GATE ECE 2005 | GATE ECE Year Wise Previous Years Questions

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GATE ECE 2005

MCQ (Single Correct Answer)

-0.6

Given the matrix $$\left[ {\matrix{ { - 4} & 2 \cr 4 & 3 \cr } } \right],$$ the eigen vector is

$$\left[ {\matrix{ 3 \cr 2 \cr } } \right]$$

$$\left[ {\matrix{ 4 \cr 3 \cr } } \right]$$

$$\left[ {\matrix{ 2 \cr { - 1} \cr } } \right]$$

$$\left[ {\matrix{ { - 2} \cr 1 \cr } } \right]$$

GATE ECE 2005

MCQ (Single Correct Answer)

-0.6

If $$A = \left[ {\matrix{ 2 & { - 0.1} \cr 0 & 3 \cr } } \right]$$ and $${A^{ - 1}} = \left[ {\matrix{ {{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}} & a \cr 0 & b \cr } } \right]$$ then $$a+b=$$

$${7 \over {20}}$$

$${3 \over {20}}$$

$${19 \over {60}}$$

$${11 \over {20}}$$

GATE ECE 2005

MCQ (Single Correct Answer)

-0.3

The value of the integral $$1 = {1 \over {\sqrt {2\pi } }}\,\,\int\limits_0^\infty {{e^{ - {\raise0.5ex\hbox{$\scriptstyle {{x^2}}$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 8$}}}}} \,\,dx\,\,\,$$ is ________.

$$1$$

$${\pi }$$

$$2$$

$${2\pi }$$

GATE ECE 2005

MCQ (Single Correct Answer)

-0.3

$$\nabla \times \left( {\nabla \times P} \right)\,\,$$ where $$P$$ is a vector is equal to

$$P \times \nabla \times P \to {\nabla ^2}P$$

$${\nabla ^2}P + \nabla \left( {\nabla .P} \right)\,$$

$${\nabla ^2}P + \left( {\nabla \times P} \right)\,\,$$

$$\nabla \left( {\nabla .P} \right) \to {\nabla ^2}P$$

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2023