(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.
GUJARAT શબ્દના અક્ષરોની મદદથી અક્ષર G આવે જ તેવી રીતે ચાર અક્ષરના કુલ કેટલા શબ્દો બને ?
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Answer
    • 112. પાંચ ચાર ત્રણ અને બે વડે પાંચ અક્ષરોના કેટલા શબ્દો બને ? 
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    Answer
    • 113.
    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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    114. (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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    115.
    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
    • 116.
    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
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