Question 1 |

Multiplication of real valued square matrices of same dimension is

associative | |

commutative | |

always positive definite | |

not always possible to compute |

Question 1 Explanation:

Matrix multiplication is associative.

Question 2 |

The value of \lim_{x \to 1} \left ( \frac{1-e^{-c(1-x)}}{1-xe^{-c(1-x)}} \right ) is

c | |

c+1 | |

\frac{c}{c+1} | |

\frac{c+1}{c} |

Question 2 Explanation:

Applying L Hospital rule

\lim_{x \to 1}\left ( \frac{1-e^{-c(1-x)}}{1-xe^{-c(1-x)}} \right )=\lim_{x \to 1}\left ( \frac{1-e^{-c+cx}}{-x(ce^{-c+x})-(e^{-c+cx})} \right ) =\frac{-c}{-c-1}=\frac{c}{c+1}

\lim_{x \to 1}\left ( \frac{1-e^{-c(1-x)}}{1-xe^{-c(1-x)}} \right )=\lim_{x \to 1}\left ( \frac{1-e^{-c+cx}}{-x(ce^{-c+x})-(e^{-c+cx})} \right ) =\frac{-c}{-c-1}=\frac{c}{c+1}

Question 3 |

The Laplace transform of a function f(t) is L(f)=\frac{1}{s^2+\omega ^2}. Then f(t) is

f(t)=\frac{1}{\omega ^2}(1-\cos \omega t) | |

f(t)=\frac{1}{\omega} \cos \omega t | |

f(t)=\frac{1}{\omega} \sin \omega t | |

f(t)=\frac{1}{\omega ^2}(1-\sin \omega t) |

Question 3 Explanation:

L(t)=\frac{1}{s^{2}+\omega ^{2}}

f(t)=L^{-1}\left \{ \frac{1}{s^{2}+\omega ^{2}} \right \}=\frac{1}{\omega }\sin \omega t

f(t)=L^{-1}\left \{ \frac{1}{s^{2}+\omega ^{2}} \right \}=\frac{1}{\omega }\sin \omega t

Question 4 |

Which of the following function f(z), of the complex variable z, is NOT analytic at all the points of the complex plane?

f(z)=z^2 | |

f(z)=e^z | |

f(z)=\sin z | |

f(z)=\log z |

Question 4 Explanation:

logz is not analytic at all points.

Question 5 |

The members carrying zero force (i.e. zero-force members) in the truss shown in the
figure, for any load P \gt 0 with no appreciable deformation of the truss (i.e. with no
appreciable change in angles between the members), are

BF and DH only | |

BF, DH and GC only | |

BF, DH, GC, CD and DE only | |

BF, DH, GC, FG and GH only |

Question 5 Explanation:

If at any joint three forces are acting out of which
two of them are collinear then force in third member
must be zero.

For member ED look at joint E.

Similarity look for other members.

For member ED look at joint E.

Similarity look for other members.

There are 5 questions to complete.