Recent questions tagged gate2020-ce-2

A prismatic linearly elastic bar of length $L$, cross-sectional area $A$, and made up of a material with Young’s modulus $E$, is subjected to axial tensile force as shown...

The planar structure $RST$ shown in the figure is roller-supported at $S$ and pin-supported at $R.$ Members $RS$ and $ST$ have uniform flexural rigidity $(EI)$ and $S$ is...

The flow-density relationship of traffic on a highway is shown in the figureThe correct representation of speed-density relationship of the traffic on this highway is

Permeability tests were carried out on the samples collected from two different layers as shown in the figure (not drawn to the scale). The relevant horizontal $(k_h)$ an...

A $10\ m$ high slope of dry clay soil $\text{( unit weight}\: = 20 kN/m^3$), with a slope angle of $45^{\circ}$and the circular slip surface, is shown in the figure (not ...

Crops are grown in a field having soil, which has field capacity of $30\%$ and permanent wilting point of $13\%.$ The effective depth of root zone is $80\ cm$. Irrigation...

Alkalinity of water, in equivalent/litre (eq/litre), is given by$${\{HC{O_3}^-}\} + 2{\{C{O_3}^{2-}}\} + {\{OH^-\}}\ –\ {\{H^+\}}$$where, $\{\ \ \}$ represents concentr...

A theodolite was set up at a station $P$. The angle of depression to a vane $2\ m$ above the food of a staff held at another station $Q$ was $45^\circ$. The horizontal di...

The Fourier series to represent $x- x^2$ for $-\pi\leq x\leq \pi$ is given by$$ x-x^2 = \dfrac{a_0}{2} + \sum_{n=1}^{\infty} a_n\ \cos nx + \sum_{n=1}^{\infty} b_n\ \si...

The diameter and height of a right circular cylinder are $3\: cm$ and $4\: cm$, respectively. The absolute error in each of these two measurements is $0.2\: cm$. The abso...

A concrete beam of span $15\: m,\ 150\: mm$ wide and $350\: mm$ deep is prestressed with a parabolic cable as shown in the figure (not drawn to the scale). Coefficient of...

The plane truss has hinge supports at $P$ and $W$ and is subjected to the horizontal forces as shown in the figure (not drawn to the scale)Representing the tensile force ...

The cross-section of the reinforced concrete beam having an effective depth of $500\: mm$ is shown in the figure (not drawn to the scale ). The grades of concrete and ste...

Two steel plates are lap jointed in a workshop using $6\ mm$ thick fillet weld as shown in the figure (not drawn to the scale). The ultimate strength of the weld is $410\...

The design speed of a two-lane two-way road is $60\: km/h$ and the longitudinal coefficient of friction is $0.36$. The reaction time of a driver is $2.5$ seconds. Conside...

A footing of size $2\: m \times 2\: m$ transferring a pressure of $200\: kN/m^2$, is place at a depth of $1.5\: m$ below the ground as shown in the figure (not drawn to t...

A constant-head permeability test was conducted on a soil specimen under a hydraulic gradient of $2.5$. The soil specimen has specific gravity of $2.65$ and saturated wat...

A $5\: m$ high vertical wall has a saturated clay backfill. The saturated unit weight and cohesion of clay are $18\: kN/m^3$ and $20\: kPa$, respectively. The angle of in...

A cast iron pipe of diameter $600\: mm$ and length $400\: m$ carries water from a tank and discharges freely into air at a point $4.5\: m$ below the water surface in the ...

A hydraulic jump occurs in a triangular $\text{(V-shaped)}$ channel with side slopes $1:1$ (vertical to horizontal). The sequent depths are $0.5\: m$ and $1.5\: m$. The f...

A concrete dam holds $10\: m$ of static water as shown in the figure (not drawn to the scale). The uplift is assumed to vary linearly from full hydrostatic head at the he...

The ion product of water $(pK_w)$ is $14$. If a rain water sample has a $pH$ of $5.6$, the concentration of $OH^-$ in the sample (in $10^{-9}\: \text{mol/litre}$, round o...

A waste to energy plant burns dry solid waste of composition: Carbon $= 35\%$, Oxygen $= 26\%$ , Hydrogen $= 10\%$, Sulphur $= 6\%$, Nitrogen $= 3\%$ and Inerts $= 20\%.$...

A sample of water contains an organic compound $C_8H_{16}O_8$ at a concentration of $10^{-3}\: \text{mol/litre}$. Given that the atomic weight of $C = 12\: \text{g/mol}, ...

A theodolite is set up at station $A$. The $RL$ of instrument axis is $212.250\: m$. The angle of elevation to the top of a $4\: m$ long staff, held vertical at station $...