Practice Questions on Engineering Mathematics

Q1.

The value of line integral \(\int_{c}^{}(3x-y)ds\) and $C$ is the portion of the circle \(x^2+y^2=18\) traversed from (-3, 3) counterclockwise around to (3, 3) followed by the line segment from (3, 3) to (1, 2) is:

A.

\(54\sqrt{2}+\dfrac{11\sqrt{5}}{2}\)

B.

\(24\sqrt{3}+\dfrac{7\sqrt{5}}{2}\)

C.

\(23\sqrt{2}+\dfrac{9\sqrt{5}}{2}\)

D.

\(54\sqrt{2}+\dfrac{7\sqrt{5}}{2}\)

 View Ans

Q2.

Given the shape of helix defined by

\(x=2\cos t,\;y=t,\;z=2\sin t\)

where \(0\leq t\leq 6\pi\) and mass density \(\rho(x,y,z)=y\)

A.

\(24\pi^2 \sqrt{6}\)

B.

\(36\pi^2 \sqrt{6}\)

C.

\(24\pi^2 \sqrt{5}\)

D.

\(18\pi^2 \sqrt{5}\)

 View Ans

Q3.

Consider two independent random variables $ X $  and $ Y $  with identical distributions. 

The  variables  $ X $ and $ Y $ take values 0, 1 and  2 with probabilities $ 1/2$, $1/4 $, $1/4 $ respectively.

What is the conditional probability,
\[ \text P(X+Y=2|X-Y=0)\]

A.

3.455

B.

2.144

C.

1.098

D.

0.166

 View Ans

Q4.

The residues of a complex function
\[x(z)=\dfrac{(1-3z)}{z(z-1)(z-3)}\]
at it's poles

A.

$ 1, 2, -1 $

B.

$\dfrac{1}{2}, 0, -1  $

C.

$  \dfrac{1}{3}, 1, -\dfrac{4}{3}$

D.

$ -\dfrac{1}{3}, 0, 1 $

 View Ans

Q5.

What is value of the integral

\[\text I=\dfrac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}\exp\left(-\dfrac{x^2}{32}\right)dx\]

A.

2

B.

3

C.

4

D.

6

 View Ans


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