MTH301 Quiz 3

Q1. {\text{In the integration of polar coordinates}} dxdy {\text{is replaced by}}

1. d
2. rdrd
3. drd
4. rdr

Correct answer: rdrd

Q2. {{\text{If a point }}p(r,\theta ) {\text{in polar coordinate system, then }}r{\text{ is the distance of }}p{\text{ from the }}}

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

Correct answer: {{{Pole}}}

Q3. {\rm{The}}\,{\rm{value}}\,{\rm{of}}\,{\rm{integral }}\int\limits_0^3 {\int\limits_0^2 {x^2 dxdy} } \,\,{\rm{is}}

1. 16
2. 4
3. 8
4. 12

Correct answer: 8

Q4. {\text{The}} \int\limits_0^1 {{e^{{y^2}}}dx} =

1. {e^{{y^2}}}
2. 0
3. e + 1
4. e - 1

Correct answer: {e^{{y^2}}}

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

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

Q6. The rose curve has 2n-equally spaced petals of loops if n is _______.

1. odd
2. even

Correct answer: even

Q7. {\text{The graph of the equation }}r\, = \,a(1 - \cos \,\theta ){\text{ is symmetric about - - - - - - - - - }}{\text{.}}

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

Correct answer: {{initial line}}

Q8. Expression for the double integral for the volume of a solid bounded above by z=8-x-y and below by rectangle R=0 \leqslant x \leqslant 4,\,5 \leqslant y \leqslant 8 is........

1. V = _5^8 {_0^4 {(8 - x - y)dxdy} }
2. V = _0^4 {_5^8 {(8 - x - y)dxdy} }
3. V = _5^8 {_0^4 {(8 - x - y)dydx} }
4. V = _5^8 {_0^4 {(8 - x - y)dx} }

Correct answer: V = _5^8 {_0^4 {(8 - x - y)dxdy} }

Q9. {\text{While changing Cartesian Integral into Polar integral, we change }}x{\text{ by - - - - - - - - - and }}y{\text{ by - - - - - - - - - - - - }}{\text{.}}

1. Sec\,\, ,\,\,\,\,\,\,Co \,\,
2. Cos\,\, ,\,\,\,\,\,Sin\,\,
3. Sin\,\, ,\,\,\,\,\,\,Cos\,\,
4. Co \,\, ,\,\,\,\,\,\,Sec\,\,

Correct answer: Cos\,\, ,\,\,\,\,\,Sin\,\,

Q10. Can we evaluate the following integral in given order of integration {\kern 1pt} \int\limits_0^{\frac{1}{2}} {\int\limits_{2x}^1 {{e^{{y^2}}}} } dydx

1. Yes
2. No

Correct answer: No