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10th class Math Notes Exercise 2 Misc

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10th Class Math Notes Exercise 2 Misc

10th Class Math Solution Notes — 10th Class Math Notes Exercise 2 Misc

“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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Math Ch#02, 10th Class

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1 / 58

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

Rational

Complex

Real

Irrational

2 / 58

The Equation is called ________

Quartic Equation

Quadratic Equation

Linear Equation

Cubic Equation

3 / 58

$\omega ^{4}$ = _______

ω²

4 / 58

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

Imaginary

Rational

None of these

Irrational

5 / 58

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

-4

-2

6 / 58

Cube Roots of -27 are _________

3, 3ω, -3ω²

-3, 3ω, 3ω²

3, -3ω, 3ω²

-3, -3ω, -3ω²

7 / 58

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

Rational, Equal

Rational, Unequal

Irrational, Equal

Irrational, Unequal

8 / 58

$\omega ^{4}$ = _______

ω²

9 / 58

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

Positive

Zero

Negative

None of these

10 / 58

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

Product of Roots

Sum of Roots

Discriminant

Synthetic Division

11 / 58

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

1 / α + 1 / β

All of thsese

α² + β²

α³ + β³

12 / 58

(1 - 3ω - 3ω² )³ = _________

-125

13 / 58

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

-3

14 / 58

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

-ω²

-ω

15 / 58

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

ω²

-1

16 / 58

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

Irrational

Unequal

Imaginary

Equal

17 / 58

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

-4

-28

18 / 58

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

Zero

Negative

None of these

Positive

19 / 58

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

-9

20 / 58

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

-1

ω³

21 / 58

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

-16

22 / 58

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

-ω

ω²

-ω²

23 / 58

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

r / p

-2q / p

-q / 2p

-q / p

24 / 58

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

-ω

-ω²

25 / 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-II

Option-IV

Option-I

Option-III

26 / 58

Sum of the cube roots of unity is ________

-1

27 / 58

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

real, unequal

irrational

real, equal

imaginary

28 / 58

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

b² + 4ac

-b² + 4ac

-b² - 4ac

b² - 4ac

29 / 58

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

30 / 58

Product of cube roots of unity is ___________

-1

31 / 58

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

x ( x+ 4 )

x ( x + 2 )

x ( x + 1 )

x ( x + 3 )

32 / 58

Cube Roots of 8 are _________

-2 , -2ω, -2ω²

2 , -2ω, -2ω²

2 , -2ω, 2ω²

2 , 2ω, 2ω²

33 / 58

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

then Roots are _______

Equal

Irrational

Complex

Rational

34 / 58

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

-1

ω²

35 / 58

α² + β² is equal to ________

α² - β²

α + β

1/α² + 1/β²

(α + β)² - 2αβ

36 / 58

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

-1

37 / 58

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

3 / 5

-5 / 3

-2 / 3

5 / 3

38 / 58

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

5x-3

3x+5

3x-5

5x+3

39 / 58

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

(5x + x)²

5 ( x + x² )

5 x² + x

5x + x²

40 / 58

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

-ω

-ω²

ω²

41 / 58

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

None of these

Rational

Irrational

Imaginary

42 / 58

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

Irrational

Imaginary

unequal

Equal

43 / 58

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

zero

perfect square

not perfect square

negative

44 / 58

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

irrational

rational

imaginray

None of these

45 / 58

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

ω²

46 / 58

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

7 / 4

-4 / 7

-1 / 7

4 / 7

47 / 58

(9 + 4ω + 4ω² )³ = _________

125

(17)³

48 / 58

Two Square Roots of unity are _________

1, ω

1, -1

ω, ω²

1, -ω

49 / 58

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

-ω²

ω²

50 / 58

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

Zero

Negative

Imaginary

Positive

51 / 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-III

Option-I

52 / 58

Cube Roots of 64 are _______

( 4 )³

4, 4ω, 4ω²

4, 16ω

-4, -4ω, -4ω²

53 / 58

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

Prefect Square

Negative

Not perfect Square

Zero

54 / 58

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

-1

55 / 58

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

-9

56 / 58

Roots of the equation are ________

irrational

rational

imaginary

None of these

57 / 58

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

2 x y

2(x + y)

2x - 2y

( x + y )²

58 / 58

Cube Roots of "-1" are ______

-1, -ω, ω²

-1, ω, -ω²

-1, -ω, -ω²

1, -ω, -ω²

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Result:

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)

Online Practice/ Test - MCQs & Short Questions

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 Misc, 10th Class Math Notes Exercise 2 Misc

Notes for Class 10th Math

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