Recent questions tagged numerical-answers

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GATE2020-ME-2-16
Consider the initial value problem below. The value of $y$ at $x= \ln 2$, (rounded off to $3$ decimal places) is _______. $\frac{dy}{dx}= 2x-y,\:\:\:\:y(0)= 1$

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-17
A three-phase $,50\: Hz,\: 4$-pole induction motor runs at no-load with a slip of $1\%.$ With full load, the slip increases to $5\%,$ The $\%$ speed regulation of the motor (rounded off to $2$ decimal places) is______.

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-18
Currents through ammeters $A2$ and $A3$ in the figure are $1\angle 10^{\circ}$ and $1\angle 70^{\circ}$, respectively. The reading of the ammeter $A1$ (rounded off to $3$ decimal places) is ________ $A.$

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-19
The Thevenin equivalent voltage, $V_{TH}$, in $V$ (rounded off to $2$ decimal places) of the network shown below, is_______.

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-20
A double pulse measurement for an inductively loaded circuit controlled by the IGBT switch is carried out to evaluate the reverse recovery characteristics of the diode$, D,$ ... your choice by entering $1,2,3$ or $4$) at which the IGBT experiences the highest current stress is _______.

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-21
A single-phase, $4\:kVA, 200\: V/100\: V, 50\:Hz$ transformer with laminated CRGO steel core has rated no-load loss of $450\: W.$ When the high-voltage winding is excited with $160\: V,40\: Hz$ ... from a $100\: V, 25\: Hz$ sinusoidal ac source, the no-load losses will be _______ $W$ (rounded off to $2$ decimal places).

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-22
A single-phase inverter is fed from a $100\: V$ dc source and is controlled using a quasi-square wave modulation scheme to produce an output waveform, $v(t)$, as shown. The angle $\sigma$ is adjusted to entirely eliminate the $3^{rd}$ harmonic ... $5^{th}$ harmonic component as a percentage of the magnitude of the fundamental component is _____ (rounded off to $2$ decimal places).

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-23
A single $50\: Hz$ synchronous generator on droop control was delivering $100\; MW$ power to a system. Due to increase in load, generator power had to be increased by $10\: MW,$ as a result of which, system frequency dropped to $49.75\: Hz.$ Further ... $49.25\: Hz.$ At this condition, the power in $MW$ supplied by the generator is_______ (rounded off to $2$ decimal places).

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-24
Consider a negative unity feedback system with forward path transfer function $G(s)= \dfrac{K}{(s+a)(s-b)(s+c)}$, where $K,a,b,c$ are positive real numbers. For a Nyquist path enclosing the entire imaginary axis and right half of the $s$-plane in the clockwise ... . Then, the number of poles of $\dfrac{G(s)}{1+G(s)}$ lying in the open right half of the $s$-plane is_______.

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-25
The cross-section of a metal-oxide-semiconductor structure is shown schematically. Starting from an uncharged condition, a bias of $+3$ V is applied to the gate contact with respect to the body contact. The charge inside the silicon dioxide layer is ... application of bias, expressed as a multiple of $Q$ (absolute value in Coulombs, rounded off to the nearest integer)is_______.

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-45
A resistor and a capacitor are connected in series to a $10\: V$ dc supply through a switch. The switch is closed at $t= 0$, and the capacitor voltage is found to cross $0\: V$ at $t= 0.4\tau$, where $\tau$ is the circuit time constant. ... required in the initial capacitor voltage if the zero crossing has to happen at $t=0.2\tau$ is ________ (rounded off to $2$ decimal places).

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-46
A cylindrical rotor synchronous generator with constant real power output and constant voltage is supplying $100\: A$ current to a $0.9$ lagging power factor load. An ideal reactor is now connected in parallel with the load, as a result of which the ... previous value while the real power remains unchanged. The armature current is now_______ $A$ (rounded off to $2$ decimal places).

