## Andhra Pradesh Board Class 10th Maths Chapter 5 Quadratic Equations Optional Exercise Textbooks Solutions PDF

Andhra Pradesh State Board STD 10th Maths Chapter 5 Quadratic Equations Optional Exercise Books Solutions with Answers are prepared and published by the Andhra Pradesh Board Publishers. It is an autonomous organization to advise and assist qualitative improvements in school education. If you are in search of AP Board Class 10th Maths Chapter 5 Quadratic Equations Optional Exercise Books Answers Solutions, then you are in the right place. Here is a complete hub of Andhra Pradesh State Board Class 10th Maths Chapter 5 Quadratic Equations Optional Exercise solutions that are available here for free PDF downloads to help students for their adequate preparation. You can find all the subjects of Andhra Pradesh Board STD 10th Maths Chapter 5 Quadratic Equations Optional Exercise Textbooks. These Andhra Pradesh State Board Class 10th Maths Chapter 5 Quadratic Equations Optional Exercise Textbooks Solutions English PDF will be helpful for effective education, and a maximum number of questions in exams are chosen from Andhra Pradesh Board.## Andhra Pradesh State Board Class 10th Maths Chapter 5 Quadratic Equations Optional Exercise Books Solutions

Board | AP Board |

Materials | Textbook Solutions/Guide |

Format | DOC/PDF |

Class | 10th |

Subject | Maths |

Chapters | Maths Chapter 5 Quadratic Equations Optional Exercise |

Provider | Hsslive |

## How to download Andhra Pradesh Board Class 10th Maths Chapter 5 Quadratic Equations Optional Exercise Textbook Solutions Answers PDF Online?

- Visit our website - Hsslive
- Click on the Andhra Pradesh Board Class 10th Maths Chapter 5 Quadratic Equations Optional Exercise Answers.
- Look for your Andhra Pradesh Board STD 10th Maths Chapter 5 Quadratic Equations Optional Exercise Textbooks PDF.
- Now download or read the Andhra Pradesh Board Class 10th Maths Chapter 5 Quadratic Equations Optional Exercise Textbook Solutions for PDF Free.

## AP Board Class 10th Maths Chapter 5 Quadratic Equations Optional Exercise Textbooks Solutions with Answer PDF Download

Find below the list of all AP Board Class 10th Maths Chapter 5 Quadratic Equations Optional Exercise Textbook Solutions for PDF’s for you to download and prepare for the upcoming exams:### 10th Class Maths 5th Lesson Quadratic Equations Optional Exercise Textbook Questions and Answers

Question 1.

Some points are plotted on a plane. Each point is joined with all remaining points by line segments. Find the number of points if the number of line segments are 10.

Answer:

Number of distinct line segments that can be formed out of n-points = n(n−1)2

Given: No. of line segments

n(n−1)2 = 10

⇒ n^{2} – n = 20

⇒ n^{2} – n – 20 = 0

⇒ n^{2} – 5n + 4n – 20 = 0

⇒ n(n – 5) + 4(n – 5) = 0

⇒ (n – 5) (n + 4) = 0

⇒ n – 5 = 0 (or) n + 4 = 0

⇒ n = 5 (or) -4

∴ n = 5 [n – can’t be negative]

Question 2.

A two digit number is such that the product of its digits, is 8. When 18 is added to the number, they interchange their places. Determine the number.

Answer:

Let the digit in the units place = x

Let the digit in the tens place = y

∴ The number = 10y + x

By interchanging the digits the number becomes 10x + y

By problem (10x + y) – (10y + x) = 18

⇒ 9x – 9y = 18

⇒ 9(x – y) =18

⇒ x – y = 189 = 2

⇒ y = x – 2

(i.e.) digit in the tens place = x – 2

digit in the units place = x

Product of the digits = (x – 2) x

By problem x^{2} – 2x = 8

x^{2} – 2x – 8 = 0

⇒ x^{2} – 4x + 2x – 8 = 0

⇒ x(x – 4) + 2(x – 4) = 0

⇒ (x – 4) (x + 2) = 0

⇒ x – 4 = 0 (or) x + 2 = 0

⇒ x = 4 (or) x = -2

∴ x = 4 [∵ x can’t be negative]

∴ The number is 24.

Question 3.

