Recent questions tagged gate2017-ce-1

The matrix $P$ is the inverse of a matrix $Q$. If $I$ denotes the identity matrix, which one of the following options is correct?$PQ=I$ but $QP \neq I$$QP=I$ but $PQ \neq...

The number of parameters in the univariate exponential and Gaussian distributions, repsectively, are$2$ and $2$$1$ and $2$$2$ and $1$$1$ and $1$

Let $x$ be a continuous variable defined over the interval $(- \infty, \infty)$, and $f(x) = e^{-x-e^{-x}}$. The integral $g(x)= \int f(x) \: dx$ is equal to$e^{e^{-x}}$$...

An elastic bar of length $L$, uniform cross sectional area $A$, coefficient of thermal expansion $\alpha$, and Young’s modulus $E$ is fixed at the two ends. The temperatu...

A simply supported beam is subjected to a uniformly distributed load. Which one of the following statements is true?Maximum or minimum shear force occurs where the curvat...

According to $IS \: 456 – 2000$, which one of the following statements about the depth of neutral axis $x_{\text{u, bal}}$ for a balanced reinforced concrete section is c...

The figure shows a two-hinged parabolic arch of span $L$ subjected to a uniformly distributed load of intensity $q$ per unit length.The maximum bending moment in the arch...

Group I lists the type of gain or loss of strength in soils. Group II lists the property or process responsible for the loss or gain of strength in soils.$\begin{array}{l...

A soil sample is subjected to a hydrostatic pressure, $\sigma$. The Mohr circle for any point in the soil sample would bea circle of radius $\sigma$ and center at the ori...

A strip footing is resting on the ground surface of a pure clay bed having an undrained cohesion $c_u$. The ultimate bearing capacity of the footing is equal to$2 \pi \: ...

A uniformly distributed line road of $500 \: kN/m$ is acting on the ground surface. Based on Boussinesq’s theory, the ratio of vertical stress at a depth $2$ m to that at...

For a steady incompressible laminar flow between two infinite parallel stationary plates, the shear stress variation islinear with zero value at the plateslinear with zer...

The reaction rate involving reactants $A$ and $B$ is given by $-k[A]^{\alpha} [B]^{\beta}$. Which one of the following statements is valid for the reaction to be first-or...

The wastewater from a city, containing a high concentration of biodegradable organics, is being steadily discharged into a flowing river at a location S. If the rate of a...

Which one of the following is NOT present in the acid rain?$HNO_3$$H_2SO_4$$H_2CO_3$$CH_3COOH$

A runway is being constructed in a new airport as per the International Civil Aviation Organization (ICAO) recommendations. The elevation and the airport reference temper...

The accuracy of an Electronic Distance Measuring Instrument (EDMI) is specified as $\pm (a \: mm + b \: ppm)$. Which one of the following statements is correct?Both $a$ a...

The number of spectral bands in the Enhanced Thematic Mapper sensor on the remote sensing satellite Landsat-$7$ is:$64$$10$$8$$15$

Consider the following partial differential equation:$$3 \frac{\partial ^2 \phi}{ \partial x^2} + B \frac{ \partial ^2 \phi}{\partial x \partial y} + 3 \frac{\partial ^2 ...

$\underset{x \to 0}{\lim} \bigg( \dfrac{\tan x}{x^2-x} \bigg)$ is equal to _________

A $3 \: m$ thick clay layer is subjected to an initial uniform pore pressure of $145 \: kPa$ as shown in the figure.For the given ground conditions, the time (in days, ro...

A triangular pipe network is shown in the figure.The head loss in each pipe is given by $h_f = rQ^{1.8}$, with the variables expressed in a consistent set of units. The v...

The ordinates of a $2$-hour unit hydrograph for a catchment are given as$$\begin{array}{llllll} \text{Time (h)} & 0 & 1 & 2 & 3 & 4 \\ \text{Ordinate } (m^3/s) & 0 & 5 &...

Vehicles arriving at an intersection from one of the approach roads follow the Poisson distribution. The mean rate of arrival is $900$ vehicles per hour. If a gap is defi...

For the function $f(x)=a+bx,0\leq x\leq1,$ to be a valid probability density function,which one of the following statements is correct?$a=1,b=4$$b=0.5,b=1$$a=0,b=1$$a=1,b...

The solution of the equation $\dfrac{dQ}{dt} +Q =1$ with $Q=0$ at $t=0$ is$Q(t)=e^{-t}-1$$Q(t)=1+ e^{-t}$$Q(t)=1 -e^t$$Q(t)=1- e^{-t}$

Consider the matrix $\begin{bmatrix} 5 & -1 \\ 4 & 1 \end{bmatrix}$. Which one of the following statements is TRUE for the eigenvalues and eigenvectors of this matrix?Eig...

A planar truss tower structure is shown in the figure.Consider the following statements about the external and internal determinacies of the truss.Externally DeterminateE...

Group I contains three broad classes of irrigation supply canal outlets, Group II presents hydraulic performance attributes.$$\begin{array}{|ll|ll|} \hline {} & \text{Gro...

A $1$ m wide rectangular channel has a bed slope of $0.0016$ and the Manning’s roughness coefficient is $0.04$ Uniform flow takes the place in the channel at a flow depth...

The following observations are made while testing aggregate for its suitability in pavement construction:Mass of oven-dry aggregate in air $=1000 $ g Mass of saturated su...

The queue length (in number of vehicles) versus time (in seconds) plot for an approach to a signalized intersection with the cycle length of $96$ seconds is shown in the ...

The radius of a horizontal circular curve on a highway is $120$ m. The design speed is $60$ km/hour, and the design coefficient of lateral friction between the tyre and r...

The observed bearings of a traverse are given below:$\begin{array}{|c|c|c|c|c|} \hline \text{Line} & \text{Bearing} & {} & \text{Line} & \text{Bearing} \\ \hline PQ & 46^...

The laboratory tests on a soil sample yields the following results: natural moisture content $=18 \%$, liquid limit $=60 \%$, plastic limit $=25 \%$, percentage of clay s...

Consider the equation $\dfrac{du}{dt}=3t^2+1$ with $u=0$ at $t=0$. This is numerically solved by using the forward Euler method with a step size, $\Delta t=2$. The absolu...

A pre-tensioned rectangular concrete beam $150$ mm wide and $300$ mm depth is prestressed with three straight tendons, each having a cross-sectional are of $50 \: mm^2$, ...

The value of $M$ in the beam ABC shown in the figure is such that the joint B does not rotate.The value of support reaction (in kN) at B should be equal to _________.

A column is subjected to a load through a bracket as shown in the figure.The resultant force (in kN, up to one decimal place) in the bolt $1$ is _______