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}

Question 6 |

A steel column is restrained against both translation and rotation at one end and is restrained only against rotation but free to translate at the other end. Theoretical and design (IS:800-2007) values, respectively, of effective length factor of the column are

1.0 and 1.0 | |

1.2 and 1.0 | |

1.2 and 1.2 | |

1.0 and 1.2 |

Question 6 Explanation:

The given support conditions indicates the following support/ end conditions of column

l_{eff} as per theoretical conditions = 1.0l_{o}

l_{eff} as per IS 800 : 2007 = 1.2 l_{o}

Considering the errors that may occur due to construction of supports on site.

l_{eff} as per theoretical conditions = 1.0l_{o}

l_{eff} as per IS 800 : 2007 = 1.2 l_{o}

Considering the errors that may occur due to construction of supports on site.

Question 7 |

If the fineness modulus of a sample of fine aggregates is 4.3, the mean size of the particles in the sample is between

150\mu m \; and \; 300\mu m | |

300\mu m \; and \; 600\mu m | |

1.18\mu m \; and \; 2.36\mu m | |

2.36\mu m \; and \; 4.75\mu m |

Question 7 Explanation:

F.M of mean size 2.36 = 5

F.M of mean size 1.18 = 4

Hence for F.M of 4.3, the mean size of aggregate will be between 1.18 mm and 2.36 mm.

F.M of mean size 1.18 = 4

Hence for F.M of 4.3, the mean size of aggregate will be between 1.18 mm and 2.36 mm.

Question 8 |

For a channel section subjected to a downward vertical shear force at its centroid, which one of the following represents the correct distribution of shear stress in flange and web?

A | |

B | |

C | |

D |

Question 8 Explanation:

Shear flow in horizontal member (flange) is linear with zero at free end and in vertical member (web) it is parabolic.

Question 9 |

Which one of the following options contains ONLY primary air pollutants?

Hydrocarbons and nitrogen oxides | |

Hydrocarbons and ozone | |

Ozone and peroxyacetyl nitrate | |

Nitrogen oxides and peroxyacetyl nitrate |

Question 9 Explanation:

Hydrocarbons and nitrogen oxides are considered primary air pollutants.

Question 10 |

Analysis of a water sample revealed that the sample contains the following species.

CO_3^{2-}, Na^{+}, H^{+}, PO_4^{3-}, AI^{3+}, H_2CO_3, CI^{-}, Ca^{2+},Mg^{2+}, HCO_3^{-}, Fe^{2+}, OH^-

Concentrationsof which of the species will be required to compute alkalinity?

CO_3^{2-}, Na^{+}, H^{+}, PO_4^{3-}, AI^{3+}, H_2CO_3, CI^{-}, Ca^{2+},Mg^{2+}, HCO_3^{-}, Fe^{2+}, OH^-

Concentrationsof which of the species will be required to compute alkalinity?

CO_3^{2-},H^+,HCO_3^{-},OH^- | |

CO_3^{2-},H^+,H_2CO_3,HCO_3^- | |

CO_3^{2-},H_2CO_3,HCO_3^-,OH^- | |

H^+,H_2CO_3,HCO_3^-,OH^- |

Question 10 Explanation:

Alkalinity is defined as ability of water to neutralize the acid or hydronium ion

\text{Alkalinity} (A_T) \text{of water} = [HCO_3^-] + [CO_3^{2-}] + [B(OH)_4^-] + [H_3(SiO_4)^-] + [HS^-] + [\text{organic anions}] + [OH^-] - [H^+]

From given options of ions in problem answer is CO_3^{2-}, H^+, HCO_3^-, OH^-

\text{Alkalinity} (A_T) \text{of water} = [HCO_3^-] + [CO_3^{2-}] + [B(OH)_4^-] + [H_3(SiO_4)^-] + [HS^-] + [\text{organic anions}] + [OH^-] - [H^+]

From given options of ions in problem answer is CO_3^{2-}, H^+, HCO_3^-, OH^-

There are 10 questions to complete.