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S.chand Class 8 Maths Solution Chapter 6 Factorisation of Algebraic Expressions Exercise 6 F

Exercise 6 F

Factorise :

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Question 1

$a^{2}+5 a+6$

Sol :

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Question 2

$x^{2}+7 x+12$

Sol :

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Question 3

$m^{2}+13 m+42$

Sol :

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Question 4

$a^{2}+25 a-54$

Sol :

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Question 5

$t^{2}+9 t-36$

Sol :

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Question 6

$a^{2}+5 a-50$

Sol :

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Question 7

$x^{2}-4 x-5$

Sol :

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Question 8

$y^{2}-10 y+16$

Sol :

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Question 9

$x^{2}-2 x-24$

Sol :

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Question 10

$y^{2}+2 y-48$

Sol :

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Question 11

$n^{2}-3 n-40$

Sol :

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Question 12

$y^{2}-11 y+24$

Sol :

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Question 13

$48+22 x-x^{2}$

Sol :

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Question 14

$x^{2}-29 x+204$

Sol :

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Question 15

$p^{2}-5 p-176$

Sol :

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Question 16

$n^{2}-19 n-92$

Sol :

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Question 17

$j^{2}-11 j-102$

Sol :

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Question 18

$2 a^{3}+10 a^{2}-28 a$ [Hint. First take out the common factor $2 a$.]

Sol :

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Question 19

$12 b+15-3 b^{2}$

Sol :

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Question 20

$3 c^{5}-18 c^{4}-48 c^{3}$

Sol :

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Question 21

$b^{2} c^{3}+8 b c^{4}+12 c^{5}$

Sol :

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Question 22

$a^{4}-5 a^{2}-36$

Sol :

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Question 23

$y^{4}+4 y^{2}-32$

Sol :

Multiple Choice Questions (MCQs)

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Question 24

Which is the correct factorisation of $x^{2}-10 x-24$ ?

(a) $(x-2)(x+12)$

(b) $(x+4)(x-6)$

(c) $(x-4)(x-6)$

(d) $(x+2)(x-12)$

Sol :

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Question 25

One of the factors of $(x-y)^{2}-4(x-y)-45$ is

(a) $(x-y+9)$

(b) $(x-y-5)$

(c) (x-y-9)

(d) (x+y+5)

High Order Thinking Skills (HOTS)

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Question 26

Which value of $b$ would make $y^{2}+b y-24$ factorable ?

(a) 14

(b) 11

(c) 5

(d) 25

Sol :

S.chand Class 8 Maths Solution Chapter 1 Rational Numbers Exercise 1A

Exercise 1A

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Question 1

Fill in the blanks :

(i) $\frac{7}{-8}$, expressed as a rational number with denominater 24=

(ii) $\frac{-4}{7} \ldots \ldots \ldots \frac{4}{-11} \quad(<,>,=)$

(iii) The absolute value of $\frac{-16}{-19}=$

(iv) The rational numbers whose absolute value is $\frac{11}{13}$ are

(v) The rational number which is neither positive nor negative is

Sol :

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Question 2

Answer True (T) or False (F):

(i) Every rational number is a whole number.

(ii) 0 is the smallest rational number.

(iii) Every fractional number is a rational number.

(iv) $\frac{4}{0}$ is a rational number.

(v) |x|=-x if x<0

Sol :

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Question 3

Write four rational numbers equivalent to each of the following rational numbers:

(i) $\frac{2}{5}$

(ii) $\frac{-5}{9}$

(iii) $\frac{8}{-11}$

(iv) $\frac{-12}{13}$

Sol :

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Question 4

Which of the symbols <,= or > should replace the blank space ?

(i) $\frac{8}{7}, \cdots \frac{12}{9}$

(ii) $\frac{-2}{3} \ldots \ldots \frac{4}{-7}$

(iii) $\frac{13}{-15}, \ldots \frac{10}{-11}$

(iv) $0 \ldots . \frac{-3}{-8}$

Sol :

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Question 5

Write the absolute value of:

(i) $\frac{5}{8}$

(ii) $\frac{-7}{10}$

(iii) 0

(iv) $\frac{11}{-12}$

Sol :

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Question 6

$-\frac{28}{84}$ expressed as a rational number with numerator 4 is

(a) $\frac{4}{12}$

(b) $\frac{4}{7}$

(c) $\frac{4}{-7}$

(d) $\frac{4}{-12}$

Sol :

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Question 7

Which of the following set of rational numbers is arranged in ascending order ?

