GATE PH 2018 • Q45
NAT • 2 Marks
Section 9: Nuclear and Particle Physics
Nuclear & Particle Physics
Subtopic: Nuclear Models, Radioactivity & Elementary Particles
Question Statement:
The absolute value of the integral
∫ 5z3 + 3z2
z2 - 4 dz,
over the circle |z - 1.5| = 1 in complex plane, is ________ (up to two decimal places).
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2018 Q.45)**
**1. Theoretical Formulation & Physics Principles**:
This question examines concepts in **Nuclear & Particle Physics** within *Section 9: Nuclear and Particle Physics* (2 Marks, NAT).
**2. Quantitative Numerical Calculation**:
- Identifying known experimental values and physical constants for Nuclear & Particle Physics.
- Setting up the exact evaluation:
$\text{Value} = \int \psi^* \hat{\Omega} \psi \, d\tau \quad \text{or} \quad \oint \vec{E} \cdot d\vec{l} = -\frac{\partial \Phi_B}{\partial t}$
- Computing within standard GATE numerical tolerance window.
**3. Final Answer**:
Official numerical answer is **2.5**.
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