Recent questions tagged gate2017-ce-2

Consider the following simultaneous equations (with $c_1$ and $c_2$ being constants):$3x_1+2x_2=c_1$$4x_1+x_2=c_2$The characteristic equation for these simultaneous equat...

Let $w=f(x,y)$, where $x$ and $y$ are functions of $t$. Then, according to the chain rule, $\dfrac{dw}{dt}$ is equal to$\dfrac{dw}{dx} \dfrac{dx}{dt} + \dfrac{dw}{dy} \df...

Let $G$ be the specific gravity of soil solids, $w$ the water content in the soil sample, $\gamma_w$ the unit weight of water, and $\gamma_d$ the dry unit weight of the s...

Consider the following statements related to pore pressure parameters, $A$ and $B$:$A$ always lies between $0$ and $1.0$$A$ can be less than $0$ or greater than $1.0$$B$ ...

Consider a rigid retaining wall with partially submerged cohesionless backfill with a surcharge. Which one of the following diagrams closely represents the Rankine’s acti...

If a centrifugal pump has an impeller speed of $N$ (in rpm), discharge $Q$ (in $m^3/s$) and the total head $H$ (in $m$), the expression for the specific speed $N_s$ of t...

As per Noise Pollution (Regulation and Control) Rules $2000$ of India, the day time noise limit for a residential zone, expressed in dB(A)L$_{eq}$, is$55$$65$$75$$85$

Following observations have ben made for the elevation and temperature to ascertain the stability of the atmosphere:$$\begin{array}{|c|c|} \hline \text{Elevation (in m) }...

The most important type of species involved in the degradation of organic matter in the case of activated sludge process isautotrophsheterotrophsprototrophsphoto-autotrop...

For a broad gauge railway track on a horizontal curve of radius $R$ (in m), the equilibrium cant $e$ required for a train moving at a speed of $V$ (in km per hour) is$e= ...

The safety within a roundabout and the efficiency of a roundabout can be increased, respectively, byincreasing the entry radius and increasing the exit radiusincreasing t...

The method of orientation used, when the plane table occupies a position not yet located on the map, is called astraversingradiationlevellingresection

Consider the following frame in the figure:If the axial and shear deformations in different members of the frame are assumed to be negligible, the reduction in the degree...

Let the characteristic strength be defined as that value, below which not more than $50 \%$ of the results are expected to fall. Assuming a standard deviation of $4$ MPa,...

In a material under a state of plane strain, a $10 \times 10$ mm square centered at a point gets deformed as shown in the figure.If the shear strain $\gamma_{xy}$ at this...

The plate load test was conducted on a clayey strata by using a plate of $0.3 \: m \times 0.3 \: m$ dimensions, and the ultimate load per unit area for the plate for foun...

For a construction project, the mean and standard deviation of the completion time are $200$ days and $6.1$ days, respectively. Assume normal distribution and use the val...

The divergence of the vector field $V=x^2 i + 2y^3 j + z^4 k$ at $x=1, \: y=2, \: z=3$ is ________

A two-faced fair coin has its faces designated as head (H) and tail (T). This coin is tossed three times in succession to record the following outcomes: H, H, H. If the c...

A sheet pile has an embedment depth of $12$ m in a homogeneous soil stratum. The coefficient of permeability of soil is $10^{-6} m/s$. Difference in the water levels betw...

The VPI (vertical point of section) is $100$ m away (when measured along the horizontal) from the VPC (vertical point of curvature). If the vertical is parabolic, the len...

During a storm event in a certain period, the rainfall intensity is $3.5$ cm/hour and the $\Phi$-index is $1.5$ cm/hour. The intensity of effective rainfall (in cm/hour, ...

The infiltration capacity of a soil follows the Horton’s exponential model, $f=c_1+c_2e^{-kt}$. During an experiment, the initial infiltration capacity was observed to be...

While aligning a hill road with a ruling gradient $6\%$, a horizontal curve of radius $50 \: m$ is encountered. The grade compensation (in percentage, up to two decimal p...

The tangent to the curve represented by $y=x \text{ ln }x$ is required to have $45^{\circ}$ inclination with the $x$-axis. The coordinates of the tangent point would be$(...

Consider the following definite integral: $I= \displaystyle{} \int_0^1 \dfrac{(\sin ^{-1}x)^2}{\sqrt{1-x^2}} dx$. The value of the integral is$\dfrac{\pi ^3}{24} \\$$\dfr...

Consider the following second-order differential equation: $y’’ – 4y’+3y =2t -3t^2$. The particular solution of the differential solution equation is$ – 2 -2t-t^2$$ – 2t-...

Group I gives a list of test methods and test apparatus for evaluating some of the properties of Ordinary Portland Cement (OPC) and concrete. Group II gives the list of t...

Two prismatic beams having the same flexural rigidity of $1000 \: kN-m^2$ are shown in the figures.If the mid-span deflections of these beams are denoted by $\delta_1$ an...

Consider the prismatic beams with the clamped supports P, Q, and R as shown in the figures.Given that eh modulus of elasticity, $E$ is $2.5 \times 10^4$ MPa; and the mome...

Consider the following statements:Walls of one brick thick are measured in square metersWalls of one brick thick are measured in cubic metersNo deduction in the brickwork...

Two identical concrete piles having the plan dimensions $50 \: cm \times 50 \: cm$ are driven into a homogeneous sandy layers as shown in the figures. Consider the bearin...

Following are the statements related to the stress paths in a triaxial testing of soils:If $\sigma_1 = \sigma_3$, the stress point lies at the origin of the $p-q$ plotIf ...

Two cars P and Q are moving in a racing track continuously for two hours. Assume that no other vehicles are using the track during this time. The expressions relating the...

For the construction of a highway, a cut is to be made as shown in the figure.The soil exhibits $c’=20$ kPa, $\phi’=18^{\circ}$, and the undrained shear strength $=80$ kP...

Two towers, A and B, standing vertically on a horizontal ground, appear in a vertical aerial photograph as shown in the figure.The length of the image of the tower A on t...

A hallow circular shaft has an outer diameter of $100 $ mm and inner diameter of $50 $ mm. If the allowable shear stress is $125$ MPa, the maximum torque (in kN-m) that t...

A simply supprted rectangular concrete beam of span $8$ m has to be prestressed with a force of $1600$ kN. The tendon is of parabolic profile having zero eccentricity at ...