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CAT 1999 — QA Question 5

Forming a committeeEasy

For a scholarship, at the most n candidates out of 2n + 1 can be selected. If the number of different ways of selection of at least one candidate is 63, the maximum number of candidates that can be selected for the scholarship is

Answer & solution

  • 3

  • B

    4

  • C

    6

  • D

    5

Solution

At least 1 and at most n are to be selected

⇒ 2n+1C1 + 2n+1C2 + ... + 2n+1Cn = 63

⇒12(22n+1 - 2) = 63

⇒ n = 3

Hence, option (a).

CAT 1999 QA Q5: For a scholarship, at the most n candidates out of 2n + 1 can be selected. If the number of different ways of — Solution | TheCATExam