The estimate of $$\int\limits_{0.5}^{1.5} {{{dx} \over x}} \,\,$$ obtained using Simpson's rule with three-point function evaluation exceeds the exact value by

The solution of the ordinary differential equation $${{dy} \over {dx}} + 2y = 0$$ for the boundary condition, $$y=5$$ at $$x=1$$ is

Is an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is

The annual precipitation data of a city is normally distributed with mean and standard deviation as $$1000$$mm and $$200$$ mm, respectively. The probability that the annual precipitation will be more than $$1200$$ mm is

For the parallelogram $$OPQR$$ shown in the sketch. $$\,\overrightarrow {OP} = a\widehat i + b\widehat j$$ and $$\,\overrightarrow {OR} = c\widehat i + d\widehat j.\,\,$$ The area of the parallelogram is

The infinite series $$1 + x + {{{x^2}} \over {2!}} + {{{x^3}} \over {3!}} + {{{x^4}} \over {4!}} + ........$$ corresponds to

The eigen values of matrix $$\left[ {\matrix{ 9 & 5 \cr 5 & 8 \cr } } \right]$$ are

A water sample has a pH of 9.25. The concentration of hydroxyl ions in the water sample is

If a small concrete cube is submerged deep in still water in such a way that the pressure exerted on all faces of the cube is p, then the maximum shear stress developed inside the cube is

The ratio of actual evapo-transpiration to potential evapo-transpiration is in the range

Wheat crop requires 55 cm of water during 120 days of base period. The total rainfall during this period is 100 mm. Assume the irrigation efficiency to be 60%. The area (in ha) of the land which can be irrigated with a canal flow of 0.01 $$m^3/s$$ is

A concrete beam prestressed with a parabolic tendon is shown in the sketch. The eccentricity of the tendon is measured from the centroid of the cross-section. The applied prestressing force at service is $$1620$$ $$kN.$$ The uniformly distributed load of $$45$$ $$kN/m$$ includes the self-weight. The stress (in $$N/m{m^2}$$) in the bottom fibre at mid-span is

Which one of the following is categorized as a long-term loss of prestress in a prestressed concrete member?

The cross-section at mid-span of a beam at the edge of a slab is shown in the sketch. $$A$$ portion of the slab is considered as the effective flange width for the beam. The grades of concrete and reinforcing steel are $$M25$$ and $$Fe415,$$ respectively. The total area of reinforcing bars $$\left( {{A_{st}}} \right),$$ is $$\,4000\,\,m{m^2}.$$ At the ultimate limit state, $${x_u}$$ denotes the depth of the neutral axis from the top fibre. Treat the section as under-reinforced and flanged $$\left( {{x_u} > 100\,\,mm} \right).$$

The ultimate moment capacity (in $$kNm$$) of the section, as per the Limit State Method of $$IS$$ $$456$$ - $$2000$$ is

The cross-section at mid-span of a beam at the edge of a slab is shown in the sketch. $$A$$ portion of the slab is considered as the effective flange width for the beam. The grades of concrete and reinforcing steel are $$M25$$ and $$Fe415,$$ respectively. The total area of reinforcing bars $$\left( {{A_{st}}} \right),$$ is $$\,4000\,\,m{m^2}.$$ At the ultimate limit state, $${x_u}$$ denotes the depth of the neutral axis from the top fibre. Treat the section as under-reinforced and flanged $$\left( {{x_u} > 100\,\,mm} \right).$$

The value of $${{x_u}}$$ (in $$mm$$) computed per the Limit State Method of $$IS$$ $$456:2000$$ is

As per $$IS$$ $$456:2000,$$ in the Limit State Design of a flexural member, the strain in reinforcing bars under tension at ultimate state should not be less than

Two plates are connected by fillet welds of size $$10$$ $$mm$$ and subjected to tension, as shown in the sketch. The thickness of each plate is $$12$$ $$mm.$$ The yield stress and the ultimate tensile stress of steel are $$250$$ $$MPa$$ and $$410$$ $$MPa,$$ respectively. The welding is done in the workshop $$\left( {{\gamma _{mw}} = 1.25} \right).$$

As per the Limit State Method of $$IS$$ $$800:2007,$$ the minimum length (rounded off to the nearest higher multiple of $$5$$ $$mm$$) of each weld to transmit a force $$P$$ equal to $$270$$ $$kN$$ (factored) is

In a steel plate with bolted connections, the rupture of the net section is a mode of failure under

If a small concrete cube is submerged deep in still water in such a way that the pressure exerted on all faces of the cube is $$p,$$ then the maximum shear stress developed inside the cube is

The sketch shows a column with a pin at the base and rollers at the top. It is subjected to an axial force $$P$$ and a moment $$M$$ at mid-height. The reaction$$(s)$$ at $$R$$ is/are

The ratio of the theoretical critical buckling load for a column with fixed ends to that of another column with the same dimensions and material, but with pinned ends, is equal to

A simply supported beam is subjected to a uniformly distributed load of intensity $$w$$ per unit length. On half of the span from one end. The length of the span and the flexural stiffness are denoted as/and $$EI$$, respectively. The deflection at mid-span of the beam is

The Poisson's ratio is defined as

The following statements are related to bending of beams:

$${\rm I}.$$ The slope of the bending moment diagram is equal to the shear force.
$${\rm II}.$$ The slope of the shear force diagram is equal to the load intensity.
$${\rm III}.$$ The slope of the curvature is equal to the flexural rotation.
$${\rm IV}.$$ The second derivative of the deflection is equal to the curvature.

The only FALSE statements is

A symmetric frame $$PQR$$ consists of two inclined members $$PQ$$ and $$QR$$, connected at $$‘Q’$$ with a rigid joint, and hinged at $$‘P’$$ and $$‘R’.$$ The horizontal length $$PR$$ is $$l.$$ If a weight $$W$$ is suspended at $$‘Q’,$$ the bending moment at $$‘Q’$$ is