2010-13-math

The Maxwell-Boltzmann velocity distribution for the \(x\)-component of the velocity at temperature \(T\), is \[ f(v_x) = \sqrt {\frac {m}{2\pi kT}}\exp \left (-\frac {mv_x^2}{2kT}\right ) \] The standard deviation of the distribution is

- \(\sqrt {2kT/m}\)
- \(kT/m\)
- \(\sqrt {kT/m}\)
- \(kT/2m\)

2013-1-math

The number of emails received on six consecutive days is 11, 9, 18, 18, 4 and 15, respectively. What are the median and the mode for these data?

- 18 and 11, respectively
- 13 and 18, respectively
- 13 and 12.5, respectively
- 12.5 and 18, respectively

2017-5-math

The marks obtained by a set of students are: \(38, 84, 45, 70, 75, 60, 48\). The mean and median marks, respectively, are:

- 45 and 75
- 55 and 48
- 60 and 60
- 60 and 70

2007-28-math

The thickness of a conductive coating in micrometers has a probability density function of \(600x^{-2}\) for \(100 ?\mu \text {m} < x < 120 ?\mu \text {m}\). The mean and the variance of the coating thickness is

- 1 \(\mu \)m, 108.39 \(\mu \)m\(^2\)
- 33.83 \(\mu \)m, 1 \(\mu \)m\(^2\)
- 105 \(\mu \)m, 11 \(\mu \)m\(^2\)
- 109.39 \(\mu \)m, 33.83 \(\mu \)m\(^2\)

2008-27-math

The normal distribution is given by \[ f(x) = \frac {1}{\sqrt {2\pi }\sigma }\exp \left (-\frac {(x-\mu )^2}{2\sigma ^2}\right ), \quad -\infty < x < \infty \] The points of inflexion to the normal curve are

- \(x=-\sigma , +\sigma \)
- \(x=\mu +\sigma , \mu -\sigma \)
- \(x=\mu +2\sigma , \mu -2\sigma \)
- \(x=\mu +3\sigma , ? \mu -3\sigma \)

2008-30-math

The Poisson distribution is given by \(\displaystyle P(r) = \frac {m^r}{r!}\exp (-m)\). The first moment about the origin for this distribution is

- 0
- \(m\)
- \(1/m\)
- \(m^2\)

2011-29-math

Fuel cell stacks are made of NINE membrane electrode assemblies (MEAs) interleaved between TEN bipolar plates (BPs) as illustrated below. The width of a membrane electrode assembly and a bipolar plate are normally distributed with \(\mu _{\text {MEA}}=0.15\), \(\sigma _{\text {MEA}}=0.01\), and \(\mu _{\text {BP}}=5\), \(\sigma _{\text {BP}}=0.1\) respectively. The widths of the different layers are independent of each other.

Which ONE of the following represents the CORRECT values of \((\mu _{\text {stack}}, \sigma _{\text {stack}})\) for the overall fuel cell stack width?

- \((51.35,0.32)\)
- \((51.35,1.09)\)
- \((5.15,0.10)\)
- \((5.15,0.11)\)

2014-29-math

Consider the following two normal distributions

\[ \begin{align*} f_1(x) &= \exp(-\pi x^2) \\ f_2(x) &= \frac{1}{2\pi}\exp\left\{-\frac{1}{4\pi}(x^2+2x+1)\right\} \end{align*} \]

If \(\mu \) and \(\sigma \) denote the mean and standard deviation, respectively, then

- \(\mu _1<\mu _2\) and \(\sigma _1^2<\sigma _2^2\)
- \(\mu _1<\mu _2\) and \(\sigma _1^2>\sigma _2^2\)
- \(\mu _1>\mu _2\) and \(\sigma _1^2<\sigma _2^2\)
- \(\mu _1>\mu _2\) and \(\sigma _1^2>\sigma _2^2\)

ME-2004-31-math

From a pack of regular from playing cards two cards are drawn random. What is the probability that both cards will be kings, if first card is NOT replaced?

- \(\dfrac {1}{26}\)
- \(\dfrac {1}{52}\)
- \(\dfrac {1}{169}\)
- \(\dfrac {1}{221}\)

ME-2013-A-24-math

Let \(X\) be a normal random variable with mean 1 and variance 4. The probability \(P\{X<0\}\) is

- 0.5
- Greater than 0 and less than 0.5
- Greater than 0.5 and less than 1.0
- 1.0

Last Modified on: 03-May-2024

Chemical Engineering Learning Resources - msubbu

e-mail: learn[AT]msubbu.academy

www.msubbu.in