# Practice Questions on Engineering Mathematics

 Q11. Find the direction directive of $f(x, y, z)=x^2+y^2+3z^2$ at P(1, 1, 1) in the direction of (1, 0, 2).
 A. $\dfrac{11}{\sqrt{5}}$ B. $\dfrac{14}{\sqrt{5}}$ C. $\dfrac{17}{\sqrt{5}}$ D. $\dfrac{21}{\sqrt{5}}$

 Q12. A solution for the differential equation $\dot{x(t)}-5x(t)=\delta (t)$ with initial condition $x(0^{-}=1)$ is:
 A. $e^{-t}u(t)$ B. $te^{5t}u(t)$ C. $2e^{5t} u(t)$ D. $te^{-2t}u(t)$

 Q13. Given \begin{align*} f(z)=\dfrac{1}{z+3}+\dfrac{1}{z+1}\\ \end{align*} What is the value of $\dfrac{1}{2\pi j}\oint f(z)dz$ if C is a counter clockwise path in the z-plane such that $|z+1|=1$ ?
 A. 3 B. 2 C. 1 D. 0

 Q14. Find the Fourier Transform of $\dfrac{1}{2}e^{-4t}u(t-2)$
 A. $\dfrac{e^{-2j\omega}}{4+j\omega}$ B. $\dfrac{1}{2}\dfrac{e^{-2(j\omega-4)}+6}{4+j\omega}$ C. $\dfrac{e^{2j\omega}}{4+j\omega}$ D. $\dfrac{1}{2}\dfrac{e^{-2(j\omega+4)}}{4+j\omega}$

 Q15. If   $f(x)=\sin 3x,\;0\leq x\leq \dfrac{\pi}{2}$  and  f'(c)=0  for $c\leftrightarrow ]0,\dfrac{\pi}{2}[$ Then, the value of $c$ is equal to:
 A. $\dfrac{\pi}{4}$ B. $\dfrac{\pi}{3}$ C. $\dfrac{\pi}{6}$ D. 0

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