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Gujarati JEE Mathematics : દ્વિપદી પ્રમેય

Multiple Choice Questions

71. (x + 5)⁶ ના વિસ્તરણમાં T₁ = 729 તો ......... .

T₃ = 30375, x = ± 3
T₄ = ± 67500, x = ±3
x = 3, T₂ = -7290
T₂ = 7290, x = -3

72.

(1 - 3x² + 10x⁵)ⁿ અને (1 + x⁷)ⁿ ના વિસ્તરણમાં સહગુણકોનો સરવાળો અનુક્રમે p અને q હોત, તો............(n>1)

p = q³
pq = 4²ⁿ
p + q = pq
p : q = 4

73. (a+b+c)¹² ના વિસ્તરણમાં a³ b⁴ c⁵ નો સહગુણક ...... છે.

$fraction numerator bold left parenthesis bold 12 bold right parenthesis bold space bold factorial over denominator bold 3 bold space bold factorial bold space bold 4 bold space bold factorial bold space bold 5 bold space bold factorial end fraction$
$open parentheses table row bold 12 row bold 5 end table close parentheses bold space bold cross times bold space open parentheses table row bold 7 row bold 3 end table close parentheses$
$open parentheses table row bold 12 row bold 3 end table close parentheses bold space open parentheses table row bold 12 row bold 4 end table close parentheses bold space open parentheses table row bold 12 row bold 5 end table close parentheses$
$open parentheses table row bold 12 row bold 4 end table close parentheses bold space bold cross times bold space open parentheses table row bold 8 row bold 3 end table close parentheses$

74. (1 + t²)¹² (1 + t¹²) (1 + t²⁴) માં t²⁴ નો સહગુણક ....... છે.

$open parentheses table row bold 12 row bold 6 end table close parentheses bold space bold plus bold space bold 1$
$open parentheses table row bold 12 row bold 6 end table close parentheses bold space bold plus bold space bold 3$
$open parentheses table row bold 12 row bold 6 end table close parentheses bold space bold plus bold space bold 3$
$open parentheses table row bold 12 row bold 6 end table close parentheses bold space bold plus bold space bold 2$

75. (1 + x)²ⁿ⁺¹² માં મોટામાં મોટો સહગુણક ...... છે.

$fraction numerator bold 2 bold space bold factorial over denominator bold left parenthesis bold n bold plus bold 6 bold right parenthesis bold space bold factorial end fraction$
$open parentheses table row cell bold 2 bold n bold plus bold 12 end cell row cell bold n bold plus bold 6 end cell end table close parentheses$
$fraction numerator bold left parenthesis bold 2 bold n bold plus bold 12 bold right parenthesis bold factorial over denominator bold left square bracket bold left parenthesis bold n bold plus bold 6 bold right parenthesis bold factorial bold right square bracket to the power of bold 2 end fraction$
$open parentheses table row cell bold 2 bold n bold plus bold 12 end cell row cell bold n bold plus bold 7 end cell end table close parentheses$

76. $open curly brackets bold left parenthesis bold 9 to the power of bold x bold minus bold 1 end exponent bold plus bold 7 bold right parenthesis to the power of begin inline style bold 1 over bold 2 end style end exponent bold plus bold space bold left parenthesis bold 3 to the power of bold x bold minus bold 1 end exponent bold plus bold 1 bold right parenthesis to the power of begin inline style fraction numerator bold minus bold 1 over denominator bold 5 end fraction end style end exponent close curly brackets to the power of bold 7$ નાં વિસ્તરણમાં T₆= 84 તો x = ......... .

3
1
2
1 અથવા 2

77. (1 + x²)⁴ (1 + x³)⁷ (1 + x⁴)¹² ના વિસ્તરણમાં x¹¹ નો સહગુણક ...... છે.

1120
1106
1113
1051

78. $open parentheses bold x over bold 2 bold minus bold 3 over bold x to the power of bold 2 close parentheses to the power of bold 10$ માં x⁴ નો સહગુણક ......... છે.

$bold 405 over bold 256$
$504 over bold 256$
$bold 450 over bold 263$
આપેલ પૈકી એક પણ નહી

bold 405 over bold 256

Tips: -

અહીં, $bold T subscript bold r bold plus bold 1 end subscript bold space bold equals bold space open parentheses table row bold 10 row bold r end table close parentheses bold space open parentheses bold x over bold 2 close parentheses to the power of bold 10 bold minus bold r end exponent open parentheses fraction numerator bold minus bold 3 over denominator bold x to the power of bold 2 end fraction close parentheses to the power of bold r bold space bold equals bold space open parentheses table row bold 10 row bold r end table close parentheses bold space bold x to the power of bold 10 bold minus bold 3 bold r end exponent bold space fraction numerator bold left parenthesis bold minus bold 1 bold right parenthesis to the power of bold r bold space bold 3 to the power of bold r over denominator bold 2 to the power of bold 10 bold minus bold r end exponent end fraction$

x⁴ ના સહગુણક માટે 10 - 3r = 4 ⇒ r = 2

x⁴ નો સહગુણક $bold equals bold space open parentheses table row bold 10 row bold 2 end table close parentheses bold space fraction numerator bold left parenthesis bold minus bold 1 bold right parenthesis to the power of bold 2 bold 3 to the power of bold 2 over denominator bold 2 to the power of bold 8 end fraction bold space bold equals bold space fraction numerator bold 45 bold cross times bold 9 over denominator bold 256 end fraction$

$bold equals bold space bold 405 over bold 256$

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Gujarati JEE Mathematics : દ્વિપદી પ્રમેય

Multiple Choice Questions

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