Recent questions tagged gate2015-ce-2

The probability density function of a random variable, $x$ is$f(x)= \begin{cases} \dfrac{x}{4} ( 4-x^2) & \text{ for } 0 \leq x \leq 2 \\ 0 & \text{ otherwise} \end{ca...

A steel strip of length $L=200$ mm is fixed at end $A$ and rests at $B$ on a vertical spring of stiffness, $k=2 \: N/mm$. The steel strip is $5$ mm wide and $10$ mm thick...

A simply supported beam AB of span, $L=24$ m is subjected to two wheel loads acting at a distance, $d=5$ m apart as shown in the figure below. Each wheel transmits a load...

According to the concept of Limit State Design as per $IS \: 456:2000$, the probability of failure of a structure is ______.

In a pre-stressed concrete beam section shown in the figure, the net loss is $10 \%$ and the final pre-stressing force applied at $X$ is $750$ kN. The initial fiber stres...

A fixed end beam is subjected to a load, W at $1/3$ rd span from the left support as shown in the figure. The collapse load of the beam is:$16.5 M_p/L$$15.5 M_p/L$$15.0 M...

A $588 \: cm^3$ volume of moist sand weighs $1010$ gm. Its dry weight is $918$ gm and specific gravity of solids, $G$ is $2.67$. Assuming density of water as $1 \: gm/cm^...

A $4$ m thick layer of normally consolidated clay has an average void ratio of $1.30$. Its compression index is $0.6$ and coefficient of consolidation is $1 \: m^2/yr$. I...

A pile of diameter $0.4$ m is fully embedded in a clay stratum having $5$ layers, each $5$ m thick as shown in the figure below. Assume a constant unit weight of soil as ...

Stress path equation for tri-axial test upon application of deviatoric stress is, $q=10 \sqrt{3}+0.5p$. The respective values of cohesion, $c$ (in kPa) and angle of inter...

A $6$ m high retaining wall having a smooth vertical back face retains a layered horizontal backfill. Top $3$ m thick layer of the backfill is sand having an angle of int...

A field channel has cultivable commanded are of $2000$ hectares. The intensities of irrigation for gram and wheat are $30 \%$ and $50\%$ respectively. Gram has a kor peri...

A triangular gate with a base width of $2$ m and a height of $1.5$ m lies in a vertical plane. The top vertex of the gate is $1.5$ m below the surface of a tank which con...

The velocity components of a two dimensional plane motion of a fluid are $:u=\dfrac{y^3}{3}+2x—x^2y$ and $v=xy^2-2y-\dfrac{x^3}{3}$. The correct statement is:Fluid is inc...

The average surface area of a reservoir in the month of June is $20 \: km^2$. In the same month, the average rate of inflow is $10 \: m^3/s$, outflow rate is $15 \: m^3/s...

A pipe of $0.7$ m diameter has a length of $6$ km and connects two reservoirs A and B. The water level in reservoir A is at an elevation $30$ m above the water level in r...

A landfill is to be designed to serve a population of $200000$ for a period of $25$ years. The solid waste (SW) generation is $2$ kg/person/day. The density of the un-com...

A water treatment plant of capacity, $1 \: m^3/s$ has filter boxed of dimensions $6 \; m \times 10 \: m$. Loading rate to the filters is $120 \: m^3/day/m^2$. When two of...

Ultimate BOD of a river water sample is $20$ mg/L. BOD rate constant (natural log) is $0.15 \: day^{-1}$. The respective values of BOD (in $\%$) exerted and remaining aft...

In a wastewater treatment plant, primary sedimentation tank (PST) designed at an overflow rate of $32.5 \: m^3/day/m^2$ is $32.5$ m long, $8.0$ m wide and liquid depth of...

The relation between speed $u$ (in km/h) and density $k$ (number of vehicles/km) for a traffic stream on a road is $u=70-0.7k$. The capacity on this road is _________ vph...

Match the information related to tests on aggregates given in Group – I with that in Group – II.$\begin{array}{ll} \text{Group – I} & \text{Group – II} \\ P. \text{Resist...

In Marshall method of mix design, the coarse aggregate, fine aggregate, fines and bitumen having respective values of specific gravity $2.60, 2.70, 2.65$ and $1.01$, are ...

The bearings of two inaccessible stations, $S_1$ (Easting $500$ m, Northing $500$ m) and $S_2$ (Easting $600$ m, Northing $450$ m) from a station $S_3$ were observed as $...

Two Pegs A and B were fixed on opposite banks of a $50$ m wide river. The level was set up at A and the staff readings on Pegs A and B were observed as $1.350$ m and $1.5...