(a) $-\frac{1}{2}, \frac{-3}{7}, \frac{-5}{14}, \frac{-25}{28}$

(b) $-\frac{25}{28},-\frac{1}{2},-\frac{3}{7},-\frac{5}{14}$

(c) $\frac{-25}{28},\frac{-5}{14},\frac{-3}{7},\frac{-1}{2}$

(d) $-\frac{5}{14},-\frac{25}{28},-\frac{3}{7},-\frac{1}{2}$

Sol :

High Order Thinking Skills

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Question 8

Find the absolute value of :

$-1 \div \frac{-1}{5} \div \frac{1}{-5} \div \frac{-1}{-5}$

Sol :

S.chand composite class 6 Mathematics Chapter 1 Numbers Exercise 1C

EXERCISE 1 C

QUESTION 1

Read the following numbers in the International system of numeration and write in words

(i) 53,673

Sol :

Fifty three thousand six hundred seventy three

(ii) 430,057

Sol :

Four hundred thirty thousand fifty seven

(iii) 78,823,761

Sol :

Seventy eight million eight hundred twenty three thousand seven hundred sixty one

(iv) 600,003

Sol :

Six hundred thousand three

(v) 1,369,864,005

Sol :

One billion three hundred twelve million five thousand four hundred fifty nine

(vi) 80,112,005,459

Sol :

Eighty billion ne hundred twelve million five thousand four hundred fifty nine

QUESTION 2

Write the numerals for the following numbers.

(i) Six hundred six thousand seven hundred twelve

Sol :

606712

(ii) Four million eight hundred thirteen thousand three hundred .

Sol :

4813300

(iii) Eight hundred nine million eight thousand seven

Sol :

809008007

(iv) Three billion eighteen million nine hundred one thousand seventeen

Sol :

3018901017

(v) Sixteen billion f‌ive hundred nineteen million nine hundred thirteen thousand seven hundred two

Sol :

One billion three hundred sixty nine million eight hundred sixty four thousand five

(vi) Thirty-eight billion five hundred thousand forty-eight

Sol :

Eighty billion one hundred twelve million five thousand four hundred fifty nine

QUESTION 3

Write the compact numeral for 8000000 + 50000 + 90 + 9 using the international system of numeration . Also write the number name .

Sol :

8050099

Eight million fifty thousand ninety nine

QUESTION 4

Write three consecutive whole numbers just preceding 729,001

Sol :

728998 , 728999 ; 729000

QUESTION 5

Write in numerals and words the largest 8-digit number having four different digits in the

(i) Indian system of numeration

Sol :

99999876

Nine crore ninety nine lakh ninety nine thousand eight hundred seventy six

(ii) International system of numeration

Sol :

99999876

Ninety nine million nine hundred ninety nine thousand eight hundred seventy six

QUESTION 6

Match column A and column B

Column A	Column B
(i) Three hundred thousand	(a) Three crore
(ii) Three billion	(b) Thirty lakh
(iii) Thirty million	(c) Three hundred crore
(iv) Three million	(d) Three lakh

Sol :

(i)→d

(ii)→c

(iii)→a

(iv)→b

S.chand composite class 6 Mathematics Chapter 1 Numbers Exercise 1B

EXERCISE 1 B

QUESTION 1

Read and write down in words , the following numbers in the Indian system of numeration.

(i) 6,80,453

Sol :

Six lakh eighty thousand four hundred eighty three

(ii) 12,36,748

Sol :

Twelve lakh thirty six thousand seven hundred forty eight

(iii) 8,30,09,007

Sol :

Eight crore thirty lakh nine thousand seven

(iv) 10,00,30,004

Sol :

Ten crore thirty thousand four

(v) 33,04,05,078

Sol :

Thirty three crore four lakh five thousand seventy eight

QUESTION 2

Write the following in figures .

(i) Five lakh three thousand seven hundred eighty-five

Sol :

503785

(ii) Eighty lakh fifteen thousand two hundred f‌ive

Sol :

8015205

(iii) Ninety crore seven lakh nine thousand four hundred three

Sol :

900709403

(iv) One crore one lakh one thousand one

Sol :

10101001

(v) Two hundred seventy crore eighty-eight lakh sixty-f‌ive thousand two hundred ninety-five

Sol :

2708865295

QUESTION 3

State the place value of 8 in each of the following

(i) 80,657

Sol :

80000

(ii) 8,10,902

Sol :

800000

(iii) 86,74,597

Sol :

8000000

(iv) 8,16,77,000

Sol :

80000000

QUESTION 4

Express each of the following numbers in expanded form.

(i) 83,596

Sol :

=80000+3000+500+90+6

(ii) 75,16,930

Sol :

=7000000+500000+10000+6000+900+30+0

(iii) 42,65,93,240

Sol :

=400000000+20000000+6000000+500000+90000+3000+200+40+0

QUESTION 5

Write the compact numeral.

