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 |

Question 6 |

As per the provisions of IS 456-2000, the (short term) modulus of elesticity of
M25 grade concrete (in N/mm^2) can be assumed to be

25000 | |

28500 | |

30000 | |

36000 |

Question 6 Explanation:

\begin{aligned} E &=5000 \sqrt{f_{c k}}=5000 \sqrt{25} \\ &=5000 \times 5=25000 \mathrm{N} / \mathrm{mm}^{2} \end{aligned}

Question 7 |

The shear modulus (G), modulus of elasticity (E) and the Poisson's ratio (v) of
a material are related as,

G=\frac{E}{2(1+v)} | |

E=\frac{G}{2(1+v)} | |

G=\frac{E}{2(1-v)} | |

E=\frac{G}{2(1-v)} |

Question 8 |

When designing steel structures, one must ensure that local buckling in webs
does not take place. This check may not be very critical when using rolled steel
sections because.

Quality control at the time of manufacture of rolled sections is very good | |

Web depths available are small | |

Web stiffeners are in-built in rolled sections | |

Depth to thickness ratios (of the web) are appropriately adjusted |

Question 9 |

An ISMB 500 is used as a beam in a multi-storey construction. From the viewpoint
of structural design, it can be considered to be 'laterally restrained' when,

The tension flange is 'laterally restrained' | |

the compression flange is 'laterally restrained' | |

the web is adequately stiffened | |

the conditions in (A) and (C) are met |

Question 10 |

Data from a sieve analysis conducted on a given sample of soil showed that 67%
of the particles passed through 75 micron IS sieve. The liquid limit and plastic
limit of the finer fraction was found to be 45 and 33 percents respectively. The
group symbol of the given soil as per IS:1498-1970 is

SC | |

MI | |

CH | |

MH |

Question 10 Explanation:

% passing 75 \mu sieve \gt 50 \%

So the soil might be, silt (M) or clay (C)

\begin{aligned} I_{p} \text { of soil } &=w_{L}-w_{p} \\ &=45-33=12 \end{aligned}

Equation of A line is given by

\begin{aligned} I_{p} &=0.73\left(w_{L}-20\right) \\ &=0.73(45-20)=18.25 \end{aligned}

\because \mathrm{I}_{\mathrm{p}}\text{ of soil } \lt \mathrm{I}_{\mathrm{p}}\text{ of A-line}

\therefore It will lie below A-line and also 35 \lt w_{L} \lt 50

So it is MI.

So the soil might be, silt (M) or clay (C)

\begin{aligned} I_{p} \text { of soil } &=w_{L}-w_{p} \\ &=45-33=12 \end{aligned}

Equation of A line is given by

\begin{aligned} I_{p} &=0.73\left(w_{L}-20\right) \\ &=0.73(45-20)=18.25 \end{aligned}

\because \mathrm{I}_{\mathrm{p}}\text{ of soil } \lt \mathrm{I}_{\mathrm{p}}\text{ of A-line}

\therefore It will lie below A-line and also 35 \lt w_{L} \lt 50

So it is MI.

There are 10 questions to complete.