Step 1: Understanding the dependency ratio.
- **Andhra Pradesh (A)** has a dependency ratio of **66.3** for 2023-24, which corresponds to **(I)**.
- **Bihar (B)** has a dependency ratio of **52.2**, which corresponds to **(II)**.
- **Kerala (C)** has a dependency ratio of **41.4**, which corresponds to **(IV)**.
- **Uttar Pradesh (D)** has a dependency ratio of **50.6**, which corresponds to **(III)**.
Step 2: Conclusion.
The correct answer is **(A) - (I), (B) - (II), (C) - (IV), (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: