GATE CE 2009

Question 1
A square matrix B is skew-symmetric if
A
B^{T}=-B
B
B^{T}=B
C
B^{-1}=B
D
B^{-1}=B^{T}
Engineering Mathematics   Linear Algebra
Question 1 Explanation: 
A square matrix B is defined as skew-symmetric if and only if B^{T}=-B
Question 2
For a scalar function f (x,y,z) = x^{2}+3y^{2}+2z^{2}, the gradient at the point P(1,2,-1) is
A
2\vec{i}+6\vec{j}+4\vec{k}
B
2\vec{i}+12\vec{j}-4\vec{k}
C
2\vec{i}+12\vec{j}+4\vec{k}
D
\sqrt{56}
Engineering Mathematics   Calculus
Question 2 Explanation: 
\begin{aligned} f&=x^{2}+3y^{2}+2z^{2} \\ \Delta f&=grad\: f=i\frac{\partial f}{\partial x}+j\frac{\partial f}{\partial y}+k\frac{\partial f}{\partial z} \\ &=i\left ( 2x \right )+j\left ( 6y \right )+k\left ( 4z \right ) \\ &\text{The gradient at P(1, 2, -1) is}\\ &=i\left ( 2\times 1 \right )+j\left ( 6\times 2 \right )+k\left ( 4\times -1 \right ) \\ &=2i+12j-4k \end{aligned}
Question 3
The analytic function f(z)=\frac{z-1}{z^{2}+1} has singularity at
A
1 and -1
B
1 and i
C
1 and -i
D
i and -i
Engineering Mathematics   Calculus
Question 3 Explanation: 
f\left ( z \right )=\frac{z-1}{z^{2}+1}=\frac{z-1}{z^{2}-i^{2}}=\frac{z-1}{\left ( z-i \right )\left ( z+i \right )}
\therefore The singularities arc at z=i and -i
Question 4
A thin walled cylindrical pressure vessel having a radius of 0.5 m and wall thickness of 25 mm is subjected to an internal pressure of 700 kPa. The hoop stress developed is
A
14MPa
B
1.4MPa
C
0.14MPa
D
0.014MPa
Solid Mechanics   Torsion of Shafts and Pressure Vessels
Question 4 Explanation: 
\begin{aligned} \text { Hoop stress } &=\frac{p d}{2 t}=\frac{700 \times 10^{3} \times 2 \times 0.5}{2 \times 25 \times 10^{-3}} \\ &=14 \times 10^{6} \mathrm{Pa}=14 \mathrm{MPa} \end{aligned}
Question 5
The modulus of rupture of concrete in terms of its characteristic cube compressive strength (f_{ck}) in MPa according to IS 456:2000 is
A
5000f_{ck}
B
0.7f_{ck}
C
5000\sqrt{f_{ck}}
D
0.7\sqrt{f_{ck}}
RCC Structures   Working Stress and Limit State Method
Question 6
In the theory of plastic bending of beams, the ratio of plastic moment to yield moment is called
A
shape factor
B
plastic section modulus
C
modulus of resilience
D
rigidity modulus
Design of Steel Structures   Plastic Analysis
Question 7
For limit state of collapse, the partial safety factors recommended by IS 456:2000 for estimating the design strength of concrete and reinforcing steel are respectively
A
1.15 and 1.5
B
1.0 and 1.0
C
1.5 and 1.15
D
1.5 and 1.0
RCC Structures   Working Stress and Limit State Method
Question 8
The point within the cross sectional plane of a beam through which the resultant of the external loading on the beam has to pass through to ensure pure bending without twisting of the cross-section of the beam is called
A
moment centre
B
centroid
C
shear centre
D
elastic center
Solid Mechanics   Theory of Columns and Shear Centre
Question 9
The square root of the ratio of moment of inertia of the cross-section to its cross-sectional area is called
A
second moment of area
B
slenderness ratio
C
section modulus
D
radius of gyration
Design of Steel Structures   Compression Member
Question 9 Explanation: 
Radius of gyration,
r=\sqrt{\frac{\text{Moment of inertia}}{\text{Cross-sectional area}}}
Question 10
Deposit with flocculated structure is formed when
A
clay particles settle on sea bed
B
clay particles settle on fresh water lake bed
C
sand particles settle on river bed
D
sand particles on sea bed
Geotechnical Engineering   Compaction of soil
Question 10 Explanation: 
Flocculated structure is formed when clay particles settle on sea bed, since sea bed is polar in nature.
There are 10 questions to complete.

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