Question 1 |

Eigen values of the following matrix are:

\begin{bmatrix} -1 &4 \\ 4&-1 \end{bmatrix}

\begin{bmatrix} -1 &4 \\ 4&-1 \end{bmatrix}

3 and -5 | |

-3 and 5 | |

-3 and -5 | |

3 and 5 |

Question 2 |

The value of the following definite integral is:

\int_{\frac{-\pi }{2}}^{\frac{\pi }{2}}\frac{sin2x}{1+cosx}dx

\int_{\frac{-\pi }{2}}^{\frac{\pi }{2}}\frac{sin2x}{1+cosx}dx

-2 ln2 | |

2 | |

0 | |

(ln 2)^{2} |

Question 2 Explanation:

Since the givem function is odd function therefore in the given limits the integral will be zero.

Question 3 |

The following function has a local minima at which value of x?

f(x)=x\sqrt{5-x^{2}}

f(x)=x\sqrt{5-x^{2}}

-\frac{\sqrt{5}}{2} | |

\sqrt{5} | |

\sqrt{\frac{5}{2}} | |

-\sqrt{\frac{5}{2}} |

Question 3 Explanation:

\begin{aligned} f\left ( x \right )&=x\sqrt{5-x^{2}} \\ {f}'\left ( x \right )&=\sqrt{5-x^{2}}+\frac{x\times -2x}{2\sqrt{5-x^{2}}} \\ 5-x^{2}&=x^{2} \\ 2x^{2}&=5 \\ x&=\pm \sqrt{\frac{5}{2}}\end{aligned}

Question 4 |

For the loading given in the figure below, two statements (I and II) are made.

I. Member AB Carries shear force and bending moment.

II. Member BC carries axial load and shear force.

Which of the following is true?

I. Member AB Carries shear force and bending moment.

II. Member BC carries axial load and shear force.

Which of the following is true?

Statement I is true but II is false | |

Statement I is false but II is true | |

Both statements I and II are true | |

Both statements I and II are false |

Question 4 Explanation:

Member AB carries shear force and bending moment both. Hence statement-I is true

Member BC carries axial load and bending moment only. Hence statement-II is false.

Question 5 |

Read the following two statements

I. Maximum strain in concrete at the outermost compression fibre is taken to be 0.0035 in bending

II. The maximum compressive strain in concrete in axial compression is taken as 0.002.

Keeping the provisions of IS 456-2000 on limit state design in mind, which of the following is true?

I. Maximum strain in concrete at the outermost compression fibre is taken to be 0.0035 in bending

II. The maximum compressive strain in concrete in axial compression is taken as 0.002.

Keeping the provisions of IS 456-2000 on limit state design in mind, which of the following is true?

Statement I is true but II is false | |

Statement I is false but II is true | |

Both statement I and II are true | |

Both statements I and II are false |

There are 5 questions to complete.