Step 1: Understanding the sentence.
The sentence talks about the time frame in which Chanakya lived, referring to the period of Chandragupta Maurya's reign. The correct preposition must indicate the period in which something happened.
Step 2: Analyzing the options.
- (A) under: This preposition refers more to a position beneath something and is not typically used for time periods. Therefore, it is incorrect.
- (B) since: "Since" is used for actions that began in the past and continue into the present, which does not fit with the context of this sentence. Hence, it is incorrect.
- (C) during: This is the correct preposition, as it correctly conveys the idea of happening within the time span of the reign.
- (D) no change / no error: There is an error in the sentence, as "for" should be replaced with "during," making this option incorrect.
Step 3: Conclusion.
The correct answer is (C) during, as it accurately conveys the time frame in which Chanakya lived.
A weight of $500\,$N is held on a smooth plane inclined at $30^\circ$ to the horizontal by a force $P$ acting at $30^\circ$ to the inclined plane as shown. Then the value of force $P$ is:
A steel wire of $20$ mm diameter is bent into a circular shape of $10$ m radius. If modulus of elasticity of wire is $2\times10^{5}\ \text{N/mm}^2$, then the maximum bending stress induced in wire is: