(a+b+c)12 ના વિસ્તરણમાં a3 b4 c5 નો સહગુણક ...... છે. from Mathematics દ્વિપદી પ્રમેય
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Gujarati JEE Mathematics : દ્વિપદી પ્રમેય

Multiple Choice Questions

71.
(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
Answer
    • 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
    Answer
    • 73. (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
    Answer
    • 74. (1 + x2)4 (1 + x3)7 (1 + x4)12 ના વિસ્તરણમાં x11 નો સહગુણક ...... છે.
    • 1120
    • 1106
    • 1113
    • 1051
    Answer
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    75. (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

    A.

    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

    B.

    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

    C.

    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

    Tips: -

    (a + b + c)12 ના વિસ્તરણમાં વ્યાપક પદ bold equals bold space fraction numerator bold left parenthesis bold 12 bold right parenthesis bold space bold factorial over denominator bold p bold space bold factorial bold space bold q bold space bold factorial bold space bold r bold space bold factorial end fraction bold space bold a to the power of bold p bold space bold b to the power of bold q bold space bold c to the power of bold r bold space bold equals bold space 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 bold space bold a to the power of bold 3 bold space bold b to the power of bold 4 bold space bold c to the power of bold 5

    ∴ માંગેલ સહગુણક bold equals bold space 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 bold space bold equals bold space fraction numerator bold left parenthesis bold 12 bold right parenthesis bold space bold factorial over denominator bold 7 bold space bold factorial bold space bold 5 bold space bold factorial end fraction bold space bold cross times bold space fraction numerator bold 7 bold space bold factorial over denominator bold space bold 3 bold space bold factorial bold space bold 4 bold space bold factorial end fraction

                          bold equals bold space 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 bold equals bold space fraction numerator bold left parenthesis bold 12 bold right parenthesis bold space bold factorial over denominator bold 8 bold space bold factorial bold space bold 4 bold space bold factorial end fraction bold space bold cross times bold space fraction numerator bold 8 bold space bold factorial over denominator bold 3 bold space bold factorial bold space bold 5 bold space bold factorial end fraction bold equals bold space 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
    Answer
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    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 7નાં વિસ્તરણમાં T6 = 84 તો x = ......... .  
    • 3
    • 1
    • 2
    • 1 અથવા 2 
    Answer
    • 77. 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
    Answer
    • 78. (x + 5)6 ના વિસ્તરણમાં T1 = 729 તો ......... .
    • T3 = 30375, x = ± 3
    • T4 = ± 67500, x = ±3
    • x = 3, T2 = -7290
    • T2 = 7290, x = -3
    Answer
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