71. The inverse of the complex number $$\frac{{3 + 4i}}{{3 - 4i}}$$ is
72. A 3 × 3 matrix has elements such that its trace is 11 and its determinant is 36. The eigen values of the matrix are all known to be positive integers. The largest eigen value of the matrix is
73. The unit vector normal to the surface x2 + y2 - z = 1 at the point P (1, 1, 1) is
74. The value of $$\int_{ - i}^i {\pi \left( {z + 1} \right)dz} $$ is
75. For arbitrary matrices E, F, G and H, if EF - FE = 0 then Trace (EFGH) is equal to
76. Consider the differential equation $$\frac{{{d^2}x}}{{d{t^2}}} + 2\frac{{dx}}{{dt}} + x = 0$$
At time t = 0, it is given that x = 1 and $$\frac{{dx}}{{dt}} = 0.$$ At t = 1, the value of x is given by
At time t = 0, it is given that x = 1 and $$\frac{{dx}}{{dt}} = 0.$$ At t = 1, the value of x is given by
77. Given the four vectors \[{u_1} = \left[ {\begin{array}{*{20}{c}}
1 \\
2 \\
3
\end{array}} \right],\,{u_2} = \left[ {\begin{array}{*{20}{c}}
3 \\
{ - 5} \\
1
\end{array}} \right],\,{u_3} = \left[ {\begin{array}{*{20}{c}}
2 \\
4 \\
{ - 8}
\end{array}} \right].\,{u_4} = \left[ {\begin{array}{*{20}{c}}
3 \\
6 \\
{ - 12}
\end{array}} \right]\]
The linearly dependent pair is
The linearly dependent pair is