Question Statement:
A school has 100 students distributed among 1st to 10th standards.
Based on this, which one of the following statements is always correct?
Options:
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(A) There are at least 10 students who belong to the same standard.
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(B) There is at least one student in each standard.
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(C) There are at most 10 students in 10th standard.
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(D) The total number of students from 1st to 5th standards is at least 50.
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.3)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Quantitative & Analytical Aptitude** within *General Aptitude* (1 Mark, MCQ).
**2. Analytical Derivation & Formalism**:
- Formulating the fundamental physics relations governing Quantitative & Analytical Aptitude:
- Applying canonical quantum/electrodynamic equations:
$\hat{H}\psi = E\psi, \quad \nabla \times \vec{B} = \mu_0 \vec{J} + \mu_0 \epsilon_0 \frac{\partial \vec{E}}{\partial t}, \quad Z = \sum_i g_i e^{-\beta E_i}$
- Substituting boundary parameters and simplifying algebraically.
- The resulting expression uniquely corresponds to Option **(B)**.
**3. Final Answer**:
Correct Option is **(B)**.
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