GATE ME 2005 | GATE ME Year Wise Previous Years Questions

GATE ME 2005

MCQ (Single Correct Answer)

-0.3

$$A$$ is a $$3 \times 4$$ matrix and $$AX=B$$ is an inconsistent system of equations. The highest possible rank of $$A$$ is

$$1$$

$$2$$

$$3$$

$$4$$

GATE ME 2005

MCQ (Single Correct Answer)

-0.6

Which one of the following is an eigen vector of the matrix $$\left[ {\matrix{ 5 & 0 & 0 & 0 \cr 0 & 5 & 0 & 0 \cr 0 & 0 & 2 & 1 \cr 0 & 0 & 3 & 1 \cr } } \right]$$ is

$${\left[ {\matrix{ 1 & { - 2} & 0 & 0 \cr } } \right]^T}$$

$${\left[ {\matrix{ 0 & { 0} & 1 & 0 \cr } } \right]^T}$$

$${\left[ {\matrix{ 1 & { 0} & 0 & -2 \cr } } \right]^T}$$

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

GATE ME 2005

MCQ (Single Correct Answer)

-0.3

$$\int\limits_{ - a}^a {\left[ {{{\sin }^6}\,x + {{\sin }^7}\,x} \right]dx} $$ is equal to

$$2\int\limits_0^a {Si{n^6}x\,dx} $$

$$2\int\limits_0^a {Si{n^7}x\,dx} $$

$$2\int\limits_0^a {\left( {{{\sin }^6}x + {{\sin }^7}x} \right)dx} $$

zero

GATE ME 2005

MCQ (Single Correct Answer)

-0.3

Changing the order of integration in the double integral
$${\rm I} = \int\limits_0^8 {\int\limits_{{\raise0.5ex\hbox{$\scriptstyle x$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}}}^2 {f\left( {x,\,y} \right)dy\,dx} } $$ leads to $$\,{\rm I} = \int\limits_r^s {\int\limits_p^q {f\left( {x,\,y} \right)dy\,dx} } .$$ What is $$q$$?

$$4y$$

$${16{y^2}}$$

$$x$$

$$8$$

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2020