GATE 2004 Civil Engineering
31 questions across 1 session
The function $$f\left( x \right) = 2{x^3} - 3{x^2} - 36x + 2\,\,\,$$ has its maxima at
A strut in a steel truss is composed of two equal angles $$ISA$$ $$150mm \times 150mm$$ of thickness $$100$$ $$mm$$ connected back-to back to the same side of a gusset plate. The c...
An $$RC$$ short column with $$300\,\,mm \times 300\,mm$$ square cross-section is made of $$M20$$ grade concrete and has $$4$$ numbers, $$20$$ $$mm$$ diameter longitudinal bars of $...
At the limit state of collapse, an $$RC$$ beam is subjected to flexural moment $$200$$ $$kN$$-$$m$$, shear force $$20$$ $$kN$$ and torque $$9$$ $$kN$$-$$m$$. The beam is $$300$$ $$...
At the limit state of collapse, an $$RC$$ beam is subjected to flexural moment $$200$$ $$kN$$-$$m$$, shear force $$20$$ $$kN$$ and torque $$9$$ $$kN$$-$$m$$. The beam is $$300$$ $$...
Two equal angles $$ISA$$ $$100\,\,mm \times 100\,\,mm$$ of thickness $$10$$ $$mm$$ are placed back-to-back and connected to the either side of a gusset plate through a single row o...
The ratio of saturated unit weight to dry unit weight of a soil is 1.25. If the specific gravity of solids (G s ) is 2.65, the void ratio of the soil is
Rivet value is defined as
The star and grid pattern of road networks are adopted in
For a linear elastic structural system, minimization of potential energy yields
An $$RC$$ square footing of side length $$2$$ $$m$$ and uniform effective depth $$200$$ $$mm$$ is provided for a $$300$$ $$mm \times 300\,mm$$ column. The line of action of the ver...
A simply supported prestressed concrete beam is $$6$$ $$m$$ long and $$300$$ $$mm$$ wide. Its gross depth is $$600$$ $$mm.$$ It is prestressed by horizontal cable tendons at a unif...
In a plate girder, the web plate is connected to the flange plates by fillet welding. The size of the fillet welds is designed to safely resist
A delayed unit step function is defined as $$$u\left( {t - a} \right) = \left\{ {\matrix{ {0,} & {t < a} \cr {1,} & {t \ge a} \cr } } \right.$$$ Its Laplace transform is __________...
The eigen values of the matrix $$\left[ {\matrix{ 4 & { - 2} \cr { - 2} & 1 \cr } } \right]$$ are
Biotransformation of an organic compound having concentration $$(x)$$ can be modeled using an ordinary differential equation $$\,{{d\,x} \over {dt}} + k\,{x^2} = 0,$$ where $$k$$ i...
The value of the function, $$f\left( x \right) = \mathop {Lim}\limits_{x \to 0} {{{x^3} + {x^2}} \over {2{x^3} - 7{x^2}}}\,\,\,$$ is
A hydraulic structure has four gates which operate independently. The probability of failure of each gate is $$0.2.$$ Given that gate $$1$$ has failed, the probability that both ga...
Real matrices $$\,\,{\left[ A \right]_{3x1,}}$$ $$\,\,{\left[ B \right]_{3x3,}}$$ $$\,\,{\left[ C \right]_{3x5,}}$$ $$\,\,{\left[ D \right]_{5x3,}}$$ $$\,\,{\left[ E \right]_{5x5,}...
The present population of a community is 28000 with an average water consumption of 4200 $$m^3/d$$. The existing water treatment plant has a design capacity of 6000 $$m^3/d$$. It i...
Most of the turbidity meters work on the scattering principle. The turbidity value obtained is expressed in
In the limit state design method of concrete structures, the recommended partial material safety factor $$\left( {{\gamma _m}} \right)$$ for steel according to $$IS:456$$-$$2000$$...
A three hinged parabolic arch $$ABC$$ has a span of $$20$$ $$m$$ and a central rise of $$4$$ $$m.$$ The arch has hinges at the ends and at the center. A train of two point loads of...
The unit load method used in Structural analysis is
A homogeneous, simply supported prismatic beam of width $$B,$$ depth $$D$$ and span $$L$$ is subjected to a concentrated load of magnitude $$P.$$ The load can be placed anywhere al...
For linear elastic frame, if stiffness matrix is doubled with respect to the existing stiffness matrix, the deflection of the resulting frame will be
A homogeneous, simply supported prismatic beam of width $$B,$$ depth $$D$$ and span $$L$$ is subjected to a concentrated load of magnitude $$P.$$ The load can be placed anywhere al...
$${U_1}$$ and $${U_2}$$ are the strain energies stored in a prismatic bar due to axial tensile forces $${P_1}$$ and $${P_2},$$ respectively. The strain energy $$U$$ stored in the s...
If principle stresses in two-dimensional case are $$\left( - \right)\,\,10\,MPa$$ and $$20$$ $$MPa$$ respectively, then maximum shear stress at the point is
A circular solid shaft of span $$L=5m$$ is fixed at one end and free at the other end. A twisting moment $$T=100$$ $$kN$$-$$m$$ is applied at the free end. The torsional rigidity $...
A sprinkler irrigation system is suitable when