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ક્રમચય અને સંચય

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JEE ગણિત પ્રશ્ન બેંક ભાગ 1

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ગણિત

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ક્રમચય અને સંચય
જો bold m bold space bold equals bold space bold sum from bold r bold equals bold 0 to bold 100 of bold space fraction numerator bold 1 over denominator open parentheses table row bold 100 row bold r end table close parentheses end fraction bold comma  તો bold sum from bold r bold equals bold 0 to bold 100 of bold space fraction numerator bold r over denominator open parentheses table row bold 100 row bold r end table close parentheses end fraction bold space bold equals bold space bold. bold. bold. bold. bold. bold. bold space
  • 100 m
  • 200 m
  • 50 m 
  • 99 m
Answer
    • m + n + p વસ્તુઓમાંથી m, n અને p વસ્તુઓને ત્રણ ખાનામાં કુલ ........ રીતે મૂકી શકાય ?
    • fraction numerator bold left parenthesis bold m bold space bold plus bold space bold n bold space bold plus bold space bold p bold right parenthesis bold space bold factorial over denominator bold m bold space bold factorial bold space bold n bold space bold factorial bold space bold p bold space bold factorial end fraction bold space bold cross times bold space bold 3
    • fraction numerator bold left parenthesis bold m bold space bold space bold n bold space bold plus bold space bold p bold right parenthesis bold space bold factorial over denominator bold m bold space bold factorial bold space bold n bold space bold factorial bold space bold p bold space bold factorial end fraction bold space bold cross times bold space bold 1 over bold 6
    • fraction numerator bold left parenthesis bold m bold space bold plus bold space bold n bold space bold plus bold space bold p bold right parenthesis bold space bold factorial over denominator bold m bold space bold factorial bold space bold n bold space bold factorial bold space bold p bold space bold factorial end fraction
    • fraction numerator bold left parenthesis bold m bold space bold plus bold space bold n bold space bold plus bold space bold p bold right parenthesis bold space bold factorial over denominator bold m bold space bold factorial bold space bold n bold space bold factorial bold space bold p bold space bold factorial end fraction bold space bold cross times bold space bold 3 bold space bold factorial
    Answer
    • કુલ m + n + p વસ્તુઓનું m, વસ્તુઓ, n વસ્તુઓ અને p વસ્તુઓના ત્રણ ભાગમાં વિભાજન કેટલી રીતે કરી શકાય ?
    • fraction numerator bold left parenthesis bold m bold space bold plus bold space bold n bold plus bold space bold p bold right parenthesis bold space bold factorial over denominator bold m bold space bold factorial bold space bold n bold space bold factorial bold space bold p end fraction bold cross times bold space bold 3
    • fraction numerator bold left parenthesis bold m bold space bold plus bold space bold n bold plus bold space bold p bold right parenthesis bold space bold factorial over denominator bold m bold space bold factorial bold space bold n bold space bold factorial bold space bold p end fraction bold cross times bold space bold 1 over bold 6
    • fraction numerator bold left parenthesis bold m bold space bold plus bold space bold n bold plus bold space bold p bold right parenthesis bold space bold factorial over denominator bold m bold space bold factorial bold space bold n bold space bold factorial bold space bold p end fraction bold cross times bold space bold 3 bold space bold factorial
    • fraction numerator bold left parenthesis bold m bold space bold plus bold space bold n bold plus bold space bold p bold right parenthesis bold space bold factorial over denominator bold m bold space bold factorial bold space bold n bold space bold factorial bold space bold p bold space bold factorial end fraction
    Answer
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    mn ભિન્ન વસ્તુઓનું n સમાન ભાગમાં ........ રીતે વિભાજન કરી શકાય.
    • fraction numerator bold left parenthesis bold m bold space bold n bold right parenthesis bold space bold factorial over denominator bold left parenthesis bold m bold space bold factorial bold right parenthesis to the power of bold n end fraction bold cross times bold space fraction numerator bold 1 over denominator bold n bold space bold factorial end fraction
    • fraction numerator bold left parenthesis bold m bold space bold n bold right parenthesis bold space bold factorial over denominator bold left parenthesis bold m bold space bold factorial bold right parenthesis to the power of bold n end fraction
    • fraction numerator bold left parenthesis bold m bold space bold n bold right parenthesis bold space bold factorial over denominator bold left parenthesis bold m bold space bold factorial bold right parenthesis to the power of bold n end fraction bold cross times bold 1 over bold n

    • આપેલ પૈકી એક પણ નહી 

    A.

    fraction numerator bold left parenthesis bold m bold space bold n bold right parenthesis bold space bold factorial over denominator bold left parenthesis bold m bold space bold factorial bold right parenthesis to the power of bold n end fraction bold cross times bold space fraction numerator bold 1 over denominator bold n bold space bold factorial end fraction

    Tips: -

    અહીં દરેક ભાગમાં bold mn over bold n bold space bold equals bold space bold m વસ્તુઓ આવે. 

    વિભાજનના પ્રકારની સંખ્યા bold equals bold space fraction numerator open parentheses table row bold mn row bold m end table close parentheses bold space open parentheses table row cell bold mn bold minus bold m end cell row bold m end table close parentheses bold space bold. bold. bold. bold space open parentheses table row bold m row bold m end table close parentheses over denominator bold n bold space bold factorial end fraction

                                    equals bold space fraction numerator begin display style fraction numerator bold left parenthesis bold mn bold right parenthesis bold space bold factorial over denominator bold m bold space bold factorial bold space bold left parenthesis bold mn bold space bold minus bold space bold m bold right parenthesis bold space bold factorial end fraction end style bold cross times bold space begin display style fraction numerator bold left parenthesis bold mn bold minus bold m bold right parenthesis bold space bold factorial over denominator bold m bold factorial bold left parenthesis bold mn bold space bold minus bold space bold 2 bold m bold right parenthesis bold factorial end fraction end style bold space bold. bold. bold. bold space begin display style fraction numerator bold m bold space bold factorial over denominator bold m bold space bold factorial bold space bold 0 bold space bold factorial end fraction end style over denominator bold n bold space bold factorial end fraction bold equals bold space fraction numerator bold left parenthesis bold mn bold right parenthesis bold space bold factorial over denominator bold left parenthesis bold m bold space bold factorial bold right parenthesis to the power of bold n end fraction bold space bold cross times bold space fraction numerator bold 1 over denominator bold n bold space bold factorial end fraction
    Answer
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