practice extra questions of chapter 10 of class 11th Maths. These books are the best books after NCERT. The languages of these books are easy. Students can easily practice extra questions of chapter 10 of class 11th Maths from these books.

##### Is chapter 10 of class 11th Math simple or complicated?

Chapter 10 of class 11th mathematics is not simple and not complicated. It lies in the middle of simple and hard because some questions of this chapter are easy, and some are difficult. But difficulty level of any chapter varies from student to student. So, Chapter 10 of class 11th mathematics is easy or not depends on students also. Some students find it complex, some find it simple, and some find it in the middle of simple and complex.