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10th class Math Notes Exercise 2.8

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10th Class Math Notes Exercise 2.8

10th Class Math Solution Notes — 10th Class Math Notes Exercise 2.8

“Math” a compulsory subject for 10th class Science students. and 10th Class Math Notes Exercise 2.8 English (Science Group) included in this book. For getting good marks in this subject, the students need more practice. Here we are providing you Math Notes 10th class Solution for your better preparation. 10th class Science Students can get more practice and prepared through these important mathematics class 10 notes solutions. We are providing you these notes in the pdf files in which you can easily download and save. 10th class general math notes pdf is available for preparation here. Lets take a visit on English Medium version and enjoy your study also share with your friends for the easiness of other classmates and colleagues.

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MCQs & Short Questions

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Math Ch#02, 10th Class

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1 / 58

If the Roots of any Quadratic Equation are equal, then its Discriminant will be ________

None of these

Zero

Positive

Negative

2 / 58

Discriminant of 2x² - 7x + 1 = 0 is __________

3 / 58

If α , β are the roots of , then αβ is ______

7 / 4

-4 / 7

-1 / 7

4 / 7

4 / 58

α² + β² is equal to ________

1/α² + 1/β²

(α + β)² - 2αβ

α + β

α² - β²

5 / 58

Sum of the cube roots of unity is ________

-1

6 / 58

For a quadratic Equation b²-4ac=49 , then Roots are Real and ________

unequal

Imaginary

Irrational

Equal

7 / 58

If any quadratic equation have b²-4ac=205,

then Roots are _______

Complex

Equal

Irrational

Rational

8 / 58

If length and width of any rectangle are x & y respectively then Parameter of said rectangle can be shown as ________

2(x + y)

( x + y )²

2x - 2y

2 x y

9 / 58

Roots of the equation are ________

None of these

rational

imaginary

irrational

10 / 58

Which of the following are symmetric function of the roots of a quadratic equation?

α³ + β³

All of thsese

α² + β²

1 / α + 1 / β

11 / 58

If α, β are the roots of x²-x-1=0 , then sum of the roots 2α and 2β is ________

-2

-4

12 / 58

Roots of the equation 4x²-4x+1=0 are _______

irrational

imaginary

real, equal

real, unequal

13 / 58

If ω is complex cube root of unity, then $\omega ^{23}$ = _____

ω²

-ω

-ω²

14 / 58

$\frac{1}{\alpha } + \frac{1}{\beta }$ is equal to __________

$\frac{1}{\alpha }$
$\frac{1}{\alpha }-\frac{1}{\beta }$
$\frac{\alpha -\beta }{\alpha \beta }$
$\frac{\alpha +\beta }{\alpha \beta }$

(Which Option is Correct)

Option-IV

Option-III

Option-I

Option-II

15 / 58

If b²-4ac > 0, but not a perfect square then roots of ax²+bx+c=0 are _______

Imaginary

Rational

Irrational

None of these

16 / 58

Cube Roots of 8 are _________

2 , -2ω, -2ω²

-2 , -2ω, -2ω²

2 , -2ω, 2ω²

2 , 2ω, 2ω²

17 / 58

If ω and ω² are complex cube root of unity, then ω.ω² = ________

-1

18 / 58

The Determinant of a Quadratic Equation is -47 , then the Roots are______

Real

Complex

Irrational

Rational

19 / 58

If 1 + ω + ω² are cube roots of unity, then ω + ω² = _______

-1

ω²

20 / 58

If Roots of a quadratic equation are rational and distinct, then its Discriminant must be ______

Negative

Zero

Not perfect Square

Prefect Square

21 / 58

If Roots of any Quadratic Equation are Real but distinct , then its Discriminant must be ___________

Imaginary

Zero

Positive

Negative

22 / 58

Roots of any quadratic equation determined as Imaginary, as its Discriminant is ____

Zero

Positive

None of these

Negative

23 / 58

$\omega ^{4}$ = _______

ω²

24 / 58

"Five less than three times a certain number" is written in equation form as _______

3x-5

5x+3

3x+5

5x-3

25 / 58

$\omega ^{4}$ = _______

ω²

26 / 58

If ω is complex cube root of unity, then $\omega ^{-27}$ = __________

-1

ω²

27 / 58

(1 - 3ω - 3ω² )³ = _________

-125

28 / 58

The Roots of x² + 8x + 16 = 0 , are _______

Irrational

Equal

Imaginary

Unequal

29 / 58

If 1, ω, ω² are cube roots of unity, then 1 + ω = _______

-ω²

ω²

30 / 58

The Equation is called ________

Linear Equation

Cubic Equation

Quartic Equation

Quadratic Equation

31 / 58

The Nature of the Roots of equation ax²+bx+c=0 can be determined by _______

Product of Roots

Sum of Roots

Synthetic Division

Discriminant

32 / 58

The Sum of five times a number and the square of the number is ________

5 ( x + x² )

