# GATE CE 2002

 Question 1
Eigen values of the following matrix are:
$\begin{bmatrix} -1 &4 \\ 4&-1 \end{bmatrix}$
 A 3 and -5 B -3 and 5 C -3 and -5 D 3 and 5
Engineering Mathematics   Linear Algebra
 Question 2
The value of the following definite integral is:
$\int_{\frac{-\pi }{2}}^{\frac{\pi }{2}}\frac{sin2x}{1+cosx}dx$
 A -2 ln2 B 2 C 0 D $(ln 2)^{2}$
Engineering Mathematics   Calculus
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 $x$?
$f(x)=x\sqrt{5-x^{2}}$
 A $-\frac{\sqrt{5}}{2}$ B $\sqrt{5}$ C $\sqrt{\frac{5}{2}}$ D $-\sqrt{\frac{5}{2}}$
Engineering Mathematics   Calculus
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

I. Member AB Carries shear force and bending moment.
II. Member BC carries axial load and shear force.

Which of the following is true?
 A Statement I is true but II is false B Statement I is false but II is true C Both statements I and II are true D Both statements I and II are false
Solid Mechanics   Shear Force and Bending Moment
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

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?
 A Statement I is true but II is false B Statement I is false but II is true C Both statement I and II are true D Both statements I and II are false
RCC Structures   Working Stress and Limit State Method
 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
 A 25000 B 28500 C 30000 D 36000
RCC Structures   Working Stress and Limit State Method
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,
 A $G=\frac{E}{2(1+v)}$ B $E=\frac{G}{2(1+v)}$ C $G=\frac{E}{2(1-v)}$ D $E=\frac{G}{2(1-v)}$
Solid Mechanics   Properties of Metals, Stress and Strain
 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.
 A Quality control at the time of manufacture of rolled sections is very good B Web depths available are small C Web stiffeners are in-built in rolled sections D Depth to thickness ratios (of the web) are appropriately adjusted
Design of Steel Structures   Beams
 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,
 A The tension flange is 'laterally restrained' B the compression flange is 'laterally restrained' C the web is adequately stiffened D the conditions in (A) and (C) are met
Design of Steel Structures   Beams
 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
 A SC B MI C CH D MH
Geotechnical Engineering   Classification of Soils and Clay Minerals
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.
There are 10 questions to complete.