(i)5×100000 + 7×1000 + 8×100 + 1×10 + 6×1

Sol :

507816

(ii) 7×1000000 + 9×100000 + 0×10000 + 6×100 + 2×10 + 8×1

Sol :

7900628

(iii) 20,00,00,000 + 4,00,00,000 + 70,000 + 600 + 5

Sol :

240070605

QUESTION 6

Compare , Use < or > for each

(i) 19,25,875 __ 19,52,875

Sol :

(ii) 60,12,40,627 __ 61,02,04,726

Sol :

QUESTION 7

Arrange the numbers in each of the following from the largest to the smallest.

(i) 6,90,672; 6,09,762; 8,95,072; 9,07,652

Sol :

907652; 895072; 690672; 609762

(ii) 8,93,45,015; 8,45,39,150; 9,01,83,726; 9,00,25,900

Sol :

90183726; 90025900; 89345015; 84539150

QUESTION 8

Arrange the numbers in each of the following from the smallest to the largest

(i) 4,60,570; 7,90,856; 5,72,803 ; 6,81,906

Sol :

460570; 572803; 681906; 790856

(ii) 64,15,23,453; 2,09,62,000; 11,00,83,000; 9,53,654

Sol :

953654; 20962000; 11008300; 641523453

QUESTION 9

(i) Write the greatest 8-digit number having three different digits

Sol :

99999987

(ii) Write the smallest 6-digit number having three different digits

Sol :

100002

QUESTION 10

How many numbers in all do we have with (i) 7 digits (ii) 9 digits

Sol :

(i) 9000000

(ii) 900000000

S.chand Composite class 6 Mathematics Chapter 1 Numbers Exercise 1A

EXERCISE 1 A

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QUESTION 1

Write the following numbers in words and expanded form

(i) 60802

Sol :

=Sixty thousand eight hundred and two

=60000+800+2

(ii) 70045

Sol :

Seventy thousand fourth five

=70000+40+5

(iii) 32001

Sol :

Thirty two thousand and one

=30000+2000+1

(iv) 89316

Sol :

Eight nine thousand three hundred sixteen

=80000+9000+300+10+6

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QUESTION 2

Write the following numbers in standard form

(i) Sixty thousand nine hundred forty

Sol :

60940

(ii) Fifty-eight thousand nine

Sol :

58009

(iii) Ninety-nine thousand nine hundred ninety-nine

Sol :

99999

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QUESTION 3

Fill in the blanks with < or > sign

(i) 61742 ___ 58965

Sol :

(ii) 902108 ___ 90018

Sol :

(iii) 34517 ___ 34751

Sol :

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QUESTION 4

Arrange the following numbers in ascending order

(i) 73419 , 74319 , 71439 , 79431

Sol :

71439 73419 , 74319 , 79431

(ii) 80605 , 80065 , 86500 , 80506

Sol :

80065 , 80506 , 80605 , 86500

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QUESTION 5

Arrange the following numbers in descending order .

(i) 56789 , 87569 , 75968 , 59876

Sol :

87569 , 75968 , 59876 , 56789

(ii) 51806 , 81506 , 80615 , 56810

Sol :

81506 , 80615 , 56810 , 51806

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QUESTION 6

Write the successor of :

(i) 10999

Sol :

11000

(ii) 89989

Sol :

89990

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QUESTION 7

Write the predecessor of :

(i) 90000

Sol :

89999

(ii) 20010

Sol :

20009

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QUESTION 8

Using the given digits without repetition form the smallest and thegreatest 4-digit numbers .

(i) 6 , 9 , 2 , 4

Sol :

Smallest : 2469

Greatest : 9642

(ii) 7 , 0 , 3 , 8

Sol :

Smallest : 3078

Greatest : 8730

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QUESTION 9

Using the given digits write the smallest and the greatest 5-digitnumbers . You can repeat any one digit twice .

(i) 4 , 3 , 2 , 6

Sol :

Smallest : 22346

Greatest : 66432

(ii) 8 , 0 , 9 , 5

Sol :

Smallest : 50089

Greatest : 99850

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QUESTION 10

Write the greatest and the smallest 5-digit numbers using any fivedifferent digits , with the condition given below.

(i) Digit 6 is always at the thousand place

Sol :

Smallest : 16023

Greatest : 96875

(ii) Digit 8 is always at the ones place

Sol :

Smallest : 10238

Greatest : 97658

S.chand Class 8 Maths Solution Chapter 6 Factorisation of Algebraic Expressions Exercise 6 F

Exercise 6 F

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20

Question 21

Question 22

Question 23

Question 24

Question 25

Question 26

S.chand Class 8 Maths Solution Chapter 1 Rational Numbers Exercise 1A

Exercise 1A

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

S.chand composite class 6 Mathematics Chapter 1 Numbers Exercise 1C

EXERCISE 1 C

S.chand composite class 6 Mathematics Chapter 1 Numbers Exercise 1B

EXERCISE 1 B

S.chand Composite class 6 Mathematics Chapter 1 Numbers Exercise 1A

EXERCISE 1 A

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