Recent questions without answers

Consider a Pelton wheel of $1 \:m$ diameter. The magnitude of relative velocity of water at the bucket inlet is same as the magnitude of relative velocity of water at the...

The state of stress at a point is shown in the figure given below. Under plane stress assumption, the normal strain along the thickness direction $(\varepsilon_{z z})$ is...

A simply supported beam of length $1 \: \text{m}$ is subjected to a uniformly distributed bending moment of $1 \: \text{N m}$ per $\text{m}$ throughout the length as show...

A pair of spur gears is required to maintain a velocity ratio of $1: 2$. The module of the gears is $10 \: mm$ and the addendum is $10 \: mm$. If the operating pressure a...

An offset slider-crank mechanism is shown in the figure below. The length of the stroke of the slider is __________ $mm$ (rounded off to nearest integer).

Two plates of thickness $10 \: mm$ each are to be joined by a transverse fillet weld on one side and the resulting structure is loaded as shown in the figure below.If the...

Two metal parts (a cylinder and a cube) of same volume are cast under identical conditions. The diameter of the cylinder is equal to its height. The ratio of the solidifi...

Cylindrical workpieces of diameter $60 \: mm$ and length $400 \:mm$ are machined on a lathe at a cutting speed of $25 \mathrm{~m} \mathrm{~min}^{-1}$ and a feed of $0.2 ...

A company uses $3000$ units of a part annually. The units are priced as given in the table below. It costs ₹ $150$ to place an order. Carrying costs are $40$ percent of t...

A project involves eight activities with the precedence relationship and duration as shown in the table below. The slack for the activity $D$ is _________ hours (answer i...

Consider the second-order linear ordinary differential equationx ^ 2 * (d ^ 2 * y)/(d * x ^ 2) + x * d/dx (y) - y = 0with the initial conditionsy(x = 1) = 6 ,The value of...

​​​In order to numerically solve the ordinary differential equation $\frac{d y}{d t}=-y$ for $t>0$, with an initial condition $y(0)=1$, the following scheme is employed\[...

​​The value of the surface integral $\oiint_S \,z \,dx \,dy$where $S$ is the external surface of the sphere $x^{2}+y^{2}+z^{2}=R^{2}$ is$0$$4 \pi R^{3}$$\frac{4 \pi}{3} R...

​​​​​Let $f(z)$ be an analytic function, where $z=x+i y$. If the real part of $f(z)$ is $\cosh x \cos y$, and the imaginary part of $f(z)$ is zero for $y=0$, then $f(z)$ ...

​​​Let $f(.)$ be a twice differentiable function from $\mathbb{R}^2 \rightarrow \mathbb{R}$. If $\boldsymbol{p}, x_0 \in \mathbb{R}^2$ where $\|p\|$ is sufficiently small...

​​​​The velocity field of a two-dimensional, incompressible flow is given by\[\vec{V}=2 \sinh x \hat{\imath}+v(x, y) \hat{\jmath}\]where $\hat{\imath}$ and $\hat{\jmath}$...

​​​​A plane, solid slab of thickness $L$, shown in the figure, has thermal conductivity $k$ that varies with the spatial coordinate $x$ as $k=A+B x$, where $A$ and $B$ ar...

​​​​​Consider incompressible laminar flow over a flat plate with freestream velocity of $u_{\infty}$. The Nusselt number corresponding to this flow velocity is $N u_{1}$....

​Consider a hydrodynamically fully developed laminar flow through a circular pipe with the flow along the axis (i.e., $z$ direction). In the following statements, $T$ is ...

​​​​A furnace can supply heat steadily at $1200 \mathrm{~K}$ at a rate of $24000 \mathrm{~kJ} / \mathrm{min}$. The maximum amount of power (in $\mathrm{kW}$ ) that can be...

​​​​Which one of the following statements regarding a Rankine cycle is FALSE?Superheating the steam in the boiler increases the cycle efficiency.The pressure at the turbi...

​​​For a ball bearing, the fatigue life in millions of revolutions is given by $L=\left(\frac{C}{P}\right)^{n}$, where $\text{P}$ is the constant applied load and $\text{...

​​​​The change in kinetic energy $\Delta E$ of an engine is $300 \mathrm{~J}$, and minimum and maximum shaft speeds are $\omega_{\min }=220 \mathrm{rad} / \mathrm{s}$ and...

​​​​A ram in the form of a rectangular body of size $l=9 \mathrm{~m}$ and $b=2 \mathrm{~m}$ is suspended by two parallel ropes of lengths $7 \mathrm{~m}$. Assume the cent...

​​​​A linear spring-mass-dashpot system with a mass of $2 \mathrm{~kg}$ is set in motion with viscous damping. If the natural frequency is $15 \mathrm{~Hz}$, and the ampl...

​​​​Which one of the following failure theories is the most conservative design approach against fatigue failure?Soderberg lineModified Goodman lineGerber lineYield line

​​​​A rigid massless tetrahedron is placed such that vertex $\mathrm{O}$ is at the origin and the other three vertices $\text{A, B}$, and $\text{C}$ lie on the coordinate...

​​​​​The phases present in pearlite areaustenite and ferritecementite and austeniteferrite and cementitemartensite and ferrite