Recent questions tagged gateme-2020-set2

The sum of two normally distributed random variables $X$ and $Y$ isalways normally distributednormally distributed, only if $X$ and $Y$ are independentnormally distribute...

Let $I=\displaystyle \int_{x=0}^1 \int_{y=0}^{x^2} xy^2 dy \: dx$. Then, $I$ may also be expressed as$\displaystyle \int_{y=0}^1 \int_{x=0}^{\sqrt{y}} xy^2 dx \: dy$$\dis...

The solution of $$\dfrac{d^2y}{dt^2}-y=1,$$ which additionally satisfies $y \bigg \vert_{t=0} = \dfrac{dy}{dt} \bigg \vert_{t=0}=0$ in the Laplace $s$-domain is$\dfrac{1}...

A circular disk of radius $r$ is confined to roll without slipping at $P$ and $Q$ as shown in the figure.If the plates have velocities as shown, the magnitude of angular ...

The equation of motion of a spring-mass-damper system is given by $$\dfrac{d^2x}{dt^2}+3 \dfrac{dx}{dt} +9x = 10 \sin(5t)$$The damping factor for the system is$0.25$$0.5$...

The number of qualitatively distinct kinematic inversions possible for a Grashof chain with four revolute pairs is$1$$2$$3$$4$

The process, that uses a tapered horn to amplify and focus the mechanical energy for machining of glass, iselectrochemical machiningelectrical discharge machiningultrason...

Two plates, each of $6$ mm thickness, are to be butt-welded. Consider the following processes and select the correct sequence in increasing order of size of the heat affe...

Which one of the following statements about a phase diagram is INCORRECT?It indicates the temperature at which different phases start to meltRelative amount of different ...

The figure below shows a symbolic representation of the surface texture in a perpendicular lay orientation with indicative values (I through VI) marking the various speci...

In Materials Requirement Planning, if the inventory holding cost is very high and the set up cost is zero, which one of the following lot sizing approaches should be used...

Which of the following conditions is used to determine the stable equilibrium of all partially submerged floating bodies?Centre of buoyancy must be above the centre of gr...

In the space above the mercury column in a barometer tube, the gauge pressure of the vapour ispositive, but more than one atmospherenegativezeropositive, but less than on...

A closed vessel contains pure water, in thermal equilibrium with its vapour at $25^\circ C$(Stage$\#1$), as shown.The vessel in this stage is then kept aside an isotherma...

For an air-standard Diesel cycle,heat addition is at constant volume and heat rejection is at constant pressureheat addition is at constant pressure and heat rejection is...

The values of enthalpies at the stator inlet and rotor outlet of a hydraulic turbomachine stage are $h_1$ and $h_3$ respectively. The enthalpy at the stator outlet (or, r...

Let $\textbf{I}$ be a $100$ dimensional identity matrix and $\textbf{E}$ be the set of its distinct (no value appears more than once in $\textbf{E})$ real eigen values. T...

A beam of negligible mass is hinged at support $P$ and has a roller support $Q$ as shown in the figure.A point load of $1200 \: N$ is applied at point $R$. The magnitude ...

A machine member is subjected to fluctuating stress $\sigma = \sigma_0 \cos (8 \pi t)$. The endurance limit of the material is $350$ MPa. If the factor of safety used in ...

A bolt head has to be made at the end of a rod of diameter $d=12$ mm by localized forging (upsetting) operation. The length of the unsupported portion of the rod is $40$ ...

Consider the following network of activities, with each activity named $\textbf{A – L}$, illustrated in the nodes of the network.The number of hours required for each act...

In a furnace, the inner and outer sides of the brick wall $(k_1=2.5 \: \text{W/m.k})$ are maintained at $1100 ^\circ C$ and $700 ^\circ C$, respectively as shown in figur...

If a reversed Carnot cycle operates between the temperature limits of $27^\circ C$ and $-3^\circ C$, then the ratio of the COP of a refrigerator to that of a heat pump (C...

A cantilever of length $l$, and flexural rigidity $EI$, stiffened by a spring of stiffness $k$, is loaded by a transverse force $P$, as shown.The transverse deflection un...

The sun (S) and the Planet (P) of an epicyclic gear train shown in the figure have identical number of teeth.If the sun (S) and the outer ring (R) gears are rotated in th...

A thin-walled cylinder of radius $r$ and thickness $t$ is open at both ends, and fits snugly between two rigid walls under ambient conditions, as shown in the figure.The ...

A helical spring has spring constant $k$. If the wire diameter, spring diameter and the number of coils are all doubled then the spring constant of the new spring becomes...

Two rollers of diameters $D_1$ (in mm) and $D_2$ (in mm) are used to measure the internal taper angle in the V-groove of a machined component. The heights $H_1$ (in mm) a...