(1 + x2)4 (1 + x3)7 (1 + x4)12 ના વિસ્તરણમાં x11 નો સહગુણક ...... છે.  from Mathematics ક્રમચય અને સંચય
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Gujarati JEE Mathematics : ક્રમચય અને સંચય

Multiple Choice Questions

111.
MATHEMATICS શબ્દમાં જે અક્ષરોનું પુનરાવર્તન થતું નથી તે અક્ષરો અયુગ્મ સ્થાને અને જે અક્ષરોનું પુનરાવર્તન થાય છે તે અક્ષરો યુગ્મ સ્થાને આવે તે રીતે છ અક્ષરોના બનતા શબ્દોની સંખ્યા ....... છે.
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Answer
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    112. (1 + x2)4 (1 + x3)7 (1 + x4)12 ના વિસ્તરણમાં x11 નો સહગુણક ...... છે. 
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    A.

    1113

    Tips: -

    અહીં x11 ગુણાકારમાં આવી રીતે શક્ય છે.
     
    bold x to the power of bold 11 bold space bold equals bold space bold x to the power of bold 0 bold space bold x to the power of bold 3 bold space bold x to the power of bold 8 bold space bold equals bold space bold left parenthesis bold x to the power of bold 2 bold right parenthesis to the power of bold 0 bold space bold left parenthesis bold x to the power of bold 3 bold right parenthesis to the power of bold 1 bold space bold left parenthesis bold x to the power of bold 4 bold right parenthesis to the power of bold 2 bold comma

         bold equals bold space bold x to the power of bold 8 bold space bold x to the power of bold 3 bold space bold x to the power of bold 0 bold space bold equals bold space bold left parenthesis bold x to the power of bold 2 bold right parenthesis to the power of bold 4 bold space bold left parenthesis bold x to the power of bold 3 bold right parenthesis to the power of bold 1 bold space bold left parenthesis bold x to the power of bold 4 bold right parenthesis to the power of bold 0 bold equals bold space bold x to the power of bold 2 bold space bold x to the power of bold 9 bold space bold x to the power of bold 0 bold space bold equals bold space bold left parenthesis bold x to the power of bold 2 bold right parenthesis to the power of bold 1 bold space bold left parenthesis bold x to the power of bold 3 bold right parenthesis to the power of bold 3 bold space bold left parenthesis bold x to the power of bold 4 bold right parenthesis to the power of bold 0 bold comma bold space bold equals bold space bold x to the power of bold 4 bold space bold x to the power of bold 3 bold space bold x to the power of bold 4 bold space bold equals bold space bold left parenthesis bold x to the power of bold 2 bold right parenthesis to the power of bold 2 bold space bold left parenthesis bold x to the power of bold 3 bold right parenthesis to the power of bold 1 bold space bold left parenthesis bold x to the power of bold 4 bold right parenthesis to the power of bold 1

    ∴ x11 નો સહગુણક = open parentheses table row bold 4 row bold 0 end table close parentheses bold space open parentheses table row bold 7 row bold 1 end table close parentheses bold space open parentheses table row bold 12 row bold 2 end table close parentheses bold space bold plus bold space open parentheses table row bold 4 row bold 4 end table close parentheses bold space open parentheses table row bold 7 row bold 1 end table close parentheses bold space open parentheses table row bold 12 row bold 0 end table close parentheses bold space bold plus bold space open parentheses table row bold 4 row bold 1 end table close parentheses bold space open parentheses table row bold 7 row bold 3 end table close parentheses bold space open parentheses table row bold 12 row bold 0 end table close parentheses bold space bold plus bold space open parentheses table row bold 4 row bold 2 end table close parentheses bold space open parentheses table row bold 7 row bold 1 end table close parentheses bold space open parentheses table row bold 12 row bold 1 end table close parentheses
     
                            bold equals bold space bold left parenthesis bold 1 bold space bold cross times bold space bold 7 bold space bold cross times bold space bold 66 bold right parenthesis bold space bold plus bold space bold left parenthesis bold space bold 1 bold space bold cross times bold space bold 7 bold space bold cross times bold space bold 1 bold right parenthesis bold space bold plus bold space bold left parenthesis bold 4 bold space bold cross times bold space bold 35 bold space bold cross times bold space bold 1 bold right parenthesis bold space bold plus bold space bold left parenthesis bold 6 bold space bold cross times bold space bold 7 bold space bold cross times bold space bold 12 bold right parenthesis bold space bold equals bold space bold 462 bold space bold plus bold space bold 7 bold space bold plus bold space bold 140 bold space bold plus bold space bold 504 bold space bold equals bold space bold 1113 bold space bold space
    Answer
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    113. પાંચ ચાર ત્રણ અને બે વડે પાંચ અક્ષરોના કેટલા શબ્દો બને ? 
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    Answer
    • 114.
    GUJARAT શબ્દના અક્ષરોની મદદથી અક્ષર G આવે જ તેવી રીતે ચાર અક્ષરના કુલ કેટલા શબ્દો બને ?
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    Answer
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    115.
    છ વ્યક્તિઓ A, B, C, D, E, F એક વત્યુળાકાર ટેબલ પર કેટલી રીતે બેસી શકે કે જેથી A ની જમણી બાજુ B અથવા C અને B ની જમણી બાજુ C અથવા D આવે ?
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    Answer
    • 116.
    અંકો 3,3,5,5,8,8,8 અને 8 નો ઉપયોગ કરીને 4000 થી મોટી ચાર અંકોની કેટલી સંખ્યા બનાવી શકાય ?
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    Answer
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