Recent questions tagged gate2019-ce-1

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The probability that the annual maximum flood discharge will exceed $25000 \: m^3/s$, at least once in next $5$ years is found to be $0.25$. The return period of this flo...
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A soil has specific gravity of its solids equal to $2.65$. The mass density of water is $1000 \: kg/m^3$. Considering zero air voids and $10 \%$ moisture content of the s...
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A rectangular open channel has a width of $5 \: m$ and a bed slope of $0.001$. For a uniform flow of depth $2 \: m$, the velocity is $2 \: m/s$. The Manning’s roughness...
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The cross-section of a built-up wooden beam as shown in the figure (not drawn to scale) is subjected to a vertical shear force of $8 \: kN$. The beam is symmetrical about...
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A survey line was measured to be $285.5 \: m$ with a tape having a nominal length of $30 \: m$. On checking, the true length of the tape was found to be $0.05 \: m$ too ...
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A $16 \: mm$ thick gusset plate is connected to the $12 \: mm$ thick flange plate of an I-section using fillet welds on both sides as shown in the figure (not drawn to sc...
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The network of a small construction project awarded to a contractor is shown in the following figure. The normal duration, crash duration, normal cost, and crash cost of ...
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A box measuring $50 \: cm \times 50 \: cm \times 50 \: cm$ is filled to the top with dry coarse aggregate of mass $187.5 \: kg$. The water absorption and specific gravity...
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A portal frame shown in figure (not drawn to scale) has a hinge support at joint P and a roller support at joint R. A point load of $50 \: kN$ is acting at joint in R in ...
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A sample of air analysed at $0^{\circ} C$ and $1 \: atm$ pressure is reported to contain $0.02 \: ppm$ (parts per million) of $NO_2$. Assume the gram molecular mass of $N...
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A $0.80 \: m$ deep bed of sand filter (length $4 \:m $ and width $3 \: m$) is made of uniform particles (diameter $=0.40 \: mm$, specific gravity $=2.65$, shape factor $=...
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A wastewater is to be disinfected with $35 \: mg/L$ of chlorine to obtain $99 \%$ kill of micro-organisms. The number of micro-organisms remaining alive $(N_t)$ at time $...
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A staff is placed on a benchmark (BM) of reduced level (RL) $100.000 \: m$ and a theodolite is placed at a horizontal distance of $50 \: m$ from the BM to measure the ver...
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Consider the ordinary differential equation $x^2 \dfrac{d^2y}{dx^2} – 2x \dfrac{dy}{dx} +2y=0$. Given the values of $y(1)=0$ and $y(2)=2$, the value of $y(3)$ (round of...
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Average free flow speed and the jam density observed on a road stretch are $60 \: km/h$ and $120$ vehicles/km, respectively. For a linear speed-density relationship, the ...
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Traffic on a highway is moving at a rate of $360$ vehicles per hour at a location. If the number of vehicles arriving on this highway follows Poisson distribution, the pr...
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A parabolic vertical curve is being designed to join a road of grade $+5 \%$ with a road of grade $-3 \%$. The length of the vertical curve is $400 \: m$ measured along t...
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Tie bars of $12 \: mm$ diameter are to be provided in a concrete pavement slab. The working tensile stress of the tie bars is $230 \: MPa$, the average bond strength betw...
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The hyetograph of a storm event of duration $140$ minutes is shown in the figure:The infiltration capacity at the start of this event $(t=0)$ is $17 \: mm/hour$, which li...
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Two water reservoirs are connected by a siphon (running full) of total length $5000$ m and diameter of $1.10$ m, as shown below (figure not drawn to scale).The inlet leg ...
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Consider a laminar flow in the x-direction between two infinite parallel plates (Couette flow). The lower plate is stationary and the upper plate is moving with a velocit...
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A reinforced concrete circular pile of $12 \: m$ length and $0.6 \: m$ diameter is embedded in stiff clay which has an undrained unit cohesion of $110 \: kN/m^2$. The adh...
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A granular soil has a saturated unit weight of $20 \:kN/m^3$ and an effective angle of shearing resistance of $30^{\circ}$. The unit weight of water is $9.81 \: kN/m^3$. ...
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A $3 \: m \times 3 \: m$ square precast reinforced concrete segments to be installed by pushing them through an existing railway embankment for making an underpass as sho...
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A square footing of $ 4 \: m$ side is placed at $1 \: m$ depth in a sand deposit. The dry unit weight $( \gamma)$ of sand is $15 \: kN/m^3$. This footing has an ultimate ...