GATE CE 2019 SET-2

Question 1
Euclidean norm (length) of the vector [4\; -2\; -6]^T is
A
\sqrt{12}
B
\sqrt{24}
C
\sqrt{48}
D
\sqrt{56}
Engineering Mathematics   Calculus
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}
Question 2
The Laplace transform of \sinh (at) is
A
\frac{a}{s^2-a^2}
B
\frac{a}{s^2+a^2}
C
\frac{s}{s^2-a^2}
D
\frac{s}{s^2+a^2}
Engineering Mathematics   Partial Differential Equation
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}?
A
0
B
1/2
C
1
D
2
Engineering Mathematics   Calculus
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
Question 4
What is curl of the vectorfield 2x^2y i+5z^2j-4yzk?
A
6zi+4xj-2x^2k
B
6zi-8xyj+2x^2yk
C
-14zi+6yj+2x^2k
D
-14zi-2x^2k
Engineering Mathematics   Calculus
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
A
0.5 \tau A_m t
B
\tau A_m t
C
2 \tau A_m t
D
4 \tau A_m t
Solid Mechanics   Torsion of Shafts and Pressure Vessels
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
A
1.0 and 1.0
B
1.2 and 1.0
C
1.2 and 1.2
D
1.0 and 1.2
Design of Steel Structures   Compression Member
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.
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
A
150\mu m \; and \; 300\mu m
B
300\mu m \; and \; 600\mu m
C
1.18\mu m \; and \; 2.36\mu m
D
2.36\mu m \; and \; 4.75\mu m
Geotechnical Engineering   Properties of Soils
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.
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
A
B
B
C
C
D
D
Design of Steel Structures   Structural Fasteners
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?
A
Hydrocarbons and nitrogen oxides
B
Hydrocarbons and ozone
C
Ozone and peroxyacetyl nitrate
D
Nitrogen oxides and peroxyacetyl nitrate
Environmental Engineering   Air and Noise Pollution
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?
A
CO_3^{2-},H^+,HCO_3^{-},OH^-
B
CO_3^{2-},H^+,H_2CO_3,HCO_3^-
C
CO_3^{2-},H_2CO_3,HCO_3^-,OH^-
D
H^+,H_2CO_3,HCO_3^-,OH^-
Environmental Engineering   Quality Characteristics of Water
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^-
There are 10 questions to complete.

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