(5x + x)²

5x + x²

5 x² + x

33 / 58

If b²-4ac <0, then the roots of ax²+bx+c=0 are __________

None of these

irrational

rational

imaginray

34 / 58

If ω is complex cube root of unity, then $\omega ^{-5}$ = _______

-ω²

-ω

35 / 58

Cube Roots of 64 are _______

4, 16ω

( 4 )³

-4, -4ω, -4ω²

4, 4ω, 4ω²

36 / 58

The discriminant of ax² + bx + c = 0 is ________

-b² - 4ac

b² - 4ac

-b² + 4ac

b² + 4ac

37 / 58

Discriminant of x² - 3x + 3 = 0 is _________

-3

38 / 58

If Roots of a quadratic equation are real, rational and equal, then the possible value of Discriminant will be __________

-9

39 / 58

If α, β are roots of , then α + β is _________

-5 / 3

-2 / 3

3 / 5

5 / 3

40 / 58

Product of cube roots of unity is ___________

-1

41 / 58

If Roots of a Quadratic Equation are imaginary, and unequal, the possible value of Discriminant is _________

-9

42 / 58

If b²-4ac > 0, but not a perfect square then roots of ax² + bx + c =0 are _________

None of these

Rational

Irrational

Imaginary

43 / 58

$(1-\omega -\omega ^2)^{5}$ = ____________

ω²

44 / 58

Which of the following shows "the product of two consecutive positive number"

x ( x + 1 )

x ( x+ 4 )

x ( x + 2 )

x ( x + 3 )

45 / 58

If ω is complex cube root of unity, then $\omega ^{-16}$ = _________

ω²

-ω²

-ω

46 / 58

Cube Roots of "-1" are ______

-1, -ω, ω²

-1, -ω, -ω²

-1, ω, -ω²

1, -ω, -ω²

47 / 58

If b²-4ac = 0 , then roots of quadratic equation ax²+bx+c=0 are ___________

Rational, Unequal

Irrational, Unequal

Rational, Equal

Irrational, Equal

48 / 58

Cube Roots of -27 are _________

-3, -3ω, -3ω²

3, 3ω, -3ω²

-3, 3ω, 3ω²

3, -3ω, 3ω²

49 / 58

If roots of a quadratic equation are irrational and distinct, then Discriminant is ________

negative

perfect square

zero

not perfect square

50 / 58

If Roots of a Quadratic Equation are real, irrational and unequal then possible value of Discriminant will be _________

-1

51 / 58

If 1, ω, ω² are cube root of unity, then 1 + ω + ω² = _______ ω³

ω³

-1

52 / 58

$(-1+\sqrt{-3})^{3}$ = _____________

-28

-4

53 / 58

If ω us complex cube root of unity, then $\omega ^{63}$ = _______

-ω²

-ω

54 / 58

Two Square Roots of unity are _________

1, -1

1, -ω

ω, ω²

1, ω

55 / 58

If $\omega = \frac{-1-\sqrt{-3}}{2}$ then ω² = ___________

$\frac{-1\pm \sqrt{3}}{2}$
$\frac{-1+ \sqrt{3}}{2}$
$\frac{-1+ \sqrt{-3}}{2}$
$\frac{-1\pm \sqrt{-3}}{2}$

(Which Option is Correct)

Option-II

Option-IV

Option-I

Option-III

56 / 58

If α, β are the roots of px²+qx+r=0 , then the sum of the roots 2α and 2β is ________

-2q / p

r / p

-q / 2p

-q / p

57 / 58

If Roots of any quadratic equation are real, rational and unequal then possible value of Discriminant will be _________

