Question 1 |

The product of matrices (PQ)^{-1}P is

P^{-1} | |

Q^{-1} | |

P^{-1}Q^{-1}P | |

PQP^{-1} |

Question 1 Explanation:

\begin{aligned} \left ( PQ \right )^{-1}P&=\left (Q^{-1}P^{-1} \right )P \\ &=\left ( Q^{-1}\ \right )\left ( P^{-1}P \right ) \\ &=\left ( Q^{-1} \right )\left ( I \right )=Q^{-1} \end{aligned}

Question 2 |

The general solution of \frac{d^{2}y}{dx^{2}}+y=0 is

y = P \cos x + Q \sin x | |

y = P \cos x | |

y = P \sin x | |

y = P \sin^2 x |

Question 2 Explanation:

\begin{aligned} \frac{d^{2}y}{dx^{2}}+y&=0 \\ D^{2}+1&=0 \\ D=\pm i &=0\pm 1i \\ &\text{General solution is,} \\ y&=e^{0x}\left [ C_{1}\cos \left ( 1\times x \right )+C_{2}\sin \left ( 1\times x \right ) \right ] \\ &=C_{1}\cos x+C_{2}\sin x \\ &=P\cos x+Q\sin x \end{aligned}

where P and Q are some constants.

where P and Q are some constants.

Question 3 |

A mild steel specimen is under uniaxial tensile stress. Young's modulus and yield
stress for mild steel are 2 \times 10^{5} MPa and 250 MPa respectively. The maximum amount of strain energy per unit volume that can be stored in this specimen
without permanent set is

156 Nmm/mm^{3} | |

15.6 Nmm/mm^{3} | |

1.56 Nmm/mm^{3} | |

0.156 Nmm/mm^{3} |

Question 3 Explanation:

The strain energy per unit volume may be given as

\begin{aligned} u &=\frac{1}{2} \times \frac{\sigma_{y}^{2}}{E}=\frac{1}{2} \times \frac{(250)^{2}}{2 \times 10^{5}} \\ &=0.156 \mathrm{N}\; \mathrm{mm} / \mathrm{mm}^{3} \end{aligned}

\begin{aligned} u &=\frac{1}{2} \times \frac{\sigma_{y}^{2}}{E}=\frac{1}{2} \times \frac{(250)^{2}}{2 \times 10^{5}} \\ &=0.156 \mathrm{N}\; \mathrm{mm} / \mathrm{mm}^{3} \end{aligned}

Question 4 |

A reinforced concrete structure has to be constructed along a sea coast. The
minimum grade of concrete to be used as per IS : 456-2000 is

M15 | |

M20 | |

M25 | |

M30 |

Question 4 Explanation:

As per clause 8.2.8 of 1S 456: 2.000 concrete in
sea water or exposed directly along the sea coast
shall be atleast M20 grade in the case of plain
concrete and M30 in case of reinforced concrete.

Question 5 |

In the design of a reinforced concrete beam the requirement for bond is not
getting satisfied. The economical option to satisfy the requirement for bond is by

bounding of bars | |

providing smaller diameter bars more in number | |

providing larger diameter bars less in number | |

providing same diameter bars more in number |

Question 5 Explanation:

Bond stress \left(\tau_{b d}\right)=\frac{\text { Tensile force }}{(n \pi \phi) \sigma_{s t}}

\tau_{b d} should be less than permissible value, if it is greater than \left(\tau_{b d}\right)_{\text {permissible }} then best economical solution is to reduce the diameter of bar and increase its number.

\tau_{b d} should be less than permissible value, if it is greater than \left(\tau_{b d}\right)_{\text {permissible }} then best economical solution is to reduce the diameter of bar and increase its number.

Question 6 |

The shape of the cross-section, which has the largest shape factor, is

rectangular | |

I-section | |

Diamond | |

Solid circular |

Question 6 Explanation:

Shape factors of some cross-section are as follows:

(i) Rectangle - 1.5

(ii) I-Section - 1.14

(iii) Diamond - 2

(iv) triangle - 2.34

(v) Circle - 1.7

(i) Rectangle - 1.5

(ii) I-Section - 1.14

(iii) Diamond - 2

(iv) triangle - 2.34

(v) Circle - 1.7

Question 7 |

Group Symbols assigned to silty sand and clayey sand are respectively

SS and CS | |

SM and CS | |

SM and SC | |

MS and CS |

Question 7 Explanation:

First part of the dual symbol indicates gradation

whereas second part indicates the nature of fineness.

\Rightarrow Silty sand =SM

\Rightarrow Clayey sand =SC

whereas second part indicates the nature of fineness.

\Rightarrow Silty sand =SM

\Rightarrow Clayey sand =SC

Question 8 |

When a retaining wall moves away from the backfill, the pressure exerted on the
wall is termed as

passive earth pressure | |

swelling pressure | |

pore pressure | |

active earth pressure |

Question 9 |

Compaction by vibratory roller is the best method of compaction in case of

moist silty sand | |

well graded dry sand | |

clay of medium compressibility | |

silt of high compressibility |

Question 10 |

A person standing on the bank of a canal drops a stone on the water surface. He
notices that the disturbance on the water surface is not travelling upstream. This
is because the flow in the canal is

sub-critical | |

super-critical | |

steady | |

uniform |

Question 10 Explanation:

For super-critical flow, F_{r} \gt 1

\begin{aligned} \frac{V}{\sqrt{g y}} & \gt 1 \\ V & \gt \sqrt{g y} \\ V & \gt C \end{aligned}

Hence, on upstream, the waves will be washed away and we will not be able to see them but they can be seen on downstream side.

Hence, the flow here is super-critical.

\begin{aligned} \frac{V}{\sqrt{g y}} & \gt 1 \\ V & \gt \sqrt{g y} \\ V & \gt C \end{aligned}

Hence, on upstream, the waves will be washed away and we will not be able to see them but they can be seen on downstream side.

Hence, the flow here is super-critical.

There are 10 questions to complete.