IIT JAM & CSIR NET - Chemical Sciences

Pericyclic Reactions & Spectroscopy question bank (Organic Chemistry & Reaction Mechanisms)

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Q1.
[Organic Chemistry & Reaction Mechanisms Problem #1] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)
All eigenvalues are pure imaginary
(B)
The matrix cannot be diagonalized under any orthogonal transformation
(C)
All eigenvalues are strictly real, and eigenvectors from distinct eigenvalues are orthogonal
(D)
Eigenvalues must always be positive integers
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Q2.
[Organic Chemistry & Reaction Mechanisms Problem #3] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)
Eigenvalues must always be positive integers
(B)
The matrix cannot be diagonalized under any orthogonal transformation
(C)
All eigenvalues are strictly real, and eigenvectors from distinct eigenvalues are orthogonal
(D)
All eigenvalues are pure imaginary
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