IIT JAM & CSIR NET - Chemical Sciences

Main Group Chemistry & Lanthanides question bank (Inorganic Chemistry & Coordination Compounds)

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Q1.
[Inorganic Chemistry & Coordination Compounds Problem #2] Regarding eigenvalues of a real symmetric matrix A: Which of the following analytical formulations is correct?

(A)
The matrix cannot be diagonalized under any orthogonal transformation
(B)
All eigenvalues are pure imaginary
(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.
[Inorganic Chemistry & Coordination Compounds Problem #4] Regarding Cauchy-Riemann equations for an analytic function f(z) = u(x,y) + i v(x,y): Which of the following analytical formulations is correct?

(A)
∂u/∂x = ∂v/∂y and ∂u/∂y = -∂v/∂x
(B)
∂u/∂x + ∂v/∂y = 0 and ∂u/∂y + ∂v/∂x = 0
(C)
∂u/∂x = -∂v/∂y and ∂u/∂y = ∂v/∂x
(D)
∂^2u/∂x^2 + ∂^2v/∂y^2 = 0 strictly
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