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.