A piece of wire 8m in length is cut into twp pieces and each piece is bent into a square. Where should the cut in the wire be made if the sum of the areas of these squares is to be 2 m^{2}?

Answer:

Let the length of the first peice = x m

Then length of the second piece = 8 – x m

∴ Side of the 1st square = 𝑥4 m and

Side of the second square = 8−𝑥4 m

sum of the areas = 2 m^{2}

⇒ x^{2} + 64 + x^{2} – 16x = 16 × 2 = 32

⇒ 2x^{2} – 16x + 64 = 32

⇒ 2x^{2} – 16x + 32 = 0

⇒ 2(x^{2} – 8x + 16)= 0

⇒ x^{2} – 8x + 16 = 0

⇒ x^{2} – 4x – 4x + 16 = 0

⇒ x(x – 4) – 4(x – 4) = 0

⇒ (x – 4) (x – 4) = 0

∴ x = 4

∴ The cut should be made at the centre making two equal pieces of length 4 m, 4 m.

Question 4.

Vinay and Praveen working together can paint the exterior of a house in 6 days. Vinay by himself can complete the job in 5 days less than Praveen. How long will it take Vinay to complete the job by himself?

Answer:

Let the time taken by Vinay to complete the job = x days

Then the time taken by Praveen to complete the job = x + 5 days

Both worked for 6 days to complete a job.

∴ Total Work done by them is

⇒ 6(2x + 5) = x^{2} + 5x

⇒ x^{2} – 7x – 30 = 0

⇒ x^{2} – 10x + 3x – 30 = 0

⇒ x(x – 10) + 3(x – 10) = 0

⇒ (x – 10) (x + 3) = 0

⇒ x – 10 = 0 (or) x + 3 = 0

⇒ x = 10 (or) x = -3

∴ x = 10 (∵ x can’t be negative)

∴ Time taken by Vinay = x = 10 days

Time taken by Praveen = x + 5 = 15 days.

Question 5.

Show that the sum of the roots of a quadratic equation ax^{2} + bx + c = 0 is −𝑏𝑎.

Answer:

Let the Q.E. = ax^{2} + bx + c = 0 (a ≠ 0)

⇒ ax^{2} + bx = -c

∴ Sum of roots of a Q.E. is −𝑏𝑎

Question 6.

Show that the product of the roots of a quadratic equation ax^{2} + bx + c = 0 is 𝑐𝑎.

Answer:

Let the Q.E. = ax^{2} + bx + c = 0 (a ≠ 0)

⇒ ax^{2} + bx = -c

Question 7.

The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 21621 find the fraction.

Answer:

Let the numerator = x

then denominator = 2x + 1

Then the fraction = 𝑥2𝑥+1

Its reciprocal = 2𝑥+1𝑥

105x^{2} + 84x + 21 = 116x^{2} + 58x

11x^{2} – 26x – 21 = 0

11x^{2} – 33x + 7x – 21 = 0

11x (x – 3) + 7 (x – 3) = 0

(x – 3) (11x + 7) = 0

⇒ x – 3 = 0 (or) 11x + 7 = 0

⇒ x = 3 (or) −711

∴ x = 3

Numerator = 3;

Denominator = 2 × 3 + 1 = 7

Fraction = 37.

Question 8.

A ball is thrown vertically upwards from the top of a building of height 29.4m and with an initial velocity 24.5m/sec. If the height H of the ball from the ground level is given by H = 29.4 + 24.5t – 4.9t^{2}, then find the time taken by the ball to reach the ground.

Answer:

Initial velocity ‘U’ = 24.5

height of the ball from the ground can be expressed as

H = 29.4 + 24.5 t – 4.9 t^{2}

The ball has to reach the ground in ‘t’ seconds, which means Height from ground H = 0

So 29.4 + 24.5t – 4.9t^{2} = 0 = H

⇒ 4.9 t^{2} – 24.5t – 29.4 = 0

⇒ 4.9 [t^{2} – 5t – 6] = 0

∴ t^{2} – 5t – 6 = 0

⇒ t^{2} – 6t + t – 6 = 0

⇒ t(t – 6) + 1 (t – 6) = 0

(t – 6) (t + 1) = 0

⇒ t – 6 = 0

∴ t = 6 or t + 1 = 0

⇒ t = -1 but ‘t’ cannot be negative

So t = 6

it means in 6 seconds of time the ball reaches ground.

