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GATE2016-3-31
A circular disc of radius $100 \: mm$ and mass $1 \: kg$, initially at rest at position $A$, rolls without slipping down a curved path as shown in figure. The speed $v$ of the disc when it reaches position $B$ is _________ $m/s$. Acceleration due to gravity $g = 10 \: m/s^2$.

A circular disc of radius $100 \: mm$ and mass $1 \: kg$, initially at rest at position $A$, rolls without slipping down a curved path as shown in figure. The speed $v$ o...

Arjun

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Arjun asked Feb 24, 2017

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GATE2016-1-30
A block of mass $m$ rests on an inclined plane and is attached by a string to the wall as shown in the figure. The coefficient of static friction between the plane and the block is $0.25$. The string can withstand a maximum force of $20$ $N$. The maximum value ... equilibrium is ____________ $kg$. Take $cos\theta$ and $sin \theta$ Acceleration due to gravity $g$ = $10$ $m$/$s^2$

A block of mass $m$ rests on an inclined plane and is attached by a string to the wall as shown in the figure. The coefficient of static friction between the plane and th...

Arjun

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Arjun asked Feb 24, 2017

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GATE2015-1-44
A cantilever beam with flexural rigidity of $200$ $N.m^2$ is loaded as shown in the figure. The deflection (in $mm$) at the tip of the beam is _______

A cantilever beam with flexural rigidity of $200$ $N.m^2$ is loaded as shown in the figure. The deflection (in $mm$) at the tip of the beam is _______

Arjun

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Arjun asked Feb 24, 2017

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GATE Mechanical 2014 Set 3 | Question: 37
A four-wheel vehicle of mass $1000 \: kg$ moves uniformly in a straight line with the wheels revolving at $10 \: rad/s$. The wheels are identical, each with a radius of $0.2 \: m$. Then a constant braking torque is applied to all the ... a uniform deceleration. For the vehicle to stop in $10 \: s$, the braking torque (in $N.m$) on each wheel is______

A four-wheel vehicle of mass $1000 \: kg$ moves uniformly in a straight line with the wheels revolving at $10 \: rad/s$. The wheels are identical, each with a radius of $...

Arjun

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Arjun asked Feb 19, 2017

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GATE Mechanical 2024 | Question: 27
In the pipe network shown in the figure, all pipes have the same cross-section and can be assumed to have the same friction factor. The pipes connecting points $W, N$, and $S$ with point $J$ have an equal length $L$. The pipe connecting points $J$ ... $\text{I}$ and $\text{II}$ are True Both $\text{I}$ and $\text{II}$ are False

In the pipe network shown in the figure, all pipes have the same cross-section and can be assumed to have the same friction factor. The pipes connecting po...

admin

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admin asked Feb 16

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GATE Mechanical 2021 Set 2 | Question: 30
Ambient pressure, temperature, and relative humidity at a location are $\text{101 kPa}$, $\text{300 K}$, and $60\%$, respectively. The saturation pressure of the water at $\text{300 K}$ is $\text{3.6 kPa}$. The specific humidity of ambient air is ____________________ $\text{g/kg}$ of dry air. $21.4$ $35.1$ $21.9$ $13.6$

Ambient pressure, temperature, and relative humidity at a location are $\text{101 kPa}$, $\text{300 K}$, and $60\%$, respectively. The saturation pressure of the water at...

go_editor

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go_editor asked Mar 1, 2021

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GATE Mechanical 2021 Set 2 | Question: 35
Find the positive real root of $x^3-x-3=0$ using Newton-Raphson method. lf the starting guess $(x_{0})$ is $2,$ the numerical value of the root after two iterations $(x_{2})$ is ______ ($\textit{round off to two decimal places}$).

Find the positive real root of $x^3-x-3=0$ using Newton-Raphson method. lf the starting guess $(x_{0})$ is $2,$ the numerical value of the root after two iterations $(x_{...

go_editor

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go_editor asked Mar 1, 2021

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GATE Mechanical 2021 Set 1 | Question: 21
A pressure measurement device fitted on the surface of a submarine, located at a depth $\text{H}$ below the surface of an ocean, reads an absolute pressure of $\text{4.2 MPa}$. The density of sea water is $\text{1050 kg/m$^{3}$ ... $}$ The depth $\text{H}$ is _____________ $\text{m}$ ($\textit{round off to the nearest integer}$).

