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CAT 2003 Slot 2 — QA Question 46

LogarithmsEasy
Passage / Data

Answer the following question based on the information given below.

A string of three English letters is formed as per the following rules:

  1. The first letter is any vowel.
  2. The second letter is m, n or p.
  3. If the second letter is m, then the third letter is any vowel which is different from the first letter.
  4. If the second letter is n, then the third letter is e or u.
    1. If the second letter is p, then the third letter is the same as the first letter.

What is the sum of n terms in the series

log⁡m+log⁡m2n+log⁡m3n2+log⁡m4n3+⋯+log⁡mnnn−1?

Answer & solution

  • A

    log[nn-1m(n+1)]n2

  • B

    log[mmnn]n2

  • C

    log[m(1-n)n(1-m)]n2

  • log[m(n+1)n(n-1)]n2

Solution

log⁡m+log⁡(m2n)+log⁡(m3n2)+log⁡(m4n3)+…+log⁡(mnnn−1)=log⁡[m×m2×m3×…×mn1×n×n2×…×nn−1]=log⁡[m1+2+3+4+…+nn0+1+2+3+…+(n−1)]=log⁡[mn2(n+1)nn2(n−1)]=log⁡[m(n+1)n(n−1)]n2

Hence, option (d).

CAT 2003 Slot 2 QA Q46: What is the sum of n terms in the series log ⁡ m + log ⁡ m 2 n + log ⁡ m 3 n 2 + log ⁡ — Solution | TheCATExam