## AP Board Textbook Solutions PDF for Class 10th Maths

- AP Board Class 10 Maths Chapter 1 Real Numbers Ex 1.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 1 Real Numbers Ex 1.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 1 Real Numbers Ex 1.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 1 Real Numbers Ex 1.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 1 Real Numbers Ex 1.5 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 1 Real Numbers Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 1 Real Numbers InText Questions Textbook Solutions PDF

- AP Board Class 10 Maths Chapter 2 Sets Ex 2.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 2 Sets Ex 2.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 2 Sets Ex 2.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 2 Sets Ex 2.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 2 Sets InText Questions Textbook Solutions PDF

- AP Board Class 10 Maths Chapter 3 Polynomials Ex 3.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 3 Polynomials Ex 3.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 3 Polynomials Ex 3.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 3 Polynomials Ex 3.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 3 Polynomials Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 3 Polynomials InText Questions Textbook Solutions PDF

- AP Board Class 10 Maths Chapter 4 Pair of Linear Equations in Two Variables Ex 4.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 4 Pair of Linear Equations in Two Variables Ex 4.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 4 Pair of Linear Equations in Two Variables Ex 4.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 4 Pair of Linear Equations in Two Variables Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 4 Pair of Linear Equations in Two Variables InText Questions Textbook Solutions PDF

- AP Board Class 10 Maths Chapter 5 Quadratic Equations Ex 5.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 5 Quadratic Equations Ex 5.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 5 Quadratic Equations Ex 5.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 5 Quadratic Equations Ex 5.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 5 Quadratic Equations Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 5 Quadratic Equations InText Questions Textbook Solutions PDF

- AP Board Class 10 Maths Chapter 6 Progressions Ex 6.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 6 Progressions Ex 6.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 6 Progressions Ex 6.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 6 Progressions Ex 6.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 6 Progressions Ex 6.5 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 6 Progressions Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 6 Progressions InText Questions Textbook Solutions PDF

- AP Board Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 7 Coordinate Geometry Ex 7.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 7 Coordinate Geometry Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 7 Coordinate Geometry InText Questions Textbook Solutions PDF

- AP Board Class 10 Maths Chapter 8 Similar Triangles Ex 8.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 8 Similar Triangles Ex 8.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 8 Similar Triangles Ex 8.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 8 Similar Triangles Ex 8.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 8 Similar Triangles Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 8 Similar Triangles InText Questions Textbook Solutions PDF

- AP Board Class 10 Maths Chapter 9 Tangents and Secants to a Circle Ex 9.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 9 Tangents and Secants to a Circle Ex 9.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 9 Tangents and Secants to a Circle Ex 9.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 9 Tangents and Secants to a Circle Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 9 Tangents and Secants to a Circle InText Questions Textbook Solutions PDF

- AP Board Class 10 Maths Chapter 10 Mensuration Ex 10.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 10 Mensuration Ex 10.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 10 Mensuration Ex 10.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 10 Mensuration Ex 10.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 10 Mensuration Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 10 Mensuration InText Questions Textbook Solutions PDF

- AP Board Class 10 Maths Chapter 11 Trigonometry Ex 11.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 11 Trigonometry Ex 11.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 11 Trigonometry Ex 11.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 11 Trigonometry Ex 11.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 11 Trigonometry Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 11 Trigonometry InText Questions Textbook Solutions PDF

- AP Board Class 10 Maths Chapter 12 Applications of Trigonometry Ex 12.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 12 Applications of Trigonometry Ex 12.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 12 Applications of Trigonometry Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 12 Applications of Trigonometry InText Questions Textbook Solutions PDF

- AP Board Class 10 Maths Chapter 13 Probability Ex 13.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 13 Probability Ex 13.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 13 Probability Optional Exercise Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 13 Probability InText Questions Textbook Solutions PDF

- AP Board Class 10 Maths Chapter 14 Statistics Ex 14.1 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 14 Statistics Ex 14.2 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 14 Statistics Ex 14.3 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 14 Statistics Ex 14.4 Textbook Solutions PDF
- AP Board Class 10 Maths Chapter 14 Statistics InText Questions Textbook Solutions PDF

## 0 Comments:

## Post a Comment