Linear Algebra MCQs Question and Answer in Engineering Maths

A. \[{\text{u}} = - \frac{2}{5}{{\text{e}}_1} - 3{{\text{e}}_2} - \frac{{11}}{5}{{\text{e}}_3}\]

B. \[{\text{u}} = - \frac{2}{5}{{\text{e}}_1} - 3{{\text{e}}_2} + \frac{{11}}{5}{{\text{e}}_3}\]

C. \[{\text{u}} = - \frac{2}{5}{{\text{e}}_1} + 3{{\text{e}}_2} + \frac{{11}}{5}{{\text{e}}_3}\]

D. \[{\text{u}} = - \frac{2}{5}{{\text{e}}_1} + 3{{\text{e}}_2} - \frac{{11}}{5}{{\text{e}}_3}\]

A. \[\frac{{{\text{n}}\left( {{\text{n}} + 1} \right)}}{2}\]

B. \[\frac{{{\text{n}}\left( {{\text{n}} - 1} \right)}}{2}\]

C. \[\frac{{{\text{n}}\left( {{\text{n}} + 1} \right)\left( {2{\text{n}} + 1} \right)}}{6}\]

D. \[{{\text{n}}^2}\]

A. 2

B. 7

C. 9

D. 11

A. \[ - \frac{4}{5}\]

B. \[ - \frac{3}{5}\]

C. \[\frac{3}{5}\]

D. \[\frac{4}{5}\]

A. Only I and III are necessarily true

B. Only II is necessarily true

C. Only I and II are necessarily true

D. Only II and III are necessarily true

A. a circle of radius \[{\sqrt {10} }\]

B. a circle of radius \[\frac{1}{{\sqrt {10} }}\]

C. an ellipse with major axis along \[\left( {\begin{array}{*{20}{c}} 1 \\ 1 \end{array}} \right)\]

D. an ellipse with minor axis along \[\left( {\begin{array}{*{20}{c}} 1 \\ 1 \end{array}} \right)\]

A. {α(4, 2, 1) |α ≠ 0, α \[ \in \] R}

B. {α(-4, 2, 1) |α ≠ 0, α \[ \in \] R}

C. {α(√2, 0, 1) |α ≠ 0, α \[ \in \] R}

D. {α(-√2, 0, 1) |α ≠ 0, α \[ \in \] R}

A. I implies II; II does not imply I

B. II implies I; I does not imply II

C. I and II are equivalent statements

D. I does not imply II; II does not imply I

A. sin x, sin²x and cos²x

B. cos x, sin x and tan x

C. cos 2x, sin² x and cos²x

D. cos 2x, sin x and cos x

A. M^{4k + 1}

B. M^{4k + 2}

C. M^{4k + 3}

D. M^4k