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-47
Bus $1$ with voltage magnitude $V_{1}= 1.1$ pu is sending reactive power $Q_{12}$ towards bus $2$ with voltage magnitude $V_{2}= 1$ pu through a lossless transmission line of reactance $X$. Keeping the voltage at bus $2$ fixed at $1$ pu, magnitude of voltage ... zero. The new value of the voltage magnitude, $V_{1}$, in pu (rounded off to $2$ decimal places), at bus $1$ is _______.

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-48
Windings $' A','B'\: \text{and}\: C'$ have $20$ turns each and are wound on the same iron core as shown, along with winding $'X'$ which has $2$ turns. The figure shows the sense (clockwise/anticlockwise) of each of the windings only and does not reflect the ... no-load $RMS$ voltage $\text{(in V, rounded off to }\:$2$\: \text{decimal places)}$ across winding $'X'$ is ________.

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-49
A cylindrical rotor synchronous generator has steady state synchronous reactance of $0.7$ pu and subtransient reactance of $0.2$ pu. It is operating at $(1+j0)$ pu terminal voltage with an internal emf of $(1+j0.7)$ pu. Following a three-phase ... at the terminal of the generator, the magnitude of the subtransient internal emf (rounded off to $2$ decimal places) is ______ pu.

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-50
In the dc-dc converter circuit shown, switch $Q$ is switched at a frequency of $10\: kHz$ with a duty ratio of $0.6$. All components of the circuit are ideal, and the initial current in the indicator is zero. Energy stored in the inductor in $mJ$ (rounded off to $2$ decimal places) at the end of $10$ complete switching cycles is________.

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-51
A single-phase, full-bridge, fully controlled thyristor rectifier feeds a load comprising a $10\:\Omega$ resistance in series with a very large inductance. The rectifier is fed from an ideal $230\: V, 50\: Hz$ sinusoidal source through cables which have negligible ... $\alpha = 45^{\circ}$, the communication overlap angle in degree (rounded off to $2$ decimal places) is ________,

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-52
A non-ideal Si-based $pn$ junction diode is tested by sweeping the bias applied across its terminal from $-5\: V$ to $+5\: V.$ The effective thermal voltage, $V_{T}$, for the diode is measured to be $(29\pm 2)\: mV.$ The resolution of the ... $2$ decimal places) in the measured current at a bias voltage of $0.02\: V$ is ________.

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-53
The temperature of the coolant oil bath for a transformer is monitored using the circuit shown. It contains a thermistor with a temperature-dependent resistance $R_{\text{thermistor}}= 2(1+\alpha T) k\Omega$, where $T$ is the temperature in $^{\circ}C$. The temperature ... . The error in the output signal (in $V,$ rounded off to $2$ decimal places) at $150^{\circ}C$ is _______.

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-54
An $8085$ microprocessor accesses two memory locations $(2001H)$ and $(2002H),$ that contain $8$-bit numbers $98H$ and $B1H,$ respectively. The following program is executed: $LXI\: H,2001H$ $MVI\: A, 21H$ $INX\: H$ $ADD\: M$ $INX\: H$ $MOV\: M, A$ $HLT$ At the end of this program, the memory location $2003H$ contains the number in decimal $(\text{base}\: 10)$ form______.

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-2-55
A conducting square loop of side length $1\:m$ is placed at a distance of $1\:m$ from a long straight wire carrying a current $I= 2\; A$ as shown below. The mutual inductance, in $nH$(rounded off to $2$ decimal places), between the conducting loop and the wire is ______.

asked Mar 1 in Others by jothee (2.7k points)

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GATE2020-ME-1: 19
For three vectors $\overrightarrow{A}=2\widehat{j}-3\widehat{k},\:\overrightarrow{B}=-2\widehat{i}+\widehat{k}\:\:\text{and}\:\overrightarrow{C}=3\widehat{i}-\widehat{j},\:\text{where}\:\widehat{i},\:\widehat{j}\:\text{and}\:\widehat{k}$ are ... system, the value of $\left ( \overrightarrow{A}.\left ( \overrightarrow{B}\times \overrightarrow{C} \right )+6 \right )$ is __________.

