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GATE Mechanical 2020 Set 1 | GA Question: 5
Define $[x]$ as the greatest integer less than or equal to $x$, for each $x\in \left (- \infty, \infty \right ).$ If $y = [x]$, then area under $y$ for $x\in \left [ 1,4 \right ]$ is _______. $1$ $3$ $4$ $6$
Define $[x]$ as the greatest integer less than or equal to $x$, for each $x\in \left (- \infty, \infty \right ).$ If $y = [x]$, then area under $y$ for $x\in \left [ 1,4 ...
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GATE Mechanical 2020 Set 1 | GA Question: 6
Crowd funding deals with mobilisation of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in the project. Based on the above paragraph ... Funds raised through coerced contributions on web-based platforms Funds raised through voluntary contributions on web-based platforms
Crowd funding deals with mobilisation of funds for a project from a large number of people, who would be willing to invest smaller amounts through web-based platforms in ...
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GATE Mechanical 2020 Set 1 | GA Question: 7
$P, Q, R$ and $S$ are to be uniquely coded using $\alpha$ and $\beta$. If $P$ is coded as $\alpha \alpha$ and $Q$ as $\alpha \beta$ , then $R$ and $S$, respectively, can be coded as ________. $\beta \alpha \:\text{and}\:\alpha \beta$ $\beta \beta \:\text{and}\:\alpha \alpha$ $\alpha \beta\:\text{and}\:\beta \beta$ $\beta\alpha \:\text{and}\:\beta \beta$
$P, Q, R$ and $S$ are to be uniquely coded using $\alpha$ and $\beta$. If $P$ is coded as $\alpha \alpha$ and $Q$ as $\alpha \beta$ , then $R$ and $S$, respectively, can ...
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GATE Mechanical 2020 Set 1 | GA Question: 8
The sum of the first $n$ terms in the sequence $8,\:88,\:888,\:8888,\dots$ is ________. $\dfrac{81}{80}\left ( 10^{n}-1 \right )+\dfrac{9}{8}n \\$ $\dfrac{81}{80}\left ( 10^{n}-1 \right )-\dfrac{9}{8}n \\$ $\dfrac{80}{81}\left ( 10^{n}-1 \right )+\dfrac{8}{9}n \\$ $\dfrac{80}{81}\left ( 10^{n}-1 \right )-\dfrac{8}{9}n$
The sum of the first $n$ terms in the sequence $8,\:88,\:888,\:8888,\dots$ is ________.$\dfrac{81}{80}\left ( 10^{n}-1 \right )+\dfrac{9}{8}n \\$$\dfrac{81}{80}\left ( 10...
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GATE Mechanical 2020 Set 1 | GA Question: 9
Select the graph that schematically represents BOTH $y=x^{m}\:\text{and}\:y=x^{1/m}$ properly in the interval $0\leq x \leq 1$, for integer values of $m,$ where $m > 1.$
Select the graph that schematically represents BOTH $y=x^{m}\:\text{and}\:y=x^{1/m}$ properly in the interval $0\leq x \leq 1$, for integer values of $m,$ where $m 1.$
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GATE Mechanical 2020 Set 1 | GA Question: 10
The bar graph shows the data of the students who appeared and passed in an examination for four schools $P, Q, R$, and $S$. The average of success rates $\text{(in percentage)}$ of these four schools is _______. $58.5\%$ $58.8\%$ $59.0\%$ $59.3\%$
The bar graph shows the data of the students who appeared and passed in an examination for four schools $P, Q, R$, and $S$. The average of success rates $\text{(in percen...
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GATE2020-ME-1: 17
For an ideal gas, the value of the Joule-Thomson coefficient is positive negative zero indeterminate
For an ideal gas, the value of the Joule-Thomson coefficient ispositivenegativezeroindeterminate
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GATE2020-ME-1: 18
For an ideal gas, a constant pressure line and a constant volume line intersect at a point, in the Temperature $(T)$ versus specific entropy $\text{(s)}$ diagram. $C_{P}$ is the specific heat at constant pressure and $C_{V}$ is the specific heat at constant volume.The ratio of the slopes of the ... $\dfrac{C_{P}}{C_{V}} \\$ $\dfrac{C_{P}-C_{V}}{C_{V}} \\$ $\dfrac{C_{V}}{C_{P}}$
For an ideal gas, a constant pressure line and a constant volume line intersect at a point, in the Temperature $(T)$ versus specific entropy $\text{(s)}$ diagram. $C_{P}$...
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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).
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...
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GATE2020-ME-1: 52
One kg of air, initially at a temperature of $127^{\circ}C$ , expands reversibly at a constant pressure until the volume is doubled. If the gas constant of air is $287\: J/kg.K$, the magnitude of work transfer is ________ $kJ$ (round off to $2$ decimal places).
One kg of air, initially at a temperature of $127^{\circ}C$ , expands reversibly at a constant pressure until the volume is doubled. If the gas constant of air is $287\: ...
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GATE Mechanical 2019 Set 2 | GA Question: 2
A final examination is the ____ of a series of evaluations that a student has to go through culmination consultation desperation insinuation
A final examination is the ____ of a series of evaluations that a student has to go throughculminationconsultationdesperationinsinuation
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GATE Mechanical 2019 Set 2 | GA Question: 3
If IMHO=JNIP; IDK=JEL; and SO=TP, then IDC=______ JDE JED JDC JCD
If IMHO=JNIP; IDK=JEL; and SO=TP, then IDC=______JDEJEDJDCJCD
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GATE Mechanical 2019 Set 2 | GA Question: 4
The product of three integers $X$, $Y$ and $Z$ is $192$. $Z$ is equal to $4$ and $P$ is equal to the average of $X$ and $Y$. What is the minimum possible value of $P$? $6$ $7$ $8$ $9.5$
The product of three integers $X$, $Y$ and $Z$ is $192$. $Z$ is equal to $4$ and $P$ is equal to the average of $X$ and $Y$. What is the minimum possible value of $P$?$6$...
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GATE Mechanical 2019 Set 2 | GA Question: 5
Are there enough seats here? There are ____ people here than I expected many most least more
Are there enough seats here? There are ____ people here than I expectedmanymostleastmore
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GATE Mechanical 2019 Set 2 | GA Question: 6
Fiscal deficit was $4 \%$ of the GDP in $2015$ and that increased to $5 \%$ in $2016$. If the GDP increased by $10 \%$ from $2015$ to $2016$, the percentage increase in the actual fiscal deficit is ____ $37.50$ $35.70$ $25.00$ $10.00$
Fiscal deficit was $4 \%$ of the GDP in $2015$ and that increased to $5 \%$ in $2016$. If the GDP increased by $10 \%$ from $2015$ to $2016$, the percentage increase in t...
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GATE Mechanical 2019 Set 2 | GA Question: 7
Two pipes $P$ and $Q$ can fill a tank in $6$ hours and $9$ hours respectively, while a third pipe $R$ can empty the tank in $12$ hours. Initially, $P$ and $R$ are open for $4$ hours, Then $P$ is closed and $Q$ is opened. After $6$ more hours $R$ is closed. The total time taken to fill the tank (in hours) is ____ $13.50$ $14.50$ $15.50$ $16.50$
Two pipes $P$ and $Q$ can fill a tank in $6$ hours and $9$ hours respectively, while a third pipe $R$ can empty the tank in $12$ hours. Initially, $P$ and $R$ are open f...
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GATE Mechanical 2019 Set 2 | GA Question: 9
Mola is a digital platform for taxis in a city. It offers three types of rides - Pool, Mini and Prime.The table below presents the number of rides for the past four months. The platform earns one US dollar per ride. What is the percentage share of the revenue ... $16.24$ $23.97$ $25.86$ $38.74$
Mola is a digital platform for taxis in a city. It offers three types of rides – Pool, Mini and Prime.The table below presents the number of rides for the past four mon...
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GATE Mechanical 2019 Set 2 | GA Question: 10
$X$ is an online media provider. By offering unlimited and exclusive online content at attractive prices for a loyalty membership, $X$ is almost forcing its customers towards its loyalty membership. If its royalty membership continues to grow ... television operators don't subscribe to $X's$ loyalty members The $X$ is cancelling accounts of non-members
$X$ is an online media provider. By offering unlimited and exclusive online content at attractive prices for a loyalty membership, $X$ is almost forcing its customers tow...
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GATE2019 ME-2: 1
In matrix equation $[A] \{X\}=\{R\}$, $[A] = \begin{bmatrix} 4 & 8 & 4 \\ 8 & 16 & -4 \\ 4 & -4 & 15 \end{bmatrix} \{X\} = \begin{Bmatrix} 2 \\ 1 \\ 4 \end{Bmatrix} \text{ and} \{ R \} = \begin{Bmatrix} 32 \\ 16 \\ 64 \end{Bmatrix}$ One of the eigen values of matrix $[A]$ is $4$ $8$ $15$ $16$
In matrix equation $[A] \{X\}=\{R\}$,$[A] = \begin{bmatrix} 4 & 8 & 4 \\ 8 & 16 & -4 \\ 4 & -4 & 15 \end{bmatrix} \{X\} = \begin{Bmatrix} 2 \\ 1 \\ 4 \end{Bmatrix} \text{...
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GATE2019 ME-2: 3
The differential equation $\dfrac{dy}{dx}+4y=5$ is valid in the domain $0 \leq x \leq 1$ with $y(0)=2.25$. The solution of the differential equation is $y=e^{-4x}+5$ $y=e^{-4x}+1.25$ $y=e^{4x}+5$ $y=e^{4x}+1.25$
The differential equation $\dfrac{dy}{dx}+4y=5$ is valid in the domain $0 \leq x \leq 1$ with $y(0)=2.25$. The solution of the differential equation is$y=e^{-4x}+5$$y=e^{...
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GATE2019 ME-2: 4
An analytic function $f(z)$ of complex variable $z=x+iy$ may be written as $f(z)=u(x,y)+iv(x,y)$. Then $u(x,y)$ and $v(x,y)$ ...
An analytic function $f(z)$ of complex variable $z=x+iy$ may be written as $f(z)=u(x,y)+iv(x,y)$. Then $u(x,y)$ and $v(x,y)$ must satisfy$\dfrac{\partial u}{ \partial x} ...
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GATE2019 ME-2: 19
If $x$ is the mean of data $3, x, 2$ and $4$, then the mode is _____
If $x$ is the mean of data $3, x, 2$ and $4$, then the mode is _____
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GATE2019 ME-2: 39
A four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link $2$ is rotating anticlockwise with a constant angular speed $\omega_2$. Length of different links are: $O_2 O_4=O_2A=L,$$AB=O_4B=\sqrt{2}L$ The magnitude of ... $O_2O_4$ as shown. The ratio $\frac{\omega_4}{\omega_2}$ is _________ (round off to two decimal places).
A four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link $2$ is rotating anticlockwise with a constant angular speed $\omega...
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GATE2019 ME-2: 54
In an orthogonal machining with a single point cutting tool of rake angle $10^{\circ}$, the uncut chip thickness and the chip thickness are $0.125$ mm and $0.22$ mm, respectively. Using Merchant’s first solution for the condition of minimum cutting force, the coefficient of friction at the chip-tool interface is _______ (round off to two decimal places).
In an orthogonal machining with a single point cutting tool of rake angle $10^{\circ}$, the uncut chip thickness and the chip thickness are $0.125$ mm and $0.22$ mm, resp...
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GATE Mechanical 2019 Set 1 | GA Question: 1
John Thomas, an _________ writer, passed away in $2018$. imminent prominent eminent dominant
John Thomas, an _________ writer, passed away in $2018$.imminentprominenteminentdominant
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GATE Mechanical 2019 Set 1 | GA Question: 4
The sum and product of two integers are $26$ and $165$ respectively. The difference between these two integers is ______ $2$ $3$ $4$ $6$
The sum and product of two integers are $26$ and $165$ respectively. The difference between these two integers is ______$2$$3$$4$$6$
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GATE2019 ME-1: 1
Consider the matrix $P=\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$ The number of distinct eigenvalues $0$ $1$ $2$ $3$
Consider the matrix$$P=\begin{bmatrix} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}$$The number of distinct eigenvalues$0$$1$$2$$3$
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GATE2019 ME-1: 3
For the equation $\dfrac{dy}{dx}+7x^2y=0$, if $y(0)=3/7$, then the value of $y(1)$ is $\dfrac{7}{3}e^{-7/3} \\$ $\dfrac{7}{3}e^{-3/7} \\$ $\dfrac{3}{7}e^{-7/3} \\$ $\dfrac{3}{7}e^{-3/7}$
For the equation $\dfrac{dy}{dx}+7x^2y=0$, if $y(0)=3/7$, then the value of $y(1)$ is$\dfrac{7}{3}e^{-7/3} \\$$\dfrac{7}{3}e^{-3/7} \\$$\dfrac{3}{7}e^{-7/3} \\$$\dfrac{3}...
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GATE2019 ME-1: 49
A steam power cycle with regeneration as shown below on the $T-s$ diagram employs a single open feedwater heater for efficiency improvement. The fluid mix with each other in an open feedwater heater. The turbine is isentropic and the input (bleed) to the feedwater ... from the turbine as a percentage of the total mass flow rate at the inlet to the turbine at state $1$ is _______
A steam power cycle with regeneration as shown below on the $T-s$ diagram employs a single open feedwater heater for efficiency improvement. The fluid mix with each other...
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GATE2019 ME-1: 51
The value of the following definite integral is __________ (round off to three decimal places) $\int_1^e (x \: \ln \: x) dx$
The value of the following definite integral is __________ (round off to three decimal places)$$\int_1^e (x \: \ln \: x) dx$$
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GATE ME 2012 | Question: 63
A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation $y=2x-0.1x^2$ where $y$ is the height of the arch in meters. The maximum possible height of the arch is $8$ meters $10$ meters $12$ meters $14$ meters
A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation $y=2x-0.1x^2$ w...
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GATE ME 2012 | Question: 60
Choose the grammatically INCORRECT sentence: They gave us the money back less the service charges of Three Hundred rupees. This country's expenditure is not less than that of Bangladesh. The committee initially asked for a funding of Fifty Lakh rupees, but later settled for a lesser sum. This country's expenditure on educational reforms is very less.
Choose the grammatically INCORRECT sentence:They gave us the money back less the service charges of Three Hundred rupees.This country's expenditure is not less than that ...
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GATE ME 2012 | Question: 59
Which one of the following options is the closest in meaning to the word given below? Mitigate Diminish Divulge Dedicate Denote
Which one of the following options is the closest in meaning to the word given below?MitigateDiminishDivulgeDedicateDenote
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GATE ME 2012 | Question: 58
Choose the most appropriate alternative from the options given below to complete the following sentence: Despite several ________ the mission succeeded in its attempt to resolve the conflict. attempts setbacks meetings delegations
Choose the most appropriate alternative from the options given below to complete the following sentence:Despite several ________ the mission succeeded in its attempt to r...
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GATE Mechanical 2018 Set 2 | GA Question: 10
An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head ans T stands for tail, the following are the observations from the four trials. HTHTHT TTHHHT HTTHHT ... Two T will occur. One H and one T will occur. Two H will occur. One H wll be followed by one T.
An unbiased coin is tossed six times in a row and four different such trials are conducted. One trial implies six tosses of the coin. If H stands for head ans T stands fo...
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GATE2018-2-27
Let $X_1$ and $X_2$ be two independent exponentially distributed random variables with means $0.5$ and $0.25$, respectively. Then $Y=\text{min}(X_1, X_2)$ is exponentially distributed with mean $1/6$ exponentially distributed with mean $2$ normally distributed with mean $3/4$ normally distributed with mean $1/6$
Let $X_1$ and $X_2$ be two independent exponentially distributed random variables with means $0.5$ and $0.25$, respectively. Then $Y=\text{min}(X_1, X_2)$ isexponentially...
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GATE2018-2-24
The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of $30$ customers/hour. The probability that the time between successive customer arrival is between $1$ and $3$ minutes is _____ (correct to two decimal places)
The arrival of customers over fixed time intervals in a bank follow a Poisson distribution with an average of $30$ customers/hour. The probability that the time between s...
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GATE2018-2-23
An engine operates on the reversible cycle as shown in the figure. The work output from the engine (in (kJ/cycle) is ____ (correct to two decimal places).
An engine operates on the reversible cycle as shown in the figure. The work output from the engine (in (kJ/cycle) is ____ (correct to two decimal places).
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GATE2018-2-21
Fatigue life of a material for a fully reversed loading condition is estimated from $\sigma_a=1100N^{-0.15}$, where $\sigma_a$ is teh stress amplitude in $MPa$ and $N$ is the failure life in cycles. The maximum allowable stress amplitude (in $MPa$) for a life of $1 \times 10^5$ cycles under the same loading condition is ________ (correct to two decimal places).
Fatigue life of a material for a fully reversed loading condition is estimated from $$\sigma_a=1100N^{-0.15}$$, where $\sigma_a$ is teh stress amplitude in $MPa$ and $N$ ...
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GATE2018-2-20
A hollow circular shaft of inner radius $10 \: mm$ outer radius $20 \: mm$ length $1 \: m$ is to be used as a torsional spring. If the shear modulus of the material of the shaft is $150 \: GPa$, the torsional stiffness of the shaft (in $kN-m/rad$) is ________ (correct to two decimal places).
A hollow circular shaft of inner radius $10 \: mm$ outer radius $20 \: mm$ length $1 \: m$ is to be used as a torsional spring. If the shear modulus of the material of th...
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