Step 1: Understanding time series patterns.
- **Seasonal Variation (A):** This is the regular and predictable pattern that repeats at fixed intervals, often based on the time of the year. It corresponds to **(I)**.
- **Random Fluctuation (B):** These are unpredictable variations in the data that cannot be attributed to any trend or cycle. They correspond to **(IV)**.
- **Business Cycles (C):** These represent periods of expansion and contraction in economic activity over time, and they correspond to **(II)**.
- **Trends (D):** Trends represent the long-term movement in data, typically upward or downward, and correspond to **(III)**.
Step 2: Conclusion.
The correct match is (A) - (I), (B) - (IV), (C) - (II), (D) - (III).
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: