GATE ECE 2005 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2005

MCQ (Single Correct Answer)

-0.6

Given an orthogonal matrix $$A = \left[ {\matrix{ 1 & 1 & 1 & 1 \cr 1 & 1 & { - 1} & { - 1} \cr 1 & { - 1} & 0 & 0 \cr 0 & 0 & 1 & { - 1} \cr } } \right]$$ then the value of $${\left( {A{A^T}} \right)^{ - 1}}$$ is

$${1 \over 4}{{\rm I}_4}$$

$${1 \over 2}{{\rm I}_4}$$

$${\rm I}$$

$${1 \over 3}{{\rm I}_4}$$

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

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

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

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

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

PREVIOUS NEXT

GATE ECE Papers

2023