Recent questions tagged numerical-answers

A particle moves along a curve whose parametric equations are: $x=t^3+2t$, $y=-3e^{-2t}$ and $z=2 \sin (5t)$, where $x$, $y$ and $z$ show variations of the distance cover...

For the truss shown below, the member $PQ$ is short by $3$ mm. The magnitude of vertical displacement of joint $R$ (in mm) is ______

A traffic office imposes on an average $5$ number of penalties daily on traffic violators. Assume that the number of penalties on different days is independent and follow...

The amount of $CO_2$ generated (in kg) while completely oxidizing one kg of $CH_4$ to the end products is _________

An incompressible homogeneous fluid is flowing steadily in a variable diameter pipe having the large and small diameters as $15$ cm and $5$ cm, respectively. If the velo...

While designing, for a steel column of $Fe250$ grade, a base plate resting on a concrete pedestal of $M20$ grade, the bearing strength of concrete (in $N/mm^2$) in limit ...

With reference to the conventional Cartesian $(x,y)$ coordinate system, the vertices of a triangle have the following coordinates: $(x_1, y_1) = (1,0)$; $(x_2,y_2) = (2,2...

Given the matrices $J=\begin{bmatrix} 3 & 2 & 1 \\ 2 & 4 & 2 \\ 1 & 2 & 6 \end{bmatrix}$ and $K = \begin{bmatrix} 1 \\ 2 \\ -1 \end{bmatrix}$, the product of $K^TJK$ is _...

The probability density function of evaporation $E$ on any day during a year in a watershed is given by$f(E) = \begin{cases} \dfrac{1}{5} & 0 \leq E \leq 5\: \text{mm/day...

For a portion of national highway where a descending gradient of $1$ in $25$ meets with an ascending gradient of $1$ in $20$, a valley curve needs to be designed for a ve...

For a portion of national highway where a descending gradient of $1$ in $25$ meets with an ascending gradient of $1$ in $20$, a valley curve needs to be designed for a ve...

A theodolite is set up at station A and a $3$ m long staff is held vertically at station B. The depression angle reading at $2.5$ m marking on the staff is $6^{\circ}10’$...

A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as shown.If load $P=80$ kN, find the reaction $R$ (in kN) correct to...

A propped cantilever made of a prismatic steel beam is subjected to a concentrated load P at mid span as shown.If the magnitude of load $P$ is increased till collapse and...

A student began experiment for determination of $5$-day, $20^{\circ}C$ BOD on Monday. Since the $5$th day fell on Saturday, the final DO readings were taken on next Monda...

A rectangular concrete beam $250$ mm wide and $600$ mm deep is pre-stressed by means of $16$ high tensile wires, each of $7$ mm diameter, located at $200$ mm from the bot...

A uniform beam $(EI = \textit{constant})PQ$ in the form of a quarter-circle of radius $R$ is fixed at end $P$ and free at the end $Q$, where a load $W$ is applied as show...

All members in the rigid-jointed frame shown are prismatic and have the same flexural stiffness $EI$. Find the magnitude of the bending moment at $Q$ (in kNm) due to give...

Laplace equation for water flow in soils is given below. $$\dfrac{\partial ^2H}{\partial x^2} + \dfrac{\partial ^2H}{\partial y^2} + \dfrac{\partial ^2H}{\partial z^2} = ...

Find the value of $\lambda$ such that the function $f(x)$ is a valid probability density function _______$f(x) = \begin{cases} \lambda (x-1)(2-x) & \text{for } 1 \leq x \...

A uniform beam weighing $1800 \: N$ is supported at E and F by cable ABCD. Determine the tension (in $N$) in segment AB of this cable (correct to $1$- decimal place). Ass...

Find the magnitude of the error (correct to two decimal places) in the estimation of following integral using Simpson’s $\dfrac{1}{3}$ Rule. Take the step length as $1$ _...

It was observed that $150$ vehicles crossed a particular location of a highway in a duration of $30$ minutes. Assuming that vehicle arrival follows a negative exponential...

A water treatment plant is designed to treat $1 \: m^3/s$ of raw water. It has $14$ sand filters. Surface area of each filter is $50 \: m^2$. What is the loading rate (in...

A symmetric I-section (with width of each flange $=50$ mm, thickness of each flange $=10$ mm, depth of web $=100$ mm, and thickness of web $=10$ mm) of steel is subjected...

The pin-jointed $2-D$ truss is loaded with a horizontal force of $15 \: kN$ at joint S and another $15 \: kN$ vertical force at joint U, as shown. Find the force in membe...

As per $IS \: 456:2000$ for $M20$ grade concrete and plain barsin tension the design bond stress $\tau_{bd}=1.2$ MPa. Further, $IS \: 456:2000$ permits this design bond s...

There is no value of $x$ that can simultaneously satisfy both the given equations. Therefore, find the ‘least squares error’ solution to the two equations, i.e., find the...

An aerial photographer of a terrain having an average elevation of $1400$ m is taken at a scale of $1:7500$. The focal length of the camera is $15$ cm. The altitude of th...

The space mean speed (kmph) and density (vehicles/km) of a traffic stream are linearly related. The free flow speed and jam density are $80$ kmph and $100$ vehicles/km re...

A schematic flow diagram of a completely mixed biological reactor with provision for recycling of solids shown in the figure. $S_0$, $S$ = readily biodegradable soluble B...

A three-fluid system (immiscible) is connected to a vacuum pump. The specific gravity values of the fluids ($S_1, \: S_2$) are given in the figure.The gauge pressure valu...

A $6$ m long simply-supported beam is prestressed as shown in the figure.The beam carries a uniformly distributed load of $6$ kN/m over its entire span. If the effective ...