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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Sequences and Series

NDA 2024 · Mathematics · Sequences and Series

Let m=77^n . The index n is given a positive integral value at...

Let m=77nm=77^n. The index nn is given a positive integral value at random. What is the probability that the value of mm will have 1 in the units place?

Options

  1. A12\frac{1}{2}
  2. B13\frac{1}{3}
  3. C14\frac{1}{4}
  4. D1n\frac{1}{n}

Correct answer

C. 14\frac{1}{4}

Step-by-step solution

∴m=77n\therefore \quad m=77^nPut,n=1,2,3,4For,n=1m=77\begin{aligned} Put, n & =1,2,3,4 \\ For, n & =1 \\ m & =77 \end{aligned}For,n=2,m=772=5929For, n=2, m=77^2=5929For,n=3,m=773=456543For,n=4,m=774=35153041= last digit will be 1\begin{aligned} For, n & =3, m=77^3=456543 \\ For, n & =4, m=77^4=35153041 \\ & =\text{ last digit will be } 1 \end{aligned}Hence,Hence, the required probability =14\frac{1}{4}
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