Recent questions tagged numerical-answers

An irrigation canal is to be designed to deliver $10$ cumec to meet the peak demand of $7500$ hectare of cropped area. The estimated canal losses are $50 \%$ of the head ...

​​​​​​The name of a person in Column $1$ is to be matched with the test mentioned in Column $2$.\[\begin{array}{|l|l|}\hline\text{Column 1} & \text{Column 2} \\\hline(I)\...

A rapid sand filter bed of depth $0.8$ m has $40 \%$ porosity during service cycle. It is recommended that during backwash operation, the expanded filter bed should have ...

Cant $C$ on a Broad Gauge railway track is calculated for an equilibrium speed $V$ (in $\mathrm{km} / \mathrm{h}$), dynamic gauge $G$ (in mm ) and radius of curve $R$ (in...

Bag $\text{I}$ contains $4$ white and $6$ black balls.Bag $\text{II}$ contains $4$ white and $3$ black balls.One ball is drawn at random from any one of the two bags and ...

A matrix is given as:\[\left[\begin{array}{cc}9 & 15 \\15 & 50\end{array}\right]\]By performing Cholesky decomposition, $\left|l_{22}\right|$ of the lower triangular matr...

It is given that $x$ and $y$ are integers in the following equation:\[(x+y-7)^{2}+(y+3 x-13)^{2}=0\]The value of $\left(x^{3}+y^{3}\right)$ is $\_\_\_\_$ (in integer).

The required centre-to-centre spacing of $10$ mm diameter bars is $150$ mm to resist the design moment in a concrete slab. Instead of $10$ mm diameter bars, if $12$ mm di...

Two steel plates are to be connected together by a $5$ mm fillet weld of length $150$ mm to transfer a design load. If the size of the fillet weld used to connect the sam...

For a liquid, the permeability of a sandy soil having a void ratio of $0.60$ was determined as $0.14 \mathrm{~cm} / \mathrm{s}$. Considering the same liquid and by using ...

To obtain undisturbed clay soil sample, an Area Ratio of $10 \%$ needs to be achieved for a thin walled sampling tube. If the outer diameter of the tube is $50.8$ mm , th...

The travel times of three vehicles on a $2$ km stretch of road are $4,5,$ and $8$ minutes. Assuming the speed of each vehicle to be constant in this stretch, the Space Me...

A $30$ m long tape is standardized at $25^{\circ} \mathrm{C}$. It was used to measure the length of a line which came out to be $200$ m. The temperature during the measur...

The height of the plane of collimation of a levelling instrument is $100.000$ m from a datum. The levelling instrument measures a Back Sight of $1.500$ m on a vertically ...

Let $f(x)$ be a continuous function defined in $[0,2] \rightarrow \mathbb{R}$ and satisfying the equation $\int_{0}^{2} f(x)[x-f(x)] d x=\dfrac{2}{3}.$The value of $f(1)$...

The plane frame has a hinge and a roller support, and is loaded as shown in the figure. Both the columns have same height.What is the absolute value of the maximum bendin...

For a hydraulic jump formed in a rectangular horizontal channel, the sequent depth ratio is $2$. The Froude number of supercritical stream is$\sqrt{3}$$\sqrt{5}$$\sqrt{6}...

In a laminar flow of a Newtonian fluid through a circular pipe of radius $5 \text{ cm}$, the maximum velocity is found to be $2 \mathrm{~m} / \mathrm{s}$. The velocity (i...

The average sewage from a city is $90$ million litres per day and the average $5$-day Biochemical Oxygen Demand ($\text{BOD5}$) is $300 ~\mathrm{mg} / \mathrm{l}$. Averag...

Starting with the first approximation as $x=0.5$, the second approximation for the root of the following function by the Newton-Raphson method is $\_\_\_\_$ (rounded off ...

Values of $y$ for different values of $x$ are tabulated below.\[\begin{array}{|c|c|c|c|}\hlinex & -2 & 1 & 2 \\\hliney & 28 & 4 & 16 \\\hline\end{array}\]If a second-degr...

Two identical blocks $\text{A}$ and $\text{B}$ are connected by a rigid rod. The blocks rest against vertical and horizontal planes, as shown in the figure. The coefficie...

A homogenous, linearly elastic rod $\text{AB}$ is connected to a linearly elastic spring $\text{BC}$ in between the fixed supports at $\text{A}$ and $\text{C}$, as shown ...

The cross-section of a steel $\text{T}$-beam is shown in the figure where all dimensions are in mm.The plastic section modulus of the given cross-section is $\_\_\_\_$ $\...

A fully-penetrating well of $20$ cm diameter is provided in an unconfined aquifer. The height of the ground water table is $30$ m from the bottom of the aquifer. After a ...

A wide unlined channel carries sediment-free water. The depth of water is $1$ m. The specific weight of water is $10 \mathrm{~kN} / \mathrm{m}^{3}$. To prevent scouring, ...

A bridge with an expected life of $50$ years is designed for a flood of $10000 \mathrm{~m}^{3} / \mathrm{s}$ corresponding to the return period of $100$ years. The risk a...

An infinite slope with slope angle $\beta=22^{\circ}$ consists of soil with the following properties:Unit weight $\gamma=15.72 ~\mathrm{kN} / \mathrm{m}^{3}$Cohesion $c^{...

A circular pile of $600 \text{ mm}$ diameter and $6 \text{ m}$ length is embedded in a saturated clayey soil. Undrained cohesion of the soil is $80 \text{ kPa}$ . Unit we...

A group of $25$ circular piles is arranged in $5 \times 5$ uniform pattern in a soft clay soil with equal spacing in both the directions. These are friction piles with ne...

A shallow strip footing of width $2$ m is embedded at a depth of $1.5$ m below the ground surface in a homogeneous pure clay with an angle of internal friction zero. Cons...

Traffic is moving on a $6$-lane dual carriageway road. Traffic volume per direction during peak hour ($08:00$ am to $09:00$ am) is $6000 \mathrm{~veh} / \mathrm{h}$. It i...

In a bituminous mix, the percentage by weight of coarse aggregate, fine aggregate, filler, and bituminous binder is $58,25,12$, and $5$, respectively. The corresponding s...

The following consecutive readings (in m) were taken with a dumpy level and a levelling staff at a common interval of $20$ m:\[0.385 ; 1.030 ; 1.925 ; 2.825 ; 3.730 ; 4.8...

An Activated Sludge Process $\text{(ASP)}$ has an inlet wastewater flowrate of $20000 \mathrm{~m}^{3} /$ day with a Biochemical Oxygen Demand $\text{(BOD)}$ concentration...

The intensity-duration relationship for a rainfall on a rectangular plot $\text{ABCD}$ of area $7$ \text{ha} ($1 \mathrm{~ha}=10^{4} \mathrm{~m}^{2}$) can be modelled by ...

The maximum demand at a water purification plant has been estimated as $12$ million litres per day. For the raw supplies, a rectangular sedimentation tank is to be design...

Three villages $P, Q$, and $R$ are located in such a way that the distance $P Q=13 \mathrm{~km}$, $Q R=14 \mathrm{~km}$, and $R P=15 \mathrm{~km}$, as shown in the figur...