A pressure measurement device fitted on the surface of a submarine, located at a depth $\text{H}$ below the surface of an ocean, reads an absolute pressure of $\text{4.2 ...

gatecse

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gatecse asked Feb 22, 2021

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GATE2020-ME-2: 45
Bars of $250$ mm length and $25$ mm diameter are to be turned on a lathe with a feed of $0.2$ mm/rev. Each regrinding of the tool costs Rs. $20$. The time required for each tool change is $1$ ... tool life $T$ is in min). The optimum tool cost per piece for maximum production rate is Rs. _______ (round off to $2$ decimal places).

Bars of $250$ mm length and $25$ mm diameter are to be turned on a lathe with a feed of $0.2$ mm/rev. Each regrinding of the tool costs Rs. $20$. The time required for ea...

go_editor

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go_editor asked Sep 18, 2020

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GATE2020-ME-1: 7
The stress state at a point in a material under plane stress condition is equi-biaxial tension with a magnitude of $10\: MPa$. If one unit on the $\sigma -\tau$ plane is $1\: MPa$, the Mohr's circle representation of the state-of-stress is given by a circle with a ... of $10$ units on the $\sigma -\tau$ plane a point on the $\tau$ axis at a distance of $10$ units from the origin

The stress state at a point in a material under plane stress condition is equi-biaxial tension with a magnitude of $10\: MPa$. If one unit on the $\sigma -\tau$ plane is ...

go_editor

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go_editor asked Feb 19, 2020

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GATE2018-1-4
$F(z)$ is a function of the complex variable $z=x+iy$ given by $F(z)+ i \: z + k \: Re(z) + i \: Im(z)$. For what value of $k$ will $F(z)$ satisfy the Cauchy-Riemann equations? $0$ $1$ $-1$ $y$

$F(z)$ is a function of the complex variable $z=x+iy$ given by $F(z)+ i \: z + k \: Re(z) + i \: Im(z)$. For what value of $k$ will $F(z)$ satisfy the Cauchy-Riemann equa...

Arjun

28.5k points

Arjun asked Feb 17, 2018

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GATE2017 ME-1: 3
Consider the following partial differential equation for $u(x, y)$, with the constant $c > 1$: $\dfrac{\partial u}{\partial y}+c\dfrac{\partial u}{\partial x}=0$ Solution of this equation is $u(x, y) = f (x+cy)$ $u(x, y) = f (x-cy)$ $u(x, y) = f (cx+y)$ $u(x, y) = f (cx-y)$

Consider the following partial differential equation for $u(x, y)$, with the constant $c 1$:$\dfrac{\partial u}{\partial y}+c\dfrac{\partial u}{\partial x}=0$Solution of...

Arjun

28.5k points

Arjun asked Feb 26, 2017

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GATE Mechanical 2016 Set 1 | GA Question: 7
In a world filled with uncertainty, he was glad to have many good friends. He had always assisted them in times of need and was confident that they would reciprocate. However, the events of the last week proved him wrong. Which of the following inference(s) is/are logically ... him last week. $(i)$ and $(ii)$ $(iii)$ and $(iv)$ $(iii)$ only $(iv)$ only

In a world filled with uncertainty, he was glad to have many good friends. He had always assisted them in times of need and was confident that they would reciprocate. How...

Arjun

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Arjun asked Feb 24, 2017

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GATE2015-3-30
For ball bearings, the fatigue life $L$ measured in number of revolutions and the radial load $F$ are related by $FL^{1/3} = K$, where $K$ is a constant. It withstands a radial load of $2$ $kN$ for a life of $540$ million revolutions. The load (in $kN$) for a life of one million revolutions is ________

For ball bearings, the fatigue life $L$ measured in number of revolutions and the radial load $F$ are related by $FL^{1/3} = K$, where $K$ is a constant. It withstands a ...

Arjun

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Arjun asked Feb 24, 2017

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GATE Mechanical 2014 Set 4 | GA Question: 10
A five digit number is formed using the digits $1,3,5,7$ and $9$ without repeating any of them. What is the sum of all such possible five digit numbers? $6666660$ $6666600$ $6666666$ $6666606$

A five digit number is formed using the digits $1,3,5,7$ and $9$ without repeating any of them. What is the sum of all such possible five digit numbers?$6666660$$6666600$...

