NIMCET 2014 — Reasoning PYQ

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Question

NIMCET 2014 — Reasoning PYQ

NIMCET | Reasoning | 2014

The arithmetic mean of $2^{10}$ and $2^{20}$ is:

Choose the correct answer:

Explanation

Solution

Step 1: Formula for Arithmetic Mean

The arithmetic mean (average) of two numbers $a$ and $b$ is given by:

\text{Average} = \frac{a + b}{2}

Step 2: Applying the values

Substitute $a = 2^{10}$ and $b = 2^{20}$ :

\text{Average} = \frac{2^{10} + 2^{20}}{2}

Step 3: Simplifying the expression

Divide each term in the numerator by the denominator:

\text{Average} = \frac{2^{10}}{2} + \frac{2^{20}}{2}

Since $2$ can be written as $2^{1}$ , use the law of exponents $\frac{x^{m}}{x^{n}} = x^{m-n}$ :

\text{Average} = 2^{10-1} + 2^{20-1}

\text{Average} = 2^{9} + 2^{19}

Conclusion:

The arithmetic mean of $2^{10}$ and $2^{20}$ is $2^{9} + 2^{19}$ .

Correct Option: 4 ( $2^{9} + 2^{19}$ )