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GATE Mechanical 2026 | Question: 29
A student council of $10$ members consists of two students from engineering school, three students from science school and five students from arts school. The university ...
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278
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GATE Mechanical 2025 | Question: 4
If two unbiased coins are tossed, then what is the probability of having at least one head?$0.25$$0.5$$0.675$$0.75$
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414
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GATE Mechanical 2025 | Question: 27
​​​​​​Considering the actual demand and the forecast for a product given in the table below, the mean forecast error and the mean absolute deviation, respectively, arePer...
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538
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GATE Mechanical 2024 | Question: 25
​​​​​A queueing system has one single server workstation that admits an infinitely long queue. The rate of arrival of jobs to the queueing system follows the Poisson dist...
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366
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GATE Mechanical 2024 | Question: 34
Let $\text{X}$ be a continuous random variable defined on $[0,1]$ such that its probability density function $f(x)=1$ for $0 \leq x \leq 1$ and $0$ otherwise. Let $Y=\log...
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GATE Mechanical 2023 | Question: 1
A machine produces a defective component with a probability of $0.015$. The number of defective components in a packed box containing $200$ components produced by the mac...
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345
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GATE Mechanical 2022 Set 1 | Question: 37
Let a random variable $X$ follow Poisson distribution such that $$\text{Prob (X = 1) = Prob (X = 2)}$$. The value of $\text{Prob (X = 3)}$ is ______________ (round off t...
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635
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GATE Mechanical 2021 Set 2 | Question: 3
The mean and variance, respectively, of a binomial distribution for $n$ independent trails with the probability of success as $p$, are$\sqrt{np},np\left ( 1-2p \right )$$...
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441
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GATE Mechanical 2021 Set 2 | Question: 8
A $\text{PERT}$ network has $9$ activities on its critical path. The standard deviation of each activity on the critical path is $3$. The standard deviation of the critic...
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557
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GATE Mechanical 2021 Set 1 | Question: 5
Consider a binomial random variable $\text{X}$. If $X_{1},X_{2},\dots ,X_{n}$ are independent and identically distributed samples from the distribution of $\text{X}$ with...
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364
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GATE Mechanical 2021 Set 1 | Question: 33
Customers arrive at a shop according to the Poisson distribution with a mean of $10$ customers/hour. The manager notes that no customer arrives tor the first $3$ minutes ...
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605
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GATE Mechanical 2021 Set 1 | Question: 35
Activities $\text{A, B, C}$ and $\text{D}$ form the critical path for a project with a $\text{PERT}$ network. The means and variances of the activity duration for each ac...
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524
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GATE2020-ME-2: 1
The sum of two normally distributed random variables $X$ and $Y$ isalways normally distributednormally distributed, only if $X$ and $Y$ are independentnormally distribute...
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622
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GATE2020-ME-2: 36
A fair coin is tossed $20$ times. The probability that ‘head’ will appear exactly $4$ times in the first ten tosses, and ‘tail’ will appear exactly $4$ times in the next ...
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675
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GATE2019 ME-2: 19
If $x$ is the mean of data $3, x, 2$ and $4$, then the mode is _____
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462
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GATE2019 ME-2: 40
The probability that a part manufactured by a company will be defective is $0.05$. If $15$ such parts are selected randomly and inspected, then the probability that at le...
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730
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GATE2019 ME-1: 28
The variable $x$ takes a value between $0$ and $10$ with uniform probability distribution. The variable $y$ takes a value between $0$ and $20$ with uniform probability di...
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734
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GATE ME 2012 | Question: 45
A box contains $4$ red balls and $6$ black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected...
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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 $Y=\text{min}(X_1, X_2)$ isexponentially...
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960
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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 s...
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