GATE EC question library

In the system shown in Figure (a), $m(t)$ is a low-pass signal with bandwidth $W$ Hz. The frequency response of the band-pass filter $H(f)$ is shown in Figure (b). If it is desired that the output signal $z(t)=10x(t)$, the maximum value of $W$ (in Hz) should be strictly less than _____________.

A source emits bit $0$ with probability $\frac{1}{3}$ and bit $1$ with probability $\frac{2}{3}$. The emitted bits are communicated to the receiver. The receiver decides for either $0$ or $1$ based on the received value $R$. It is given that the conditional density functions of $R$ are as …

The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric conductor is given by the following expression $$H_z (x,y,z,t) = 0.1 \: cos(25 \pi x) \: \: \cos(30.3 \: \pi y) \: \: \cos(12 \pi \times 10^9 t- \beta z) \: \: (A/m)$$ The cross-sectional dimensions of the waveguide are give as …

The electric field intensity of a plane wave traveling in free space is given by the following expression $$\textbf{E}(x,t)=\textbf{a}_y \: 24 \: \pi \: \: \cos(\omega t – k_0 x) \: \: (V/m)$$ In this field, consider a square area $10 \: \text{cm} \times 10 \: \text{cm}$ on a plane $x+y=1$. The total time-averaged power (in mW) passing through the square …

Consider a uniform plane wave with amplitude $(E_0)$ of $10 \: V/m$ and $1.1$ GHz frequency travelling in air, and incident normally on a dielectric medium with complex relative permittivity $(\varepsilon _r)$ and permeability $(\mu _r)$ as shown in the figure. The magnitude of the transmitted electric field component (in V/m) after it has …

Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence: Dhoni, as well as the other team members of Indian team,______ present on the occasion.

Choose the word most similar in meaning to the given word: Awkward

What is the adverb for the given word below? Misogynous

An electric bulb has onboard instruments that report the total electricity consumed since the start of the trip as well as the total distance covered. During a single day of operation, the bus travels on stretches $M, N, O,$ and $P,$ in that order. The cumulative distance travelled and the corresponding electricity consumption are shown in the Table …

Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram's selection is $1/6$ and that of Ramesh is $1/8$. What is the probability that only one of them will be selected?

In the following sentence certain parts are underlined and marked P,Q and R. One of the parts may contain certain error or may not be acceptable in standard written communication.select the part containing an error. Choose D as your answer if there is no error. …

Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows. Statements: All film stars are playback singers. All film directors are film stars Conclusions: All film directors are playback singers some film stars are film director

A tiger is $50$ leaps of its own behind a tree. The tiger takes $5$ leaps per minute to the deer's $4$. If the tiger and the deer cover $8$ meter and $5$ meter per leap respectively, what distance in meters will the tiger have to run before it catches the deer?

if $a^2+b^2+c^2=1$ then $ab+bc+ac$ lies in the interval

Lamenting the gradual sidelining of the arts in school curricula, a group of prominent artists wrote to the chief minister last year, asking him to allocate more funds to support art education in schools. However, no such increase has been announced in this year's Budget. The artists expressed their deep anguish at their request not being approved, but many …

The bilateral Laplace transform of a function $f(t) = \begin{cases} 1 & \text{if } a \leq t \leq b \\ 0 & \text{otherwise} \end{cases}$ is

The value of $x$ for which all the eigen-values of the matrix given below are real is $$\begin{bmatrix} 10&5+j &4 \\ x&20 &2 \\4 &2 &-10 \end{bmatrix}$$

Let $f(z)=\dfrac{az+b}{cz+d}.$ If $f(z_{1})=f(z_{2})$ for all $z_{1}\neq z_{2},a=2,b=4$ and $c=5,$ then $d$ should be equal to ________.

The general solution of the differential equation $\dfrac{\mathrm{d} y}{\mathrm{d} x} = \dfrac{1+\cos 2y}{1-\cos 2x}$ is

The magnitude and phase of the complex Fourier series coefficients ܽ$a_{k}$ of a periodic signal $x(t)$ are shown in the figure. Choose the correct statement from the four choices given. Notation