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

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

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

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

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

3
1
2
1 અથવા 2

1 અથવા 2

Tips: -

$bold T subscript bold 6 bold space bold equals bold space open parentheses table row bold 7 row bold 5 end table close parentheses bold space open parentheses bold 9 to the power of bold x bold minus bold 1 end exponent bold plus bold 7 close parentheses to the power of begin inline style bold 2 over bold 2 end style end exponent bold space open parentheses bold 3 to the power of bold x bold minus bold 1 end exponent bold plus bold 1 close parentheses to the power of begin inline style fraction numerator bold minus bold 5 over denominator bold 5 end fraction end style end exponent bold space bold equals bold space bold 84 bold space bold therefore bold space bold 21 bold space bold left parenthesis bold 9 to the power of bold x bold minus bold 1 end exponent bold plus bold 7 bold right parenthesis bold space bold equals bold space bold 84 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 bold therefore bold space bold 3 to the power of bold 2 bold x end exponent over bold 9 bold space bold plus bold space bold 7 bold space bold equals bold space bold 4 bold space open parentheses bold 3 to the power of bold x over bold 3 bold plus bold 1 close parentheses bold therefore bold space bold 3 to the power of bold 2 bold x end exponent bold space bold plus bold space bold 63 bold space bold equals bold space bold 12 bold space bold times bold space bold 3 to the power of bold x bold space bold plus bold space bold 36 bold space bold therefore bold space bold left parenthesis bold 3 to the power of bold x bold right parenthesis to the power of bold 2 bold space bold minus bold space bold 12 bold space bold times bold space bold 3 to the power of bold x bold space bold plus bold space bold 27 bold space bold equals bold space bold 0 bold space bold therefore bold space bold left parenthesis bold 3 to the power of bold x bold minus bold 3 bold right parenthesis bold space bold left parenthesis bold 3 to the power of bold x bold minus bold 9 bold right parenthesis bold space bold equals bold space bold 0$
$bold therefore bold space bold 3 to the power of bold x bold space bold equals bold space bold 3$ અથવા $bold 3 to the power of bold x bold space bold equals bold space bold 9$

$bold therefore bold space bold x bold space bold equals bold space bold 1$ અથવા x = 2

75.

(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

76. (1 + x)²ⁿ⁺¹² માં મોટામાં મોટો સહગુણક ...... છે.

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

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

1120
1106
1113
1051

78. (1 + t²)¹² (1 + t¹²) (1 + t²⁴) માં t²⁴ નો સહગુણક ....... છે.

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

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Gujarati JEE Mathematics : દ્વિપદી પ્રમેય

Multiple Choice Questions

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