Arjun

28.5k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 4 | Question: 26
If $z$ is a complex variable, the value of $\displaystyle{} \int_{5}^{3i}\dfrac{dz}{z}$ is $− 0.511−1.57i$ $− 0.511+1.57i$ $0.511− 1.57i$ $0.511+1.57i$

If $z$ is a complex variable, the value of $\displaystyle{} \int_{5}^{3i}\dfrac{dz}{z}$ is$− 0.511−1.57i$$− 0.511+1.57i$$0.511− 1.57i$$0.511+1.57i$

Arjun

28.5k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 4 | Question: 13
A reversed Carnot cycle refrigerator maintains a temperature of −$5^{\circ}$ $C$. The ambient air temperature is $35^{\circ}$ $C$. The heat gained by the refrigerator at a continuous rate is $2.5$ kJ/s. The power (in watt) required to pump this heat out continuously is _______

A reversed Carnot cycle refrigerator maintains a temperature of −$5^{\circ}$ $C$. The ambient air temperature is $35^{\circ}$ $C$. The heat gained by the refrigerator a...

Arjun

28.5k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 4 | Question: 5
Laplace transform of $\cos(\omega t)$ is $\dfrac{s}{s^2+\omega ^2}$. The Laplace transform of $e^{-2t} \cos(4t)$ is $\dfrac{s-2}{(s-2)^2+16} \\$ $\dfrac{s+2}{(s-2)^2+16} \\$ $\dfrac{s-2}{(s+2)^2+16} \\$ $\dfrac{s+2}{(s+2)^2+16}$

Laplace transform of $\cos(\omega t)$ is $\dfrac{s}{s^2+\omega ^2}$. The Laplace transform of $e^{-2t} \cos(4t)$ is$\dfrac{s-2}{(s-2)^2+16} \\$$\dfrac{s+2}{(s-2)^2+16} \\...

Arjun

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Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 3 | Question: 5
The definite integral $\int_{1}^{3}\dfrac{1}{x}$ is evaluated using Trapezoidal rule with a step size of $1$. The correct answer is _______

The definite integral $\int_{1}^{3}\dfrac{1}{x}$ is evaluated using Trapezoidal rule with a step size of $1$. The correctanswer is _______

Arjun

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Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 2 | GA Question: 10
It takes $30$ minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. What is the rate at which water has to be pumped in so that it gets ... $4$ times the draining rate $3$ times the draining rate $2.5$ times the draining rate $2$ times the draining rate

It takes $30$ minutes to empty a half-full tank by draining it at a constant rate. It is decided to simultaneously pump water into the half-full tank while draining it. W...

Arjun

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Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 2 | Question: 52
For the CNC part programming, match Group A with Group B: ... $P-I, Q-III, R-II, S-IV$ $P-I, Q-IV, R-II, S-III$ $P-II, Q-I, R-III, S-IV$

For the CNC part programming, match Group A with Group B:$\begin{array}{|l|l|l|l|} \hline & \textbf{Group A} && \textbf{Group B} \\ \hline P: & \text{circular interpolati...

Arjun

28.5k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 2 | Question: 6
A steel cube, with all faces free to deform, has Young's modulus, $E$, Poisson's ratio, $ν$, and coefficient of thermal expansion, $\alpha$. The pressure (hydrostatic stress) developed within the cube, when it is subjected to a uniform increase in temperature, $\Delta T$, ... $-\dfrac{\alpha (\Delta T)E}{1-2V} \\$ $\dfrac{\alpha (\Delta T)E}{3(1-2V)}$

A steel cube, with all faces free to deform, has Young’s modulus, $E$, Poisson’s ratio, $ν$, and coefficient of thermal expansion, $\alpha$. The pressure (hydrostati...

Arjun

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Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 1 | Question: 23
The main cutting force acting on a tool during the turning (orthogonal cutting) operation of a metal is $400$ $N$. The turning was performed using $2$ $mm$ depth of cut and $0.1$ $mm/rev$ feed rate. The specific cutting pressure (in $N$/$mm^2$) is $1000$ $2000$ $3000$ $4000$

The main cutting force acting on a tool during the turning (orthogonal cutting) operation of a metal is $400$ $N$. The turning was performed using $2$ $mm$ depth of cut a...

