Question 1 |

There is no value of x that can simultaneously satisfy both the given equations. Therefore, find the
'least squares error' solution to the two equations, i.e., find the value of x that minimizes the sum of
squares of the errors in the two equations. __________

2x= 3

4x= 1

2x= 3

4x= 1

0.5 | |

1.5 | |

2 | |

4 |

Question 2 |

What is the minimum number of multiplications involved in computing the matrix product PQR?

MatrixP has 4 rows and 2 columns, matrixQ has 2 rows and 4 columns, and matrixR has 4 rows and 1 column. __________

MatrixP has 4 rows and 2 columns, matrixQ has 2 rows and 4 columns, and matrixR has 4 rows and 1 column. __________

256 | |

32 | |

16 | |

128 |

Question 2 Explanation:

If we multiply QR first then,

Q_{2\times 4}\times R_{\left ( 2\times 1 \right )} having multiplication number 8.

Therefore P_{\left ( 4\times 2 \right )}QR_{\left ( 2\times 1 \right )} will have minimum number of multiplication =(8+8)=16.

Q_{2\times 4}\times R_{\left ( 2\times 1 \right )} having multiplication number 8.

Therefore P_{\left ( 4\times 2 \right )}QR_{\left ( 2\times 1 \right )} will have minimum number of multiplication =(8+8)=16.

Question 3 |

A 1-h rainfall of 10 cm magnitude at a station has a return period of 50 years. The probability that
a 1-h rainfall of magnitude 10 cm or more will occur in each of two successive years is:

0.04 | |

0.2 | |

0.02 | |

0.0004 |

Question 3 Explanation:

Return period of rainfall,

T&=50 years

\therefore probability of occurrence once in 50 years,

p&=\frac{1}{50}&=0.02

Probability of occurrence in each of 2 successive year =p^{2}=\left ( 0.02 \right )^{2}=0.0004

T&=50 years

\therefore probability of occurrence once in 50 years,

p&=\frac{1}{50}&=0.02

Probability of occurrence in each of 2 successive year =p^{2}=\left ( 0.02 \right )^{2}=0.0004

Question 4 |

Maximum possible value of Compacting Factor for fresh (green) concrete is:

0.5 | |

1 | |

1.5 | |

2 |

Question 5 |

As per IS 800:2007, the cross-section in which the extreme fiber can reach the yield stress, but
cannot develop the plastic moment of resistance due to failure by local buckling is classified as

plastic section | |

compact section | |

semi-compact section | |

slender section |

Question 5 Explanation:

As per clause 3.7.2 of IS 800:2007

There are 5 questions to complete.