Question

Choose the FALSE statement from the following.

• A. Generally, in conductors the valence and conducting bands overlap.
• B. The resistivity of a semiconductor increases with increase in temperature.
• C. The conductivity of a semiconductor increases with increase in temperature.
• D. Substances with energy gap of the order of $10\ \text{eV}$ are insulators.

Hint:

Options (B) and (C) are absolute logical opposites of one another. Since both talk about a semiconductor's response to a temperature increase, one of them must be false. Identifying mutually exclusive option pairs right away allows you to hone in on the right choice within seconds!

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
Two answer options are direct logical opposites regarding a semiconductor's temperature response. Use this to quickly narrow down the correct choice.

Step 2: Key Formula or Approach:
When two options are mutual negations of each other, by the law of excluded middle, exactly one must be true and the other false. This logical structure allows immediate elimination of the remaining options.

Step 3: Detailed Explanation:
Options (B) and (C) make contradictory claims about how a semiconductor's property changes with increasing temperature. Since they cannot both be correct, the true answer must lie within this pair, instantly ruling out (A) and (D). Analyzing the physics—semiconductor resistivity decreases as temperature rises due to increased charge carrier generation—confirms the correct choice. Identifying logical opposites first dramatically narrows the field.

Step 4: Final Answer:
Spotting mutually exclusive options allows rapid elimination of distractors.