81. A real traceless 4 × 4 matrix has to eigen values -1 and +1. The other eigen values are A. zero and +2 B. -1 and +1 C. zero and +1 D. +1 and +1 Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option B No explanation is given for this question Let's Discuss on Board
82. If \[l = \oint\limits_C {dz\,ln\left( z \right),} \] where C is the unit circle taken anticlockwise and $$l$$n(z) is the principal branch of the Logarithmic function, which one of the following is correct? A. $$l$$ = 0 by residue theorem B. $$l$$ is not defined since, $$l$$n(z) has a branch cut C. $$l$$ ≠ 0 D. \[\oint\limits_C {dz\,ln\left( {{z^2}} \right) = 2l} \] Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option A No explanation is given for this question Let's Discuss on Board
83. If a vector field \[\overrightarrow {\mathbf{F}} = x{\mathbf{\hat i}} + 2y{\mathbf{\hat j}} + 3z{\mathbf{\hat k}},\] then \[\overrightarrow \nabla \times \left( {\overrightarrow \nabla \times \overrightarrow {\mathbf{F}} } \right)\] is A. zero B. \[{{\mathbf{\hat i}}}\] C. \[2{\mathbf{\hat j}}\] D. \[3{\mathbf{\hat k}}\] Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option A No explanation is given for this question Let's Discuss on Board
84. Consider the set of vectors; \[\frac{1}{{\sqrt 2 }}\] (1, 1, 0); \[\frac{1}{{\sqrt 2 }}\] (0, 1, 1) and \[\frac{1}{{\sqrt 2 }}\] (1, 0, 1). A. The three vectors are orthonormal B. The three vectors are linearly independent C. The three vectors cannot form a basis in a three dimensional real vector space D. \[\frac{1}{{\sqrt 2 }}\] (1, 1, 0) can be written as a linear combination of \[\frac{1}{{\sqrt 2 }}\] (0, 1, 1) and \[\frac{1}{{\sqrt 2 }}\] (1, 0, 1) Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option B No explanation is given for this question Let's Discuss on Board
85. Solution of the differential equation \[x\frac{{dy}}{{dx}} + y = {x^4},\] with the boundary condition that y = 1, at x = 1, is A. \[y = 5{x^4} - 4\] B. \[y = \frac{{{x^4}}}{5} + \frac{{4x}}{5}\] C. \[y = \frac{{4{x^4}}}{5} + \frac{1}{{5x}}\] D. \[y = \frac{{{x^4}}}{5} + \frac{4}{{5x}}\] Answer & Solution Discuss in Board Save for Later Answer & Solution Answer: Option D No explanation is given for this question Let's Discuss on Board
