Recent questions without answers

Consider the following statements about four numbers:(S$1$) The average of the four numbers is $25$(S$2$) Each number is at most $40$(S$3$) Each number is at least $20$Ch...

Domain $A$ is bounded by curve $x^{2}=4 y$, ordinate $x=2$, and $x$ axis.The value of $\iint_{A} y d x d y$ is$1 / 5$$1 / 3$$5 / 12$$1 / 2$

Let $\varphi$ be a scalar function. Then, $\nabla \varphi$ isalways perpendicular to the surface of constant $\varphi$always parallel to the surface of constant $\varphi$...

The order and degree of the following differential equation are $m$ and $n$, respectively.\[\frac{\partial^{3} \varphi}{\partial x^{3}}+\frac{\partial^{2} \varphi}{\parti...

Newton-Raphson method for solving algebraic equations is based onTaylor seriesFourier seriesLaurent seriesPower series

The exact solution of $\int_{0}^{4} \frac{d x}{1+x}$ is represented as $n$.If $m$ represents numerically evaluated value of the above integral using Trapezoidal rule by c...

A horizontal disk has a radial frictionless slot in which a small block is confined to slide. The disk turns anticlockwise about its centre with a constant angular veloci...

A gear train with five gears is shown in the figure below. The number of teeth on each gear is $\mathrm{N}_{1}, \mathrm{~N}_{2}, \mathrm{~N}_{3}, \mathrm{~N}_{4}$, and $\...

In a single degree of freedom vibrating system with only viscous damping, the critical damping coefficient is $350 \mathrm{~N} \mathrm{~s} / \mathrm{m}$ and the damping c...

A closely coiled helical compression spring of mean coil diameter $D$ and wire diameter $d$, is loaded by an axial force $F$.The maximum shear stress developed in the wir...

The rotor of an aeroplane engine has a mass moment of inertia $1.0 \mathrm{~kg} \mathrm{~m}^{2}$. The engine rotates at a speed of $500$ RPM in the clockwise direction if...

A rectangular plate is perfectly welded to a gusset plate with parallel fillet weld joints as shown in the figure below. The length of the weld is $l$ and the fillet weld...

Worm gearsets are used for transmitting rotary motion betweennon-parallel and non-intersecting shaftsintersecting shaftsparallel shaftsnon-parallel and intersecting shaft...

For an ideal gas, starting from state point $1$, two different processes take place. The corresponding final states in these two processes are $2$ and $3$, lying on same ...

A steady incompressible laminar flow passes through a $90^{\circ}$ tube bend placed on a horizontal surface. In horizontal diametric plane, two pressure taps $P_{i}$ and ...

An ideal gas passes isothermally through a long horizontal uniform cross-section pipe under steady flow. Consider that the pressure gradient in the pipe is sufficient for...

Bernoulli's equation CANNOT be applied betweenany two arbitrary points in the flow field for steady incompressible rotational flowany two arbitrary points in the flow fie...

A quiescent fluid at temperature $\mathrm{T}_{3}$ is confined between two vertical parallel plates. While plate $1$ is kept at temperature $\mathrm{T}_{1}$ and plate $2$ ...

For the isothermal expansion of an ideal gas in a piston cylinder system, the net heat supplied during the process is equal to the net work. Which one of the following st...

A hydraulic crane supports a mass of $500$ kg with its piston-cylinder actuator, inclined at $60^{\circ}$ with horizontal, as shown in the figure below. The diameter of t...

In relation to metal casting defects, match the followingDefectDescription$\mathrm{P}$Dross$\mathrm{I}$Shallow blow found on a flat casting surface$\mathrm{Q}$Scab$\mathr...

Which one of the following options is NOT an error associated with STereoLithography (STL) file in additive manufacturing?Staircase effectMissing facetNon-manifold topolo...

A work piece is to be firmly held in a fixture. It is to be machined by using a plain slab milling cutter as shown in the figure below.Which one of the following options ...

A two-dimensional surface profile is obtained over a sampling length by using a contact type stylus profilometer as shown in the figure below. A line AA parallel to the g...

A steel plate having yield strength of $550$ MPa , is subjected to biaxial state of stress as $\sigma_{x}=\sigma$ and $\sigma_{y}=-2 \sigma$. Using distortion energy theo...

A sphere of radius $5$ mm is initially in equilibrium at $400^{\circ} \mathrm{C}$ in a furnace. It is suddenly removed from the furnace and dipped in a well-stirred water...

If $w=\log _{e} z=\log _{e}(x+i y)$, where $i=\sqrt{-1}$, then which one of the following statements is correct?$w$ is analytic everywhere except at $z=0$$w$ is non-analy...

Consider the following differential equation\[\frac{\partial y}{\partial x}=3 \frac{\partial y}{\partial t}+y\]If $y(x, 0)=10 e^{-2 x}$, then the solution of the differen...

Let $f(t)$ be a function of $t$ defined for all positive values of $t$. The Laplace transform of $f(t)$ denoted by $L\{f(t)\}=\int_{0}^{\infty} e^{-s t} f(t) d t$, provid...

A cantilever beam of length $L$ is subjected to a concentrated load $P$ and a moment $M$ as shown in the figure below. Neglecting the mass of the beam, which one of the f...