Match the list-I with list-II and choose the correct option.
List-I | List-II | ||
(A). | Microwave | (P). | 1 nm - 400nm |
(B). | Ultraviolet | (Q). | 1 nm - 1nm |
(C). | X-rays | (R). | 2.5 µm - 750nm |
(D). | Infrared | (S). | 1 µm - 1nm |
Understanding the Problem
We are given different types of electromagnetic waves and their corresponding wavelength ranges. We need to match the waves with their correct uses based on their wavelengths.
Solution
1. Microwave:
Has a wavelength \( \lambda > 700 \, \text{nm} \).
Suitable for communication purposes.
2. Ultraviolet:
Has wavelengths less than \( 400 \, \text{nm} \).
Typically used for sterilization and curing.
3. X-Ray:
Has a very short wavelength in the range of \( 1 \, \text{nm} \) to \( 10^{-3} \, \text{nm} \).
Ideal for medical imaging.
4. Infra-red:
With a wavelength between \( 400 \, \text{nm} \) to \( 700 \, \text{nm} \).
Used in thermal cameras and night vision technologies.
Matching Waves with Wavelengths
Based on the wavelength ranges and uses, we can match the waves as follows:
Microwave - Communication
Ultraviolet - Sterilization
X-Ray - Medical Imaging
Final Answer
Therefore, matching the waves with their wavelengths gives us the correct answer as option (2).
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is:
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