MTH301 Quiz 3 Set 2

Q1. {{\text{In polar coordinate system, x - axis is also called}}}

1. {{{None of these}}}
2. {{{Imaginary axis}}}
3. {{{Polar axis}}}
4. {{{Pole}}}

Correct answer: {{{Polar axis}}}

Q2. {\text{The}}\,\,{\text{curve}},\,\,r = \theta \,\,(\theta \geqslant

Q0. ,\,\,{\text{is}}\,\,{\text{an}}\,\,{\text{equation}}\,\,{\text{of}}\,\,\_\_\_\_\_\_\_\_\_.

1. {{cardioids}}
2. {{limacons}}
3. {{roses}}
4. {{spiral}}\,\,{{with}}\,\,a = 1

Correct answer: {{spiral}}\,\,{{with}}\,\,a = 1

Q3. The rose curve has 2n-equally spaced petals of loops if n is _______.

1. even
2. odd

Correct answer: even

Q4. {\text{In the integration in polar coordinates, }}dx\,dy{\text{ is replaced by - - - - - - - - - - - }}{\text{.}}

1. d
2. r\,dr\,d
3. dr\,d
4. r\,\,dr

Correct answer: r\,dr\,d

Q5. \begin{gathered} {\text{The }}\,\,{\text{position }}\,\,{\text{of }}\,\,{\text{the}}\,\,{\text{ limacon }}\,\,{\text{relative }}\,\,{\text{to}}\,\,{\text{ the}}\,\,{\text{ polar}}\,\,{\text{ axis}}\,\,{\text{ depends}}\,\,{\text{ on }}\,\,{\text{whether}}\,\,{\text{ _________ }}\,\, \hfill \\ {\text{appears}}\,\,{\text{ in}}\,\,{\text{ the}}\,\,{\text{ equation }}\,\,{\text{and}}\,\,{\text{ whether}}\,\,\, + {\text{ }}\,\,{\text{or}}\,\,{\text{ }} - \,\,{\text{occurs}}{\text{.}} \hfill \\\ \end{gathered}

1. {{(d)}}\,\,\,{{Both}}\,\,{{(a)}}\,\,{{or}}\,\,{{(b)}}{{.}}
2. (c)\,\,\,
3. (a)\,\,\,
4. (b)\,\,\,

Correct answer: {{(d)}}\,\,\,{{Both}}\,\,{{(a)}}\,\,{{or}}\,\,{{(b)}}{{.}}

Q6. \int\limits_0^\pi {\int\limits_0^1 {{r^2}\,\,dr\,\,d\theta } } \,\, = \,\,\, - - - - - - - -

1. { }{5}
2. { }{2}
3. { }{4}
4. { }{3}

Correct answer: { }{3}

{\text{Area}}\,\,{\text{of}}\,\,{\text{double}}\,\,{\text{integral}}\,\,{\text{can}}\,\,{\text{be}}\,\,{\text{calculated}} = {\text{___________}}{\text{.}} A. {1}{{{{area}}\,\,{{of}}\,\,R}}_R {dA} B. _R {f(x,y)\,dx\,dy} C. _R {f(x,y)\,dy}

D. _R {dA}

Q8. \begin{gathered} {\text{The}}\,\,{\text{lemniscates}}\,\,{\text{are}}\,\,{\text{centered}}\,\,{\text{at}}\,\,{\text{the}}\,\,{\text{origin, \hfill \\ {\text{depends}}\,\,{\text{on}}\,\,{\text{the}}\,\,{\text{sign}}\,\,{\text{preceding}}\,\,{\text{the}}\,\,{a^2}\,\,{\text{ \hfill \\\ \end{gathered}

1. (a)\,\,\, 2
2. (b)\,\,\, 2
3. {{(d)}}\,\,\,{{Both}}\,\,{{(a)}}\,\,{{or}}\,\,{{(b)}}{{.}}
4. (c)\,\,\,

Correct answer: {{(d)}}\,\,\,{{Both}}\,\,{{(a)}}\,\,{{or}}\,\,{{(b)}}{{.}}

Q9. {\text{If}} p(r,\theta ) {\text{is a point in polar coordinate system, then}} \theta {\text{is called}}

1. {{Reflex angle of }}p
2. {{Acute angle of }}p
3. {{Reflex angle of }}p
4. {{Polar angle of }}p

Correct answer: {{Polar angle of }}p

Q10. {\text{The graph of the equation }}r\, = \,a(1 - \cos \,\theta ){\text{ is symmetric about - - - - - - - - - }}{\text{.}}

1. {{y - axis}}
2. {{pole}}
3. {{None of these}}{{.}}
4. {{initial line}}

Correct answer: {{initial line}}