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MTH301 Final Term Unsolved

Q400

\eqalign{ & {\text{Wallis sine formula when n is even}} \cr & \int\limits_0^{\frac{\pi }{2}} {Si{n^n}x} dx = \cr}

A) \frac{{n - 1}}{n} \cdot \frac{{n - 3}}{{n - 2}} \cdot \frac{{n - 5}}{{n - 4}} \cdot \frac{{n - 7}}{{n - 6}} \cdot \cdot \cdot \frac{6}{7} \cdot \frac{4}{5} \cdot \frac{2}{3}
B) \frac{{n - 1}}{2} \cdot \frac{{n - 1}}{2} \cdot \frac{{n - 1}}{2} \cdot \frac{{n - 1}}{2} \cdot \cdot \cdot \frac{5}{6} \cdot \frac{3}{4} \cdot \frac{1}{2} \cdot \frac{\pi }{2}
C) \frac{n}{2} \cdot \frac{{n - 2}}{2} \cdot \frac{{n - 4}}{2} \cdot \frac{{n - 6}}{2} \cdot \cdot \cdot \frac{6}{7} \cdot \frac{4}{5} \cdot \frac{2}{3}
D) \frac{{n - 1}}{n} \cdot \frac{{n - 3}}{{n - 2}} \cdot \frac{{n - 5}}{{n - 4}} \cdot \frac{{n - 7}}{{n - 6}} \cdot \cdot \cdot \frac{5}{6} \cdot \frac{3}{4} \cdot \frac{1}{2} \cdot \frac{\pi }{2}

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MTH301 Final Term Unsolved

Q401

$${\text{One of the line integral properties is}} \int\limits_{AB} {Pdx + Qdy} = - \int\limits_{BA} {Pdx + Qdy} $$

A) False
B) True
C)
D)

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MTH301 Final Term Unsolved

Q402

\[{\text{To}}\,\,{\text{evaluate}}\,\,{\text{the}}\,\,{\text{line}}\,\,{\text{integral,}}\,\,\int\limits_C {V(r)\,dr\,{\text{,}}\,\,{\text{the}}\,\,{\text{integrand}}\,\,{\text{is}}\,\,{\text{expressed}}\,\,{\text{in}}\,\,{\text{terms}}\,\,{\text{of}}\,\,x,\,\,y,\,\,z\,\,{\text{with}}\,\,d\vec r = \_\_\_\_\_\_\_\_\_.} \]

A) \[dx\,\hat i\]
B) \[dx\,\hat i + dy\,\hat j + dz\,\hat k\]
C) \[\sqrt {dx\,\hat i + dy\,\hat j + dz\,\hat k} \]
D) \[dx\,\hat i + dy\,\hat j\]

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MTH301 Final Term Unsolved

Q403

A smooth vector-valued function has a _________ line at every point on its graph.

A) secant
B) straight
C) tangent
D) curved

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MTH301 Final Term Unsolved

Q404

\[\begin{gathered} {\text{If}}\,\,{\text{a}}\,\,\_\_\_\_\_\_\_\_\_\,\,V(r)\,\,{\text{exists}}\,\,{\text{for}}\,\,{\text{all}}\,\,{\text{points}}\,\,{\text{on}}\,\,{\text{the}}\,{\text{curve,}}\,\,{\text{then}}\,\,\sum\limits_{p = 1}^n {V(r)\,d{r_p}} \,\,{\text{with}}\,\,dr \to 0\,\,{\text{defines}}\,\, \hfill \\ {\text{the}}\,\,{\text{line}}\,\,{\text{integral}}\,\,{\text{of}}\,\,V\,\,{\text{i}}{\text{.e}}{\text{.}}\,\,{\text{line}}\,\,{\text{integral}} = \int\limits_C {V(r)\,dr.} \hfill \\\ \end{gathered} \]

A) \[{\text{vector}}\,\,{\text{field}}\]
B) \[{\text{scalar}}\,\,{\text{field}}\]
C) \[{\text{vector}}\,\,{\text{space}}\]
D) \[{\text{vector}}\,\,{\text{quantity}}\]

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MTH301 Final Term Unsolved

Q405

The path traversal in calculating the Green’s Theorem is --------

A) outwards
B) clockwise
C) inwards
D) anticlockwise

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