GATE-CH-2010-13-math-1mark

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

• $\sqrt{2kT/m}$

• $kT/m$

• $\sqrt{kT/m}$

• $kT/2m$

GATE-CH-2013-1-math-1mark

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

GATE-CH-2017-5-math-1mark

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

GATE-CH-2007-28-math-2mark

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${}^2$

GATE-CH-2008-27-math-2mark

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

• $x=-\sigma ,+\sigma$

• $x=\mu +\sigma ,\mu -\sigma$

• $x=\mu +2\sigma ,\mu -2\sigma$

• $x=\mu +3\sigma ,?\mu -3\sigma$

GATE-CH-2008-30-math-2mark

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

• $m$

• $1/m$

• $m^2$

GATE-CH-2011-29-math-2mark

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?

• $(51.35,0.32)$

• $(51.35,1.09)$

• $(5.15,0.10)$

• $(5.15,0.11)$

GATE-CH-2014-29-math-2mark

Consider the following two normal distributions 

$$\begin{array}{rl}{f}_1(x)& =\exp (-\pi x^2)\\ f_2(x)& =\frac{1}{2\pi }\exp \{-\frac{1}{4\pi }(x^2+2x+1)\}\end{array}$$

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 ${\sigma }_1^2>{\sigma }_2^2$

GATE-ME-2004-31-math-2mark

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?

• ${\displaystyle \frac{1}{26}}$

• ${\displaystyle \frac{1}{52}}$

• ${\displaystyle \frac{1}{169}}$

• ${\displaystyle \frac{1}{221}}$

GATE-ME-2013-A-24-math-1mark

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