GATE EC question library

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SubjectTopicYearType

The following differential equation has

3 \frac{d^{2} y}{d t^{2}}+4\left(\frac{d y}{d t}\right)^{3}+y^{2}+2=x

Choose the function

f(t); – \infty < 1 < \infty,

for which a Fourier series cannot be defined.

A fair dice is rolled twice. The probability that an odd number will follow an even number is

A solution of the following differential equation is given by

\frac{d^{2} y}{d x^{2}}-5 \frac{d y}{d x}+6 y=0

The function

x(t)

is shown in the figure. Even and odd parts of a unit-step function

u(t)

are respectively,

The region of convergence of

Z

-transform of the sequence

\left(\frac{5}{6}\right)^{n} u(n)-\left(\frac{6}{5}\right)^{n} u(-n-1)

must be

The condition on

\mathrm{R}, \mathrm{L}

and

\mathrm{C}

such that the step response

y(t)

in the figure has no oscillations, is

The

\text{ABCD}

parameters of an ideal

n: 1

transformer shown in the figure are

\left[\begin{array}{ll}n & 0 \\ 0 & \mathrm{X}\end{array}\right]

. The value of

X

will be

In a series

\mathrm{RLC}

circuit,

\mathrm{R}=2 \; \mathrm{k} \Omega, \mathrm{L}=1 \; \mathrm{H}

, and

\mathrm{C} \frac{1}{400}=\mu \mathrm{F}

. The resonant frequency is

The maximum power that can be transferred to the load resistor

R_{L}

from the voltage source in the figure is

The bandgap of Silicon at room temperature is

A Silicon PN junction at a temperature of

20^{\circ} \mathrm{C}

has a reverse saturation current of

10

picoAmperes

(\mathrm{pA})

. The reverse saturation current at

40^{\circ} \mathrm{C}

for the same bias is approximately

The primary reason for the widespread use of Silicon in semiconductor device technology is

The effect of current shunt feedback in an amplifier is to

The input resistance

\text{R}_{\mathrm{i}}

of the amplifier shown in the figure is

The first and the last critical frequency of an

\text{RC}

-driving point impedance function must respectively be

The cascode amplifier is a multistage configuration of

Decimal

43

in Hexadecimal and

\text{BCD}

number system is respectively

The Boolean function

f

implemented in the figure using two input multiplexers is

Let

x(n)=\left(\frac{1}{2}\right)^{n} u(n), y(n)=x^{2}(n)

and

\mathrm{Y}\left(e^{j i e}\right)

be the Fourier transform of

y(n)

. Then

Y\left(e^{j i e}\right)