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KVPY Sample Paper KVPY Stream-SX Model Paper-2

  • question_answer
    If \[{}^{m}{{C}_{3}}+{}^{m}{{C}_{4}}{{>}^{m+1}}{{C}_{3}},\] then least value of m is

    A) 6                                 

    B) 7

    C) 5                                 

    D) none of these

    Correct Answer: B

    Solution :

    \[{}^{m}{{C}_{3}}+{}^{m}{{C}_{4}}{{>}^{m+1}}{{C}_{3}}\]
    \[\Rightarrow \] \[{}^{m+1}{{C}_{4}}>{}^{m+1}{{C}_{3}}\]
    \[\Rightarrow \] \[\frac{(m+1)!}{(m-3)!4!}>\frac{(m+1)!}{(m-2)!3!}\]         
    \[\Rightarrow \] \[m-2>4\]
    \[\Rightarrow \] \[m>6\]  
    \[\Rightarrow \] The least value of m is 7.


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