Mathematical Physics - Study Mode

[#6] The value of the residue of $$frac{{sin z}}{{{z^6}}}$$ xa0is
Correct Answer

(B) $$frac{1}{{5!}}$$

[#7] Which one of the following curves gives the solution of the differential equation $${k_1}frac{{dx}}{{dt}} + {k_2}x = {k_3},$$ xa0 xa0where k 1 , k 2 and k 3 are positive constant with initial conditions x = 0 and t = 0?
Correct Answer

[#8] The eigen values and eigen vectors of the matrix [left[ {x08egin{array}{*{20}{c}}
5&4 \
1&2
end{array}}
ight]] xa0are
Correct Answer

(A) 6, 1 and [left[ {x08egin{array}{*{20}{c}} 4 \ 1 end{array}} ight],,left[ {x08egin{array}{*{20}{c}} 1 \ { - 1} end{array}} ight]]

[#9] If a force [overrightarrow {mathbf{F}} ] is derivable from a potential function V(r), where r is the distance from the origin of the coordinate system, it follows that
Correct Answer

(A) [overrightarrow abla imes overrightarrow {mathbf{F}} = 0]

[#10] If two matrices A and B can be diagonalized simultaneously, which of the following is true?
Correct Answer

(C) AB = BA