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

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

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

3
1
2
1 અથવા 2

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

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

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

Tips: -

$bold left parenthesis bold 1 bold space bold plus bold space bold t to the power of bold 2 bold right parenthesis to the power of bold 12 bold space bold left parenthesis bold 1 bold space bold plus bold space bold t to the power of bold 12 bold right parenthesis bold space bold left parenthesis bold 1 bold plus bold t to the power of bold 24 bold right parenthesis bold space bold equals bold space bold left parenthesis bold 1 bold plus bold t to the power of bold 12 bold plus bold t to the power of bold 24 bold plus bold t to the power of bold 36 bold right parenthesis bold left parenthesis bold 1 bold plus bold t to the power of bold 2 bold right parenthesis to the power of bold 12 bold equals bold space bold left parenthesis bold 1 bold space bold plus bold space bold t to the power of bold 12 bold space bold plus bold space bold t to the power of bold 24 bold space bold plus bold space bold t to the power of bold 36 bold right parenthesis bold space open square brackets open parentheses table row bold 12 row bold 0 end table close parentheses bold space bold plus bold space open parentheses table row bold 12 row bold 1 end table close parentheses bold space bold t to the power of bold 2 bold space bold plus bold space open parentheses table row bold 12 row bold 2 end table close parentheses bold space bold r to the power of bold 4 bold space bold plus bold space bold. bold. bold. bold space bold plus bold space open parentheses table row bold 12 row bold 12 end table close parentheses bold space bold t to the power of bold 24 close square brackets$

t²⁴ નો સહગુણક $bold equals bold space bold 1 bold space bold cross times bold space open parentheses table row bold 12 row bold 12 end table close parentheses bold space bold plus bold space bold 1 bold space bold cross times bold space open parentheses table row bold 12 row bold 6 end table close parentheses bold space bold plus bold space bold 1 bold space bold cross times bold space open parentheses table row bold 12 row bold 0 end table close parentheses$

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

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.

$bold 405 over bold 256$
$504 over bold 256$
$bold 450 over bold 263$
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Gujarati JEE Mathematics : દ્વિપદી પ્રમેય

Multiple Choice Questions

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