Q1.
show that each eigenvalue of A is 0 or 1, if A2 = A;
(i) find the trace of the matrix B = A + A3 + A^{-1}, if the eigenvalues of A are 2, 3, -2.
(ii) Evaluate the linear density in atoms per mm in the following directions in BCC
(a)
Suppose A is a 3 × 3 diagonalizable matrix. Then-
1. show that each eigenvalue of A is 0 or 1, if A2 = A;
(i) find the trace of the matrix B = A + A3 + A^{-1}, if the eigenvalues of A are 2, 3, -2.
(ii) Evaluate the linear density in atoms per mm in the following directions in BCC
(b)
iron, which has lattice constant of 2.89 Å: [1 0 0]
(i) [1 1 0]
(ii) [1 1 1].
(iii) Derive an expression for capacitance
(c)
of concentric spheres having radii a (a < b) with single dielectric.
Find the hybrid parameters of the following circuit:
(d) \\lessgtr 5 \\Omega 6 \Omega ≤ 5I1 2V2 Construct full-
(e)
conjunctive normal form for the statement P \→ Q;
(i) disjunctive normal form for the statement (P \→ (Q \\lor R)) \\land (P \\lor Q). 6 + 6 = 12
(ii) (i) Obtain the half-range cosine series for the function $f
(x) = \sin x in 0 \≤ x \≤ π$
2. (a) and hence, find the value of \∑n=1\∞ \(1)/(4n2 - 1).