Arjun

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Arjun asked Feb 19, 2017

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GATE ME 2013 | Question: 63
Find the sum of the expression $\dfrac{1}{\sqrt{1}+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{4}}+ \dots \dots +\dfrac{1}{\sqrt{80}+\sqrt{81}}$ $7$ $8$ $9$ $10$

Find the sum of the expression$\dfrac{1}{\sqrt{1}+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{4}}+ \dots \dots +\dfrac{1}{\sqrt{80}+\sqrt{81}}$$7$$8$$...

piyag476

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piyag476 asked Feb 19, 2017

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GATE Mechanical 2022 Set 2 | Question: 43
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 $A$ ... and assuming maximum shear stress theory, the minimum required shaft diameter is _____________ $\text{mm}$ (round off to $2$ decimal places).

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 ...

Arjun

28.5k points

Arjun asked Feb 15, 2022

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GATE Mechanical 2022 Set 1 | Question: 32
Activities $A$ to $K$ are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is to be completed in the minimum possible time, the latest finish time for the activity $G$ is _______________ ... $5$ $10$ $8$ $9$

Activities $A$ to $K$ are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is ...

Arjun

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Arjun asked Feb 15, 2022

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GATE2020-ME-1: 1
Multiplication of real valued square matrices of same dimension is associative commutative always positive definite not always possible to compute

Multiplication of real valued square matrices of same dimension isassociativecommutativealways positive definitenot always possible to compute

go_editor

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go_editor asked Feb 19, 2020

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GATE2020-ME-1: 26
The evaluation of the definite integral $\int ^{1.4}_{ – 1}x \mid x \mid dx$ by using Simpson’s $1/3^{rd}$ (one - third) rule with step size $h=0.6$ yields $0.914$ $1.248$ $0.581$ $0.592$

The evaluation of the definite integral $\int ^{1.4}_{ – 1}x \mid x \mid dx$ by using Simpson’s $1/3^{rd}$ (one - third) rule with step size $h=0.6$ yields$0.914$$1.2...

go_editor

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go_editor asked Feb 19, 2020

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GATE ME 2012 | Question: 13
Which one of the following is NOT a decision taken during the aggregate production planning stage? Scheduling of machines Amount of labour to be committed Rate at which production should happen Inventory to be carried forward

Which one of the following is NOT a decision taken during the aggregate production planning stage?Scheduling of machinesAmount of labour to be committedRate at which prod...

Andrijana3306

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Andrijana3306 asked Mar 19, 2018

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ISRO2009-1
A hydraulic press has a ram of $15 \: \text{cm}$ diameter and plunger of $1.5 \: \text{cm}$. It is required to lift a mass of $1000 \: \text{kg}$. The force required on plunger is nearly equal to $100\;\text{N}$ $1000\;\text{N}$ $10000\;\text{N}$ $10\;\text{N}$

A hydraulic press has a ram of $15 \: \text{cm}$ diameter and plunger of $1.5 \: \text{cm}$. It is required to lift a mass of $1000 \: \text{kg}$. The force required on p...

m2n037

940 points

m2n037 asked Mar 6, 2018

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GATE2017 ME-2: 21
The crystal structure of aluminium is. body-centered cubic. face-centered cubic. close-packed hexagonal. body-centered tetragonal.

The crystal structure of aluminium is.body-centered cubic.face-centered cubic.close-packed hexagonal.body-centered tetragonal.

Arjun

28.5k points

Arjun asked Feb 26, 2017

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GATE2016-3-48
Spot welding of two steel sheets each $2 \: mm$ thick is carried out successfully by passing $4 \: kA$ of current for $0.2$ seconds through the electrodes. The resulting weld nugget formed between the sheets is $5 \: mm$ in diameter. Assuming cylindrical shape for the nugget, the ...

Spot welding of two steel sheets each $2 \: mm$ thick is carried out successfully by passing $4 \: kA$ of current for $0.2$ seconds through the electrodes. The resulting ...

