Consider the set {1, x, x2}. An orthonormal basis in x ∈ [-1,1] is formed from
these three terms , where the normalization of a function f(x) is defined via
∫ x2[f(x)]2dx = 1
1
-1 . If the orthonormal basis set is
(√
3
2 , √
5
2 x ,
1
2 √
21
N (5x2 - 3)) , then the value of N (in integer) is ______
Official Answer Key:
2.5
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2025 Q.61)**
**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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