# 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. $54\sqrt{2}+\dfrac{7\sqrt{5}}{2}$

 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. $18\pi^2 \sqrt{5}$

 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

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

 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

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