asked Feb 19 in Others by jothee (2.7k points)

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GATE2020-ME-1: 20
A flywheel is attached to an engine to keep its rotational speed between $100\: rad/s$ and $110\: rad/s $. If the energy fluctuation in the flywheel between these two speeds is $1.05\: kJ$ then the moment of inertia of the flywheel is____________$kg \cdot m^{2}$ (rounded off to $2$ decimal places).

asked Feb 19 in Others by jothee (2.7k points)

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GATE2020-ME-1: 21
A balanced rigid disc mounted on a rigid rotor has four identical point masses, each of $10\:\text{grams}$, attached to four points on the $100\: mm$ radius circle shown in the figure. The rotor is driven bt a motor at uniform angular speed of ... gets detached then the magnitude of the resultant unbalance force on the rotor is ________$N$ (rounded off to $2$ decimal places).

asked Feb 19 in Others by jothee (2.7k points)

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GATE2020-ME-1: 22
A sheet metal with a stock hardness of $250\: HRC$ has to be sheared using a punch and a die having a clearance of $\text{1 mm}$ between them. If the stock hardness of the sheet metal increases to $400\: HRC$, the clearance between the punch and the die should be _________ $mm.$

asked Feb 19 in Others by jothee (2.7k points)

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GATE2020-ME-1: 23
A company is hiring to fill four managerial vacancies. The candidates are five men and three women. If every candidate is equally likely to be chosen then the probability that at least one woman will be selected is _______(round off to $2$ decimal places).

asked Feb 19 in Others by jothee (2.7k points)

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GATE2020-ME-1: 24
The compressor of a gas turbine plant, operating on an ideal intercooled Brayton cycle, accomplishes an overall compression ratio of $6$ in a two-stage compression process. Intercooling is used to cool the air coming out from the first stage to the ... gas are constant, the intercooling pressure for minimum compressor work is __________ $kPa$ (rounded off to $2$ decimal places).

asked Feb 19 in Others by jothee (2.7k points)

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GATE2020-ME-1: 25
In a concentric tube counter-flow heat exchanger, hot oil enters at $102^{\circ}C$ and leaves at $65^{\circ}C$. Cold water enters at $25^{\circ}C$ and leaves at $42^{\circ}C$. The log mean temperature difference $(LMTD)$ is ________ $^{\circ}C$ (round off to one decimal place).

asked Feb 19 in Others by jothee (2.7k points)

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GATE2020-ME-1: 35
Consider two exponentially distributed random variables $\text{X and Y}$, both having a mean of $0.50$. Let $Z=X+Y$ and $r$ be the correlation between $\text{X and Y}$.If the variance of $Z$ equals $0$, then the value of $r$ is __________ (roundoff to $2$ decimal places).

asked Feb 19 in Others by jothee (2.7k points)

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GATE2020-ME-1: 36
An analytic function of a complex variable $z=x + iy \left ( i=\sqrt{-1} \right )$ is defined as $f\left ( z \right )=x^{2}-y^{2}+i\psi \left ( x,y \right ),$ where $\psi \left ( x,y \right )$ is a real function. The value of the imaginary part of $f(z)$ at $z=\left ( 1+i \right )$ is __________ (round off to $2$ decimal places).

asked Feb 19 in Others by jothee (2.7k points)

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GATE2020-ME-1: 37
In a disc-type axial clutch, the frictional contact takes place within an annular region with outer and inner diameters $250\:mm$ and $50\:mm$, respectively. An axial force $F_{1}$ is needed to transmit a torque by a new clutch. However, to transmit the same ... coefficient of friction does not change, then the ratio $F_{1}/F_{2}$ is _________ (round off to $2$ decimal places).

