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The question asks which of the following equations is linear. Let's go through each equation to determine linearity:

1. **Equation (A):** \( 2x_1^2 + 3x_2^2 + 4x_3^4 = 5 \)  
   - This is **not linear** because it contains terms like \(x_1^2\), \(x_2^2\), and \(x_3^4\), which are powers higher than 1.

2. **Equation (B):** \( \sqrt{3}x_1 - \sqrt{2}x_2 + x_3 = 5 \)  
   - This equation **is linear**. Each variable \(x_1\), \(x_2\), and \(x_3\) appears to the first power, and there are no non-linear functions applied to the variables (e.g., squares, square roots, cosines).

3. **Equation (C):** \( \sqrt{5}x_1 + 5\sqrt{x_2} - x_3 = 1 \)  
   - This is **not linear** because of the term \( \sqrt{x_2} \), which introduces a non-linear element.

4. **Equation (D):** \( 2^2x_1 + \cos(x_2) + 4x_3 = 7 \)  
   - This is **not linear** because of the cosine function, \( \cos(x_2) \), which is a non-linear operation.

### Conclusion:
The only linear equation is **(B)**.

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Would you like further details or have any questions?  
Here are 5 related questions to explore further:

1. What are the general characteristics of a linear equation?
2. How does the presence of powers or roots affect the linearity of an equation?
3. Can trigonometric functions be part of a linear equation?
4. What is the difference between linear and non-linear terms?
5. How do we graphically represent linear versus non-linear equations?

**Tip:** In a linear equation, each variable is raised to the first power and is not involved in any non-linear operations (e.g., trigonometric, exponential, or logarithmic functions).

Which of the following equations is linear?

Learn how to identify a linear equation by examining terms and understanding linearity. This problem provides a comparison of different algebraic equations, exploring which one is linear. Suitable for high school students in Grades 9-12.

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