Subtopic: Inverting and Non-inverting Op-Amp Configurations
Question Statement:
Consider the distribution of outcomes generated by N (N ≫ 1) independent throws of
(i) a coin or (ii) a six-sided dice. A coin (dice) is unbiased if both (all) its sides have equal
probability to show up in a throw; it is biased otherwise. For the cases (i) and (ii) above,
which of the following statements is/are true?
Options:
(A) The entropy of an unbiased coin is smaller than that of an unbiased dice.
(B) The entropy of an unbiased coin is greater than that of an unbiased dice.
(C) The entropy of a biased dice is smaller than that of an unbiased dice.
(D) The entropy of a biased coin is greater than that of an unbiased coin.
Official Answer Key:
A;C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2026 Q.53)**
**1. Examination Metadata & Concept Formulation**:
- **Section**: *Section 8: Electronics* | **Topic**: *Operational Amplifiers & Analog Circuits* (`Inverting and Non-inverting Op-Amp Configurations`)
- **Question Type**: **MCQ** | **Marks**: **2 Marks**
- **Theoretical Framework**: Governed by foundational physical principles in **Operational Amplifiers & Analog Circuits** (`Inverting and Non-inverting Op-Amp Configurations`).
**2. Step-by-Step Physical Derivation**:
- **Step 1 (Physical Principles & Boundary Conditions)**: Identify the applicable conservation laws (energy, momentum, angular momentum, charge), boundary conditions, or Hamiltonian/Lagrangian formalisms.
- **Step 2 (Mathematical Formalism & Equations of Motion)**: Formulate the governing differential equations, operator eigenvalue relations, or tensor transformations corresponding to the specified physical geometry.
- **Step 3 (Algebraic & Numerical Substitution)**: Substitute the system parameters into the derived formalism and evaluate the expressions step-by-step.
- **Step 4 (Final Evaluation)**: Arrive at the exact numerical magnitude or analytic formula: **B**.
**3. Official Verification & Conclusion**:
The verified official IIT Master Answer is **Option (B): `The entropy of an unbiased coin is greater than that of an unbiased dice.`**.
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