Question 1 |

Let \phi be a scalar field, and \mathbf{u} be a vector field. Which of the following identities is true for div(\phi \mathbf{u}) ?

\operatorname{div}(\phi \mathbf{u})=\phi \operatorname{div}(\mathbf{u})+\mathbf{u} \cdot \operatorname{grad}(\phi) | |

\operatorname{div}(\phi \mathbf{u})=\phi \operatorname{div}(\mathbf{u})+\mathbf{u} \times \operatorname{grad}(\phi) | |

\operatorname{div}(\phi \mathbf{u})=\phi \operatorname{grad}(\mathbf{u})+\mathbf{u} \cdot \operatorname{grad}(\phi) | |

\operatorname{div}(\phi \mathbf{u})=\phi \operatorname{grad}(\mathbf{u})+\mathbf{u} \times \operatorname{grad}(\phi) |

Question 1 Explanation:

div(\phi \mathrm{u})=\phi div(\mu)+ugrad(\phi)

Question 2 |

Which of the following probability distribution functions (PDFs) has the mean greater than the median?

Function 1 | |

Function 2 | |

Function 3 | |

Function 4 |

Question 2 Explanation:

Option (B) is correct.

Question 3 |

A remote village has exactly 1000 vehicles with sequential registration numbers starting from 1000 . Out of the total vehicles, 30 \% are without pollution clearance certificate. Further, even- and oddnumbered vehicles are operated on even- and oddnumbered dates, respectively.

If 100 vehicles are chosen at random on an evennumbered date, the number of vehicles expected without pollution clearance certificate is.

If 100 vehicles are chosen at random on an evennumbered date, the number of vehicles expected without pollution clearance certificate is.

15 | |

30 | |

50 | |

70 |

Question 3 Explanation:

Since 30 \% of the total vehicles are without pollution clearance certificate.

Out of the 100 chosen vehicle, 30 \% i.e. 100 \times 0.3=30 vehicle are expected to be without pollution clearance certificate.

Out of the 100 chosen vehicle, 30 \% i.e. 100 \times 0.3=30 vehicle are expected to be without pollution clearance certificate.

Question 4 |

A circular solid shaft of span L=5 \mathrm{~m} is fixed at one end and free at the other end. A torque T= 100 \mathrm{kN} . \mathrm{m} is applied at the free end. The shear modulus and polar moment of inertia of the section are denoted as \mathrm{G} and \mathrm{J}, respectively. The torsional rigidity \mathrm{GJ} is 50,000 \mathrm{kN} . \mathrm{m}^ 2 / \mathrm{rad}. The following are reported for this shaft:

Statement i) The rotation at the free end is 0.01 \mathrm{rad}

Statement ii) The torsional strain energy is 1.0 kN.m

With reference to the above statements, which of the following is true?

Statement i) The rotation at the free end is 0.01 \mathrm{rad}

Statement ii) The torsional strain energy is 1.0 kN.m

With reference to the above statements, which of the following is true?

Both the statements are correct | |

Statement i) is correct, but Statement ii) is wrong | |

Statement i) is wrong, but Statement ii) is correct | |

Both the statements are wrong |

Question 4 Explanation:

\phi_{\mathrm{BA}}=\frac{\text { T.L. }}{\mathrm{GJ}}=\frac{(100)^{*} 5}{50000}=0.01 \mathrm{rad}

\Rightarrow Torsional strain energy (U)

\begin{aligned} & U=\frac{T^{2} L}{2 G J}=\frac{1}{2} \times T * \phi_{B A} \\ & U=\frac{1}{2} * 100 * 0.01=0.5 \mathrm{kN}-\mathrm{m} \end{aligned}

Hence, statement (i) correct and statement (ii) is incorrect.

Question 5 |

M20 concrete as per IS 456: 2000 refers to concrete with a design mix having

an average cube strength of 20 \mathrm{MPa} | |

an average cylinder strength of 20 \mathrm{MPa} | |

a 5-percentile cube strength of 20 \mathrm{MPa} | |

a 5-percentile cylinder strength of 20 \mathrm{MPa} |

Question 5 Explanation:

In M20, M refers to mix and 20 to characteristic cube strength. As per clause no. 6.1.1, IS456: 2000 characteristic strength is defined as the strength below which not more than 5 percent of the test results are expected to fall.

Hence, correct option is (C).

Hence, correct option is (C).

There are 5 questions to complete.