Arjun

28.5k points

Arjun asked Feb 24, 2017

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GATE2016-3-15
Steady one-dimensional heat conduction takes place across the faces $1$ and $3$ of a composite slab consisting of slabs $A$ and $B$ in perfect contact as shown in the figure, where $k_A$ , $k_B$ denote the respective thermal conductivities. Using the data as given in the figure, the interface temperature $T_2$ (in $^\circ C$) is __________

Steady one-dimensional heat conduction takes place across the faces $1$ and $3$ of a composite slab consisting of slabs $A$ and $B$ in perfect contact as shown in the fig...

Arjun

28.5k points

Arjun asked Feb 24, 2017

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GATE Mechanical 2014 Set 4 | Question: 8
Which one of the following is used to convert a rotational motion into a translational motion? Bevel gears Double helical gears Worm gears Rack and pinion gears

Which one of the following is used to convert a rotational motion into a translational motion?Bevel gearsDouble helical gearsWorm gearsRack and pinion gears

Arjun

28.5k points

Arjun asked Feb 19, 2017

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GATE Mechanical 2014 Set 2 | Question: 27
The general solution of the differential equation $\dfrac{dy}{dx}=\cos(x+y)$, with $c$ as a constant, is $y+\sin \left (x+y \right )=x+c \\$ $\tan \left (\dfrac{x+y}{2} \right)=y+c \\$ $\cos \left (\dfrac{x+y}{2} \right )=x+c \\$ $\tan \left (\dfrac{x+y}{2} \right )=x+c$

The general solution of the differential equation $\dfrac{dy}{dx}=\cos(x+y)$, with $c$ as a constant, is$y+\sin \left (x+y \right )=x+c \\$$\tan \left (\dfrac{x+y}{2} \ri...

Arjun

28.5k points

Arjun asked Feb 19, 2017

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GATE ME 2013 | Question: 53
In orthogonal turning of a bar of $100$ $mm$ diameter with a feed of $0.25$ $mm$/$rev$, depth of cut of $4$ $mm$ and cutting velocity of $90$ $m$/$min$, it is observed that the main (tangential) cutting force is perpendicular to the friction force ... ) cutting force is $1500$ $N$. The normal force acting at the chip-tool interface in $N$ is $1000$ $1500$ $2000$ $2500$

In orthogonal turning of a bar of $100$ $mm$ diameter with a feed of $0.25$ $mm$/$rev$, depth of cut of $4$ $mm$ and cutting velocity of $90$ $m$/$min$, it is observed th...

piyag476

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piyag476 asked Feb 19, 2017

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GATE ME 2013 | Question: 24
Let $X$ be a normal random variable with mean $1$ and variance $4$. The probability $P \left \{ X \right.<\left. 0 \right \}$ is $0.5$ greater than zero and less than $0.5$ greater than $0.5$ and less than $1.0$ $1.0$

Let $X$ be a normal random variable with mean $1$ and variance $4$. The probability $P \left \{ X \right.<\left. 0 \right \}$ is$0.5$greater than zero and less than $0.5...

piyag476

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piyag476 asked Feb 19, 2017

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GATE ME 2013 | Question: 14
In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing constant must be close to $-1$ $\text{zero}$ $0.5$ $1.0$

In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing constant must be close to$-1$$\text{zero}$$0.5$$1.0$

piyag476

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piyag476 asked Feb 19, 2017

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GATE ME 2013 | Question: 9
Consider one-dimensional steady state heat conduction, without heat generation, in a plane wall; with boundary conditions as shown in the figure below. The conductivity of the wall is given by $k$ = $k_0$ + $bT$ ; where $k_0$ and $b$ are positive ... $x$ increases, the temperature gradient ( $dT$/ $dx$ ) will remain constant be zero increase decrease

Consider one-dimensional steady state heat conduction, without heat generation, in a plane wall; with boundary conditions as shown in the figure below. The conductivity o...

piyag476

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piyag476 asked Feb 19, 2017

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GATE Mechanical 2024 | Question: 53
In an arc welding process, the voltage and current are $30 \mathrm{~V}$ and $200 \mathrm{~A}$, respectively. The cross-sectional area of the joint is $20 \mathrm{~mm}^{2}$ ... $2$ decimal places).

In an arc welding process, the voltage and current are $30 \mathrm{~V}$ and $200 \mathrm{~A}$, respectively. The cross-sectional area of the joint is $20 \mathrm{~mm}^{2}...

admin

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admin asked Feb 16