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NIMCET 2010 — Reasoning PYQ

NIMCET | Reasoning | 2010

There are 6561 balls out of them 1 is heavy. Find the minimum number of times the balls have to be weighed for finding out the heavy ball.

Choose the correct answer:

Explanation

1. Formula:

If we have $n$ weighings, the maximum number of balls we can check to find one heavy ball is $3^n$ .

Therefore, the relationship is:

3^n \ge \text{Total number of balls}

2. Calculation:

Given the total number of balls is 6561. We need to find the smallest integer $n$ such that:

3^n \ge 6561

We can express 6561 as a power of 3:

3^1 = 3

3^2 = 9

3^3 = 27

3^4 = 81

3^5 = 243

3^6 = 729

3^7 = 2187

3^8 = 6561

So,

3^8 = 6561

3. Conclusion:

The minimum number of weighings required is $n = 8$ .

Correct Option: (c) 8