KVPY Sample Paper KVPY Stream-SX Model Paper-12

  • question_answer
    Let \[1\le m<n\le p\]. The number of subsets of the Set \[A=\text{ }\left\{ 1,2,3,\text{ }.......p \right\}\]having in, n as the least and the greatest elements respectively, is

    A) \[{{2}^{n-m-1}}-1\]

    B) \[{{2}^{n-m-1}}\]

    C) \[{{2}^{n-m}}\]

    D) none of these

    Correct Answer: B

    Solution :

    total number of subsets = the number of selections of at least two elements including \[m,n\]and natural numbers lying between \[m,\]and \[,n\]=total number of selection from \[n-m-1\]Different things\[{{2}^{n-m-1}}\]


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