Question 1 |
A square matrix B is skew-symmetric if
B^{T}=-B | |
B^{T}=B | |
B^{-1}=B | |
B^{-1}=B^{T} |
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
2\vec{i}+6\vec{j}+4\vec{k} | |
2\vec{i}+12\vec{j}-4\vec{k} | |
2\vec{i}+12\vec{j}+4\vec{k} | |
\sqrt{56} |
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
1 and -1 | |
1 and i | |
1 and -i | |
i and -i |
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
\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
14MPa | |
1.4MPa | |
0.14MPa | |
0.014MPa |
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
5000f_{ck} | |
0.7f_{ck} | |
5000\sqrt{f_{ck}} | |
0.7\sqrt{f_{ck}} |
Question 6 |
In the theory of plastic bending of beams, the ratio of plastic moment to yield
moment is called
shape factor | |
plastic section modulus | |
modulus of resilience | |
rigidity modulus |
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
1.15 and 1.5 | |
1.0 and 1.0 | |
1.5 and 1.15 | |
1.5 and 1.0 |
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
moment centre | |
centroid | |
shear centre | |
elastic center |
Question 9 |
The square root of the ratio of moment of inertia of the cross-section to its cross-sectional
area is called
second moment of area | |
slenderness ratio | |
section modulus | |
radius of gyration |
Question 9 Explanation:
Radius of gyration,
r=\sqrt{\frac{\text{Moment of inertia}}{\text{Cross-sectional area}}}
r=\sqrt{\frac{\text{Moment of inertia}}{\text{Cross-sectional area}}}
Question 10 |
Deposit with flocculated structure is formed when
clay particles settle on sea bed | |
clay particles settle on fresh water lake bed | |
sand particles settle on river bed | |
sand particles on sea bed |
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.
