JEE Main & Advanced JEE Main Paper (Held On 22 April 2013)

  • question_answer
    The number of ways in which an examiner can assign 30 marks to 8 question, giving not less than 2 marks to any question, is:     JEE Main  Online Paper (Held On 22 April 2013)

    A)  \[^{30}{{C}_{7}}\]                               

    B)  \[^{21}{{C}_{8}}\]

    C)  \[^{21}{{C}_{7}}\]                                               

    D)  \[^{30}{{C}_{8}}\]

    Correct Answer: C

    Solution :

     30 marks to be alloted to 8 questions. Each question has to be given \[\ge 2\] marks Let questions be \[a,\text{ }b,\text{ }c,\text{ }d,\text{ }e,\text{ }f,\text{ }g,\text{ }h\]          and \[a\text{ }+\text{ }b\text{ }+\text{ }c\text{ }+\text{ }d\text{ }+\text{ }e\text{ }+f+\text{ }g\text{ }+\text{ }h\text{ }=\text{ }30\] Let a \[a={{a}_{1}}+2\] so, \[{{a}_{1}}\ge 0\] \[b={{a}_{2}}+2\]so, \[{{a}_{2}}\ge 0,......,{{a}_{g}}\ge 0\] So, \[\left. \begin{matrix}    {{a}_{1}}+{{a}_{2}}+......+{{a}_{8}}  \\    +2+2+......+2  \\ \end{matrix} \right\}=30\] \[\Rightarrow \] \[{{a}_{1}}+{{a}_{2}}+.....+{{a}_{8}}=30-16=14\] So, this is a problem of distributing 14   articles in 8 groups.                    Number of ways \[={{\,}^{14+8-1}}{{C}_{8-1}}={{\,}^{21}}{{C}_{7}}\]

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