Algebra

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Question

A complete factorization of $left parenthesis straight x squared plus 64 right parenthesis$ is

$left parenthesis straight x squared plus 8 right parenthesis squared$
$left parenthesis straight x squared plus 8 right parenthesis thin space left parenthesis straight x squared minus 8 right parenthesis$
$left parenthesis straight x squared minus 4 straight x plus 8 right parenthesis thin space left parenthesis straight x squared minus 4 straight x minus 8 right parenthesis$
$left parenthesis straight x squared plus 4 straight x plus 8 right parenthesis thin space left parenthesis straight x squared minus 4 straight x plus 8 right parenthesis$

Solution

left parenthesis straight x squared plus 4 straight x plus 8 right parenthesis thin space left parenthesis straight x squared minus 4 straight x plus 8 right parenthesis

straight x to the power of 4 plus 64 space equals space left parenthesis straight x squared right parenthesis squared space plus space left parenthesis 8 right parenthesis squared or space left parenthesis straight x squared space plus space 8 right parenthesis squared space minus space 2 space cross times space 8 straight x squared

open square brackets because space straight a squared plus straight b squared space equals space left parenthesis straight a plus straight b right parenthesis squared minus 2 ab close square brackets

equals space left parenthesis straight x squared plus 8 right parenthesis squared space minus space left parenthesis 4 straight x right parenthesis squared space equals space left parenthesis straight x squared plus 4 straight x plus 8 right parenthesis space left parenthesis straight x squared minus 4 straight x plus 8 right parenthesis

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Question

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A man loses $20 1 half percent sign$ of his money and after spending 80% of the remainder, he is left with ₹ 159. How much did he have at first?

₹ 500

₹ 800

₹ 1000

₹ 1200

Solution

₹ 1000

Let the money be ₹ x.
According to the question,
[(100 - 20.5)% of x] of (100 - 80)% = 159
$rightwards double arrow space space space space fraction numerator 79.5 over denominator 100 end fraction cross times straight x cross times 20 over 100 space equals space 159 rightwards double arrow space space space space straight x space space equals space fraction numerator 159 space cross times space 100 space cross times space 100 over denominator 79.5 space cross times space 20 end fraction space equals space ₹ space 1000$

Question

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Among below expressions which one can be expressed as the difference of two cubic expressions?

$straight x cubed plus straight y cubed plus 3 straight x plus 3 straight y$
$straight x cubed plus 2 straight x squared plus 3 straight x plus straight x squared$
$straight x cubed plus 3 straight x squared plus 3 straight x minus 2$
$straight x cubed plus 3 straight x squared plus 3 straight x minus 7$

Solution

straight x cubed plus 3 straight x squared plus 3 straight x minus 7

Question

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Find the sum of:
$open parentheses 1 minus fraction numerator 1 over denominator straight n plus 1 end fraction close parentheses space plus space open parentheses 1 minus fraction numerator 2 over denominator straight n plus 1 end fraction close parentheses space plus space open parentheses 1 minus fraction numerator 3 over denominator straight n plus 1 end fraction close parentheses plus...... open parentheses 1 minus fraction numerator straight n over denominator straight n plus 1 end fraction close parentheses$

n

$1 half straight n$

(n + 1)

$1 half left parenthesis straight n plus 1 right parenthesis$

Solution

1 half straight n

open parentheses 1 minus fraction numerator 1 over denominator straight n plus 1 end fraction close parentheses plus space open parentheses 1 minus fraction numerator 2 over denominator straight n plus 1 end fraction close parentheses plus open parentheses 1 minus fraction numerator 3 over denominator straight n plus 1 end fraction close parentheses space plus...... open parentheses 1 minus fraction numerator straight n over denominator straight n plus 1 end fraction close parentheses

equals straight n minus open parentheses fraction numerator 1 over denominator straight n plus 1 end fraction plus fraction numerator 2 over denominator straight n plus 1 end fraction plus fraction numerator 3 over denominator straight n plus 1 end fraction plus.... fraction numerator straight n over denominator straight n plus 1 end fraction close parentheses equals space straight n minus fraction numerator straight n left parenthesis straight n plus 1 right parenthesis over denominator 2 left parenthesis straight n plus 1 right parenthesis end fraction space equals space straight n minus straight n over 2 space equals space straight n over 2

Question

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For two positive numbers a and b, if a² + b² = 24 and ab = 6, then (a³ + b³) is equal to

96

10

102

108

Solution

108

a² + b² = 24 and ab = 6

therefore space space left parenthesis straight a plus straight b right parenthesis squared space equals space straight a squared space plus space straight b squared space plus space 2 ab space equals space 24 space plus space 2 space cross times 6 space equals space 36 therefore space space straight a space plus space straight b space equals space square root of 36 space equals space 6

therefore space left parenthesis straight a cubed space plus space straight b cubed right parenthesis space equals space left parenthesis straight a space plus space straight b right parenthesis thin space left parenthesis straight a squared space minus space ab space plus space straight b squared right parenthesis space equals space 6 space left parenthesis 24 space minus space 6 right parenthesis space equals space 6 space cross times space 18 space equals space 108

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Algebra

A man loses $20 1 half percent sign$ of his money and after spending 80% of the remainder, he is left with ₹ 159. How much did he have at first?

₹ 500

₹ 800

₹ 1000

₹ 1200

For two positive numbers a and b, if a² + b² = 24 and ab = 6, then (a³ + b³) is equal to

96

10

102

108

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NCERT Sample Papers

Entrance Exams Preparation

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For Daily Free Study Material Join wiredfaculty

WhatsApp Group

Download Android App

Ncert Book Download

Algebra

A complete factorization of is

A man loses of his money and after spending 80% of the remainder, he is left with ₹ 159. How much did he have at first? ₹ 500 ₹ 800 ₹ 1000 ₹ 1200

Among below expressions which one can be expressed as the difference of two cubic expressions?

Find the sum of: n (n + 1)

For two positive numbers a and b, if a2 + b2 = 24 and ab = 6, then (a3 + b3) is equal to 96 10 102 108

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A man loses $20 1 half percent sign$ of his money and after spending 80% of the remainder, he is left with ₹ 159. How much did he have at first?

₹ 500

₹ 800

₹ 1000

₹ 1200

For two positive numbers a and b, if a² + b² = 24 and ab = 6, then (a³ + b³) is equal to

96

10

102

108