NIMCET 2009 — Reasoning PYQ

Step 1: Identify the relevant digit

To find the unit digit of a large power, we only need to consider the unit digit of the base.

Step 2: Determine the cyclicity of 7

The unit digits of powers of $7$ follow a repeating pattern (cyclicity):

• $7^1=7$

• $7^2=49\to 9$

• $7^3=343\to 3$

• $7^4=2401\to 1$

  The pattern $7,9,3,1$ repeats every $4$ steps. So, the cyclicity of $7$ is $4$.

Step 3: Divide the exponent by the cyclicity

Now, divide the exponent $3265$ by $4$ to find the remainder.

Step 4: Find the unit digit

The unit digit will be the same as $7^{\text{remainder}}$:

The unit digit is 7.

Correct Option: (c)