asked Feb 19 in Others by jothee (2.7k points)

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GATE2020-ME-1: 38
A cam with a translating flat-face follower is desired to have the follower motion $y\left ( \theta \right )=4\left [ 2\pi \theta -\theta ^{2} \right ],\:\:\:0\leq \theta \leq 2\pi .$ Contact stress considerations dictate that the radius ... should not be less than $40\:mm$ anywhere. The minimum permissible base circle radius is _________$mm$ (round off to one decimal place).

asked Feb 19 in Others by jothee (2.7k points)

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GATE2020-ME-1: 39
A rectangular steel bar of length $500\: mm$, width $100\: mm$, and thickness $15\: mm$ is cantilevered to a $200\: mm$ steel channel using $4$ bolts, as shown For an external load of $10\: kN$ applied at the tip of the steel bar, the resultant shear load on the bolt at $B$, is _______$kN$ (round off to one decimal place).

asked Feb 19 in Others by jothee (2.7k points)

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GATE2020-ME-1: 40
The barrier shown between two water tanks of unit width $(1\: m)$ into the plane of the screen in modeled as a cantilever. Taking the density of water as $1000\:kg/m^{3}$ , and the acceleration due to gravity as $10\:m/s^{2}$ , the maximum absolute bending moment developed in the cantilever is _________$kN\cdot m$ (round off to the nearest integer).

asked Feb 19 in Others by jothee (2.7k points)

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GATE2020-ME-1: 41
The magnitude of reaction force at joint $C$ of the hinge-beam shown in the figure is __________$kN$ (round off to $2$ decimal places).

asked Feb 19 in Others by jothee (2.7k points)

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GATE2020-ME-1: 42
A slot of $25\:mm\times 25\:mm$ is to be milled in a workpiece of $300\: mm$ length using a side and face milling cutter of diameter $100\: mm$, width $25\: mm$ and having $20$ teeth.For a depth of cut $5\: mm$ ... and approach and over travel distance of $5\: mm$ each, the time required for milling the slot is ________ minutes (round off to one decimal place).

asked Feb 19 in Others by jothee (2.7k points)

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GATE2020-ME-1: 44
A steel part with surface area of $125\:cm^{2}$ is to be chrome coated through an electroplating process using chromium acid sulphate as an electrolyte. An increasing current is applied to the part according to the following current time relation: $I=12+0.2t$ ... $\mu m$ (round off to one decimal place).

asked Feb 19 in Others by jothee (2.7k points)

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GATE2020-ME-1: 46
The thickness of a steel plate with material strength coefficient of $210\: MPa$, has to be reduced from $20\: mm$ to $15\: mm$ in a single pass in a two-high rolling mill with a roll radius of $450\: mm$ and rolling velocity of $28\: m/min$. If the ... ). Note: $\text{Average Flow Stress = Material Strength Coefficient}\times \dfrac{\left (\text{True Strain} \right )^{n}}{(1+n)}$

asked Feb 19 in Others by jothee (2.7k points)

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GATE2020-ME-1: 47
Two business owners Shveta and Ashok run their business in two different states. Each of them, independent of the other, produces two products $A$ and $B$, sells them at $Rs.\:2,000$ per kg and $Rs.\:3,000$ per kg, respectively, and uses ... value of the difference in daily (optimal) revenue of Shveta and Ashok is _________ thousand Rupees (round off to $2$ decimal places).

asked Feb 19 in Others by jothee (2.7k points)

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GATE2020-ME-1: 49
Consider steady, viscous, fully developed flow of a fluid through a circular pipe of internal diameter $\text{D}$. We know that the velocity profile forms a paraboloid about the pipe centre line, given by: $V=-C\left(r^{2}-\dfrac{D^{2}}{4}\right) m/s$ ... the control surface $\text{A-B}$, as shown in the figure, is proportional to $D^{n}$. The value of $n$ is ________.

asked Feb 19 in Others by jothee (2.7k points)

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