-16

58 / 58

(9 + 4ω + 4ω² )³ = _________

125

(17)³

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User Name	Start	Score
Her	22:39:31 Feb 19, 2024	77%
h	00:34:39 Feb 18, 2024	77%
Rk	08:57:45 Dec 31, 2023	6%
Gulraiz	00:30:46 Jan 16, 2023	74%
Gulraiz	00:24:48 Jan 16, 2023	72%
Ayesha	17:55:44 Jan 15, 2023	81%
King	14:27:29 Jan 09, 2023	93%
Julia Kathleen Murney	14:23:20 Jan 09, 2023	91%
Gulraiz	14:18:57 Jan 09, 2023	93%
Gulraiz	22:32:03 Jan 08, 2023	98%
Gulraiz	22:22:38 Jan 08, 2023	96%
Gulraiz	22:13:13 Jan 08, 2023	94%
Gulraiz	19:52:17 Jan 08, 2023	94%
Gulraiz	19:42:11 Jan 08, 2023	93%
Gulraiz	19:28:23 Jan 08, 2023	87%
Gulraiz	02:39:34 Jan 08, 2023	87%
Gulraiz	02:35:46 Jan 08, 2023	81%
Gulraiz	02:32:02 Jan 08, 2023	81%
Gulraiz	02:26:38 Jan 08, 2023	84%
Gulraiz	02:22:27 Jan 08, 2023	84%
Gulraiz	02:17:27 Jan 08, 2023	82%
Gulraiz	02:13:03 Jan 08, 2023	75%
Gulraiz	02:08:25 Jan 08, 2023	74%
Gulraiz	02:03:07 Jan 08, 2023	63%
Gulraiz	01:56:39 Jan 08, 2023	56%
Gulraiz	01:44:38 Jan 08, 2023	37%
Gulraiz	14:55:07 Jan 02, 2023	37%
Gulraiz	00:23:45 Jan 02, 2023	27%
bisma	06:38:42 Oct 15, 2022	31%
Faria Imran	13:33:44 Oct 14, 2022	87%
hehe	23:23:10 Sep 05, 2022	20%
Muhammad Ijaz	23:07:44 Sep 02, 2022	44%
Mahnoor fatima	07:26:22 Aug 24, 2022	81%
Mahnoor fatima	11:02:38 Aug 23, 2022	82%
Mahnoor fatima	10:52:35 Aug 23, 2022	74%
Mahnoor fatima	10:36:45 Aug 23, 2022	60%
abdulrahman	05:55:42 Jun 19, 2022	36%
sheraz	14:57:30 May 30, 2022	3%
fiza nayab mughal	22:37:49 Apr 14, 2022	51%
Zulqarnain Umar	02:40:44 Oct 28, 2021	70%
a	12:42:52 Aug 15, 2021	50%
Aimen	11:25:00 Aug 15, 2021	74%
HAMMAD	21:16:05 Apr 18, 2021	13%
Faisslriaz	05:11:32 Apr 07, 2021	27%
Imran	21:31:43 Apr 06, 2021	81%

Math Solution 10th Class (Science Group)

Chapter 01 - QUADRATIC EQUATIONS

Exercise 1.1 (English) (Urdu)

Exercise 1.2 (English) (Urdu)

Exercise 1.3 (English) (Urdu)

Exercise 1.4 (English) (Urdu)

Ex 1-Misc (English) (Urdu)

Online Practice/ Test - MCQs & Short Questions

Chapter 02 - THEORY OF QUADRATIC EQUATIONS

Exercise 2.1 (English) (Urdu)

Exercise 2.2 (English) (Urdu)

Exercise 2.3 (English) (Urdu)

Exercise 2.4 (English) (Urdu)

Exercise 2.5 (English) (Urdu)

Exercise 2.6 (English) (Urdu)

Exercise 2.7 (English) (Urdu)

Exercise 2.8 (English) (Urdu)

Ex 2-Misc (English) (Urdu)

Online Practice/ Test - MCQs & Short Questions

Chapter 03 - VARIATIONS

Exercise 3.1 (English) (Urdu)

Exercise 3.2 (English) (Urdu)

Exercise 3.3 (English) (Urdu)

Exercise 3.4 (English) (Urdu)

Exercise 3.5 (English) (Urdu)

Exercise 3.6 (English) (Urdu)

Exercise 3.7 (English) (Urdu)

Ex 3-Misc (English) (Urdu)

Online Practice/ Test - MCQs & Short Questions

Chapter 04 - PARTIAL FRACTIONS

Exercise 4.1 (English) (Urdu)

Exercise 4.2 (English) (Urdu)

Exercise 4.3 (English) (Urdu)

Exercise 4.4 (English) (Urdu)

Ex 4-Misc (English) (Urdu)

Online Practice/ Test - MCQs & Short Questions

Chapter 05 - SETS AND FUNCTIONS

Exercise 5.1 (English) (Urdu)

Exercise 5.2 (English) (Urdu)

Exercise 5.3 (English) (Urdu)

Exercise 5.4 (English) (Urdu)

Exercise 5.5 (English) (Urdu)

Ex 5-Misc (English) (Urdu)

Online Practice/ Test - MCQs & Short Questions

Chapter 06 - BASIC STATISTICS

Exercise 6.1 (English) (Urdu)

Exercise 6.2 (English) (Urdu)

Exercise 6.3 (English) (Urdu)

Ex 6-Misc (English) (Urdu)

Online Practice/ Test - MCQs & Short Questions

Chapter 07 - INTRODUCTION TO TRIGONOMETRY

Exercise 7.1 (English) (Urdu)

Exercise 7.2 (English) (Urdu)

Exercise 7.3 (English) (Urdu)

Exercise 7.4 (English) (Urdu)

Exercise 7.5 (English) (Urdu)

Ex 7-Misc (English) (Urdu)

Online Practice/ Test - MCQs & Short Questions

Chapter 08 - PROJECTION OF A SIDE OF A TRIANGLE

Exercise 8.1 (English) (Urdu)

Exercise 8.2 (English) (Urdu)

Ex 8-Misc (English) (Urdu)

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Chapter 09 - CHORDS OF A CIRCLE

Exercise 9.1 (English) (Urdu)

Exercise 9.2 (English) (Urdu)

Ex 9-Misc (English) (Urdu)

Online Practice/ Test - MCQs & Short Questions

Chapter 10 - TANGENT TO A CIRCLE

Exercise 10.1 (English) (Urdu)

Exercise 10.2 (English) (Urdu)

Exercise 10.3 (English) (Urdu)

Ex 10-Misc (English) (Urdu)

Online Practice/ Test - MCQs & Short Questions

Chapter 11 - CHORDS AND ARCS

Exercise 11.1 (English) (Urdu)

Ex 11-Misc (English) (Urdu)

Online Practice/ Test - MCQs & Short Questions

Chapter 12 - ANGLE IN A SEGMENT OF A CIRCLE

Exercise 12.1 (English) (Urdu)

Ex 12-Misc (English) (Urdu)

Online Practice/ Test - MCQs & Short Questions

Chapter 13 - PRACTICAL GEOMETRY - CIRCLES

Exercise 13.1 (English) (Urdu)

Exercise 13.2 (English) (Urdu)

Exercise 13.3 (English) (Urdu)

Ex 13-Misc (English) (Urdu)

Online Practice/ Test - MCQs & Short Questions

Math Past Papers

2018

2019

2020

2021

2022

Other Math Notes

10th Class Math Science Group (English Medium)

10th Class Math Science Group (Urdu Medium)

10th Math Past Papers (Science Group)

10th Math Past Papers (Arts Group)

9th Class Math Science Group (English Medium)

9th Class Math Science Group (Urdu Medium)

9th Class Math Arts Group (Urdu Medium)

9th Class Math Past Papers (Science Group)

9th Class Math Past Papers (Arts Group)

Class 10th Math Notes pdf (Solution)

There are total 13 Chapters in Mathematics 10th Class for Punjab Textbook Board, Lahore. Solutions of all the chapters are given below. Anyone can download the PDF file of the notes. Note that, you can view these notes only if you have PDF reader software/ App on your device. However online view of the notes is also available on eStudent.pk . You can find all solution along with , Math MCQs Class 10. if you are searching the topics like 10^th Class Math Notes, Notes of 10^th Class math, 10^th Class Math Solution, 10^th Class Math, 10^th Class math solution pdf, 10^th class Math solution pdf download, 10^th class math guess paper 2022, Past Papers 10^th Class Math, 10^th class math solution pdf download, past papers 10^th class math, 10^th class math key book pdf free download, 10^th class math solution pdf free download, 10^th class math book solved all chapters pdf download, 10^th class math MCQs pdf download, 10^th class math pairing scheme 2022, 10^th class math guide pdf download, 10^th Class Math Notes Chapter 2, 10th Class Math Notes in Urdu (Science Group), math class 10 notes Punjab board, key book of mathematics 10th class punjab text book pdf, math notes class 10 urdu medium, Math Notes Class 10 Solution Exercise 2.8, 10th Class Math Notes Exercise 2.8

Notes for Class 10th Math

Math Notes Class 10, 10^th class math notes, Math notes for class 10, math notes class 10 pdf, class 10 math notes pdf, 10^th class math solution pdf free download, key book of mathematics 10^th class Punjab text book board, math class 10 notes kpk board pdf, class 10 math notes pdf, math class 10 notes punjab board, math notes class 10 kpk board, math notes class 10 adamjee notes, math class 10 notes, 10^th class math notes chapter 2, 10^th class math solution chapter 2 pdf, math notes class 10 chapter 2, then this post is specially for you and your future. All Boards of Intermediate & Secondary Educations in Punjab, Federal Board of Intermediate and Secondary Education, kpd board, Sindh board, Agha Khan Board and also Allama Iqbal Open University are taking examination according to Mathematics 10th Class. 10th Class Math key book pdf in urdu.