Recent questions tagged gate2020-ce-1

For the Ordinary Differential Equation ${\large\frac{d^2x}{dt^2}}-5{\large\frac{dx}{dt}}+6x=0$, with initial conditions $x(0)=0$ and ${\large\frac{dx}{dt}}(0)=10$, the s...

The relationship between traffic flow rate (q) and density (D) is shown in the figure The shock wave condition is depicted byflow with respect to point $1\:(q_1=q_{max})$...

The appropriate design length of a clearway is calculated on the basis of ‘Normal Take-off’ condition. Which one of the following options correctly depicts the length of ...

The total stress paths corresponding to different loading conditions, for a soil specimen under the isotropically consolidated stress state (O), are shown below $\begin{...

The soil profile at a site up to a depth of $10\:m$ is shown in the figure ( not drawn to the scale). The soil is preloaded with a uniform surcharge (q) of $70\:kN/m^2$ a...

Water flows at the rate of $12\:m^3/s$ in a $6\:m$ wide rectangular channel. A hydraulic jump is formed in the channel at a point where the upstream depth is $30\:cm$ (ju...

A water supply scheme transports $10\:MLD$ (MIllion Litres per Day) water through a $450\:mm$ diameter pipeline for a distance of $2.5\:km$. A chlorine dose of $3.50\:mg/...

An open traverse PQRST is surveyed using theodolite and the consecutive coordinates obtained are given in the tableIf the independent coordinates (Northing, Easting) of s...

If $C$ represents a line segment between $(0,0,0)$ and $(1,1,1)$ in Cartesian coordinate system, the value (expressed as integer) of the line integral$$\int_C [(y+z)dx+(x...

Consider the system of equations$$\begin{bmatrix}1&3&2 \\2&2&-3 \\ 4&4&-6 \\ 2&5&2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \\ x_3 \end{bmatrix} = \begin{bmatrix} 1 \\ 1 ...

A rigid, uniform, weightless, horizontal bar is connected to three vertical members P , Q and R as shown in the figure (not drawn to the scale). All three members have id...

The flange and web plates of the doubly symmetric built-up section are connected by continuous $10\:mm$ thick fillet welds as shown in figure (not drawn to the scale). Th...

The singly reinforced concrete beam section shown in the figure (not drawn to the scale) is made of $M25$ grade concrete and $Fe500$ grade reinforcing steel. The total cr...

A simply supported prismatic concrete beam of rectangular cross-section, having a span of $8\:m$, is prestressed with an effective prestressing force of $600\:kN$. The ec...

Traffic volume count has been collected on a $2$-lane road section which needs upgradation due to severe traffic flow condition. Maximum service flow rate per lane is obs...

A vertical retaining wall of $5\:m$ height has to support soil having unit weight of $18\:kN/m^3$ , effective cohesion of $12\:kN/m^2$, and effective friction angle of $3...

Water flows in the upward direction in a tank through $2.5\;m$ thick sand layer as shown in the figure. The void ratio and specific gravity of sand are $0.58$ and $2.7$, ...

A $10\:m$ thick clay layer is resting over a $3\:m$ thick sand layer and is submerged. A fill of $2\:m$ thick sand with unit weight of $20\:kN/m^3$ is placed above the cl...

Three reservoirs $P,Q$ and $R$ are interconnected by pipes as shown in the figure (not drawn to the scale). Piezometric head at the junction $S$ of the pipes is $100\:m$....

In a homogenous unconfined aquifer of area $3.00\:km^2$, the water table was at an elevation of $102.00\:m$. After a natural recharge of volume $0.90$ million cubic meter...

A circular water tank of $2\:m$ diameter has a circular orifice of diameter $0.1\:m$ at the bottom. Water enters the tank steadily at a flow rate of $20\:litre/s$ and esc...

Surface Overflow Rate (SOR) of a primary settling tank (discrete settling) is $20000\:litre/m^2$ per day. Kinematic viscosity of water in the tank is $1.01\times10^{-2}\:...

A gaseous chemical has a concentration of $41.6\:\mu mol/m^3$ in air at $1$ atm pressure and temperature $293\:K$. The universal gas constant $R$ is $82.05\times10^{-6}\;...

A stream with a flow rate of $5\:m^3/s$ is having an ultimate BOD of $30\:mg/litre$. A wastewater discharge of $0.20\:m^3/s$ having $BOD_5\:\text{of}\:500\:mg/litre$ join...

The lengths and bearings of a traverse $PQRS$ are:$$\begin{array}{|c|c|c|}\hline \text{Segment}&\text{Length}\:(m) &\text{Bearing}\\\hline PQ&40&80^\circ{} \\\hline QR&...