GATE EC Engineering Mathematics questions

Practise Engineering Mathematics questions for GATE EC. Explore official PYQs and original subject-wise quizzes, check answers and view available solutions. Free, no sign-in.

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A=\left[\begin{array}{cc}-2 & 2 \\ 1 & -3\end{array}\right]

, then

\sin A t

A random variable

\mathrm{X}

with uniform density in the interval

0

1

is quantized as follows:

\begin{array}{ll} \qquad \text{If 0 < X < 0.3,} & \text{x}_{4} = 0 \\ \qquad \text{If 0.3 < X < 1,} & \text{x}_{4} = 0.7 \end{array}

where

\text{x}_{4}

is the quantized value of

\text{X}

. The root-mean square value of …

Let

X

and

Y

be two statistically independent random variables uniformly distributed in the ranges

(-1,1)

and

(-2,1)

respectively. Let

Z=X+Y

. Then the probability that

(Z \leq-2)

Data for Q. 65-66 are given below. Solve the problems and choose the correct answers. Let

X

be the Gaussian random variable obtained by sampling the process at

t=t_{i}

and let

\mathrm{Q}(\alpha)=\int_{\alpha}^{\infty} \frac{1}{\sqrt{2 \pi}} e^{\frac{x^{2}}{2}} d y

The probability that

[x \leq 1]

Let

Y

and

Z

be the random variables obtained by sampling

X(t)

t=2

and

t=4

respectively. Let

W

=Y-Z

. The variance of

W

If the electric field intensity is given by

\mathrm{E}=\left(x u_{x}+y u_{y}+z u_{z}\right) \text{ volt } / \mathrm{m} \text{, }

the potential difference between

X(2,0,0)

and

Y(1,2,3)

The PDF of a Gaussian random variable

X

is given by

\operatorname{Px}(x)=\frac{1}{3 \sqrt{2 \pi}} e^{\frac{-(x-4)^{2}}{18}}

The probability of the event

\{X=4\}

During transmission over a communication channel, bit errors occur independently with probability p. If a block of

n

bits is transmitted, the probability of at most one bit error is equal to

The eigen values of the matrix

\left[\begin{array}{rrrr}2 & -1 & 0 & 0 \\ 0 & 3 & 0 & 0 \\ 0 & 0 & -2 & 0 \\ 0 & 0 & -1 & 4\end{array}\right]

are

f(t)=\frac{\omega}{s^2+\omega^2}

, then the value of

\lim _{t \rightarrow \infty} f(t)

The eigen values of the matrix

A=\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]

are

The probability density function of the envelope of narrow band Gaussian noise is

A probability density fucntion is given by

p(x)=\mathrm{K} e^{-x^2 / 2}-\infty<x<\infty

. The value of

K

should be

The solution of

X=A(t) X(t)

, is

e^{A t}

can be expanded as

\lim _{x \rightarrow 0} \frac{x\left(e^{x}-1\right)+2(\cos x-1)}{x(1-\cos x)}

For a random variable

x

following the probability density function,

\mathrm{p}(x)

, shown in given figure the mean and the variance are, respectively,