Assertion (A): The resistivity of semiconductor' decreases with increase of temperature.
Reason (R): in a conducting solid, the rate of collision increases with increase of temperature.

Options

A. Both (A) and (R) are true and (R) is the correct explanation of (A).
B. Both (A) and (R) are true but (R) is not the correct explanation of (A).
C. (A) is true but (R) is false.
D. (A) is false and (R) is also false.

Explanation

To solve the question, we need to analyze both the assertion (A) and the reason (R) given in the problem.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that "The resistivity of a semiconductor decreases with an increase in temperature."
- In semiconductors, as the temperature increases, more electrons gain enough energy to jump from the valence band to the conduction band. This results in an increase in the number of charge carriers, which increases conductivity and consequently decreases resistivity.

2. **Understanding the Reason (R)**:
- The reason states that "In a conducting solid, the rate of collision increases with an increase in temperature."
- In general, as temperature increases, the atoms in a solid vibrate more vigorously. This increased vibration leads to more frequent collisions between charge carriers (like electrons) and the vibrating atoms, which can affect conductivity.

3. **Analyzing the Relationship**:
- While both statements are true, they refer to different phenomena. The assertion is specifically about semiconductors, while the reason discusses conductors in general.
- In conductors, increasing temperature typically increases resistivity due to more collisions, while in semiconductors, the increased temperature leads to decreased resistivity due to increased charge carriers.

4. **Conclusion**:
- The assertion (A) is true, and the reason (R) is also true, but the reason does not correctly explain the assertion. Therefore, the correct option is that both statements are true, but the reason is not the correct explanation of the assertion.

### Final Answer:
- Both the assertion and reason are true, but the reason is not the correct explanation for the assertion.

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