Question 1 |
Euclidean norm (length) of the vector [4\; -2\; -6]^T is
\sqrt{12} | |
\sqrt{24} | |
\sqrt{48} | |
\sqrt{56} |
Question 1 Explanation:
Let X=\begin{bmatrix} 4\\ -2\\ -6 \end{bmatrix}
\begin{aligned} \text{Norm} \; X&=||X|| \\ &=\sqrt{(4)^2 +(-2)^2 +(-6)^2} \\ &= \sqrt{16+4+36}\\ &= \sqrt{56} \end{aligned}
\begin{aligned} \text{Norm} \; X&=||X|| \\ &=\sqrt{(4)^2 +(-2)^2 +(-6)^2} \\ &= \sqrt{16+4+36}\\ &= \sqrt{56} \end{aligned}
Question 2 |
The Laplace transform of \sinh (at) is
\frac{a}{s^2-a^2} | |
\frac{a}{s^2+a^2} | |
\frac{s}{s^2-a^2} | |
\frac{s}{s^2+a^2} |
Question 2 Explanation:
L(\sinh (at))=\frac{a}{s^2-a^2}
Question 3 |
The following inequality is true for all x close to 0.
2-\frac{x^2}{3} \lt \frac{xsinx}{1-cosx} \lt 2
What is the value of \lim_{x \to 0}\frac{xsinx}{1-cosx}?
2-\frac{x^2}{3} \lt \frac{xsinx}{1-cosx} \lt 2
What is the value of \lim_{x \to 0}\frac{xsinx}{1-cosx}?
0 | |
1/2 | |
1 | |
2 |
Question 3 Explanation:
\lim_{x \to 0}\frac{x \sin x}{1-\cos x}
\lim_{x \to 0}\frac{\frac{\sin x}{x}}{\frac{1-\cos x}{x^2}}=\frac{1}{\frac{1}{2}}=2
\lim_{x \to 0}\frac{\frac{\sin x}{x}}{\frac{1-\cos x}{x^2}}=\frac{1}{\frac{1}{2}}=2
Question 4 |
What is curl of the vectorfield 2x^2y i+5z^2j-4yzk?
6zi+4xj-2x^2k | |
6zi-8xyj+2x^2yk | |
-14zi+6yj+2x^2k | |
-14zi-2x^2k |
Question 4 Explanation:
\begin{aligned} \text{curl}\bar{F}&=\begin{vmatrix} \bar{i} & \bar{j} & \bar{k}\\ \frac{\partial }{\partial x} & \frac{\partial }{\partial y} & \frac{\partial }{\partial z}\\ 2x^2y & 5z^2 & -4yz \end{vmatrix} \\ &=\bar{i}(-4z-10z)-\bar{j}(0-0)+\bar{k}(0-2x^2) \\ &= 14zi-2x^2k \end{aligned}
Question 5 |
A closed thin-walled tube has thickness, t, mean enclosed area within the boundary of the centerline of tube's thickness, A_m, and shear stress, \tau. Torsional moment of resistance, T, of the section would be
0.5 \tau A_m t | |
\tau A_m t | |
2 \tau A_m t | |
4 \tau A_m t |
Question 5 Explanation:

Shear Stress,
\begin{aligned} \tau &=\frac{T}{J}R=\frac{T}{2 \pi R^3 t}R \\ \tau &=\frac{T}{2 \pi R^2 t}=\frac{T}{2 A_m t} \\ T &=2\tau A_mt \end{aligned}
There are 5 questions to complete.