Recent questions tagged gateme-2022-set2

For a dynamical system governed by the equation.$$\ddot{x}\left ( t \right ) + 2\zeta \omega _{n}\dot{x}\left ( t \right )+\omega _{n}^{2}x\left ( t \right ) = 0$$the dam...

An electric car manufacturer underestimated the January sales of car by $20$ units, while the actual sales was $120$ units. If the manufacturer uses exponential smoothing...

The demand of a certain part is $1000$ parts/year and its cost is ₹$1000$/part. The orders are placed based on the economic order quantity $\text{(EOQ)}$. The cost of ord...

Consider $1$ $\text{kg}$ of an ideal gas at $1$ bar and $300$ $K$ contained in a rigid and perfectly insulated container. The specific heat of the gas at constant volume ...

Wien's law is stated as follows: $\lambda _{m}T = C$, where $C$ is $2898$ $\mu m \cdot K$ and $\lambda_{m}$ is the wavelength at which the emissive power of a black body ...

For the exact differential equation,$$\frac{du}{dx}= \frac{-xu^{2}}{2+x^{2}u},$$which one of the following is the solution?$u^{2} + 2x^{2} =$ constant$xu^{2} + u =$ const...

A rigid homogeneous uniform block of mass $1$ $\text{kg}$, height $h = 0.4 \:m$ and width $b = 0.3\: m$ is pinned at one corner and placed upright in a uniform gravitatio...

A rigid body in the $\text{X-Y}$ plane consists of two point masses ($1$ $\text{kg}$ each) attached to the ends of two massless rods, each of $1$ $\text{cm}$ length, as s...

A spring mass damper system (mass $m$, stiffness $k$, and damping coefficient $c$) excited by a force $F(t) = B \sin w t$, where $B$, $w$ and $t$ are the amplitude, frequ...

Parts $P1 – P7$ are machined first on a milling machine and then polished at a separate machine. Using the information in the following table, the minimum total completio...

A manufacturing unit produces two products $P1$ and $P2$. For each piece of $P1$ and $P2$, the table below provides quantities of materials $\text{M1, M2}$ and $M3$ requi...

A tube of uniform diameter $D$ is immersed in a steady flowing inviscid liquid stream of velocity $V$, as shown in the figure. Gravitational acceleration is represented b...

The steady velocity field in an inviscid fluid of density $1.5$ is given to be $\vec{V} = \left ( y^{2}-x^{2} \right )\hat{i} + \left ( 2xy \right )\hat{j}.$ Neglecting b...

In a vapour compression refrigeration cycle, the refrigerant enters the compressor in saturated vapour state at evaporator pressure, with specific enthalpy equal to $250$...

$A$ is a $3 \times 5$ real matrix of rank $2$. For the set ot homogeneous equations $Ax = 0$, where $0$ is a zero vector and $x$ is a vector of unknown variables, which o...

The lengths of members $\text{BC}$ and $\text{CE}$ in the frame shown in the figure are equal. All the members are rigid and lightweight, and the friction at the joints i...

Given $z = x + iy, i = \sqrt{-1}$. $C$ is a circle of radius $2$ with the centre at the origin. If the contour $C$ is traversed anticlockwise, then the value of the integ...

A shaft of length $L$ is made of two materials, one in the inner core and the other in the outer rim, and the two are perfectly joined together (no slip at the interface)...

A rigid beam $\text{AD}$ of length $3a = 6\:m$ is hinged at frictionless pin joint $A$ and supported by two strings as shown in the figure. String $\text{BC}$ passes over...

In the configuration of the planar four-bar mechanism at a certain instant as shown in the figure, the angular velocity of the $2$ $\text{cm}$ long link is $w_{2} = 5$ $...

A shaft $\text{AC}$ rotating at a constant speed carries a thin pulley of radius $r= 0.4\:m$ at the end $C$ which drives a belt. A motor is coupled at the end $A$ of the ...

A straight-teeth horizontal slab milling cutter is shown in the figure. It has $4$ teeth and diameter $(D)$ of $200$ $\text{mm}$. The rotational speed of the cutter is $1...

ln an orthogonal machining operation, the cutting and thrust forces are equal in magnitude. The uncut chip thickness is $0.5$ $\text{mm}$ and the shear angle is $15^{\cir...

The best size wire is fitted in a groove of a metric screw such that the wire touches the flanks of the thread on the pitch line as shown in the figure. The pitch $(p)$ a...

In a direct current arc welding process, the power source has an open circuit voltage of $100\: V$ and short circuit current of $1000 \:A$. Assume a linear relationship b...

A cylindrical billet of $100$ $\text{mm}$ diameter and $100$ $\text{mm}$ length is extruded by a direct extrusion process to produce a bar of $L$-section. The cross secti...

A project consists of five activities $\text{(A, B, C, D and E)}$. The duration of each activity follows beta distribution. The three time estimates (in weeks) of each ac...

A rigid tank of volume of $8 \:m^{3}$ is being filled up with air from a pipeline connected through a valve. Initially the valve is closed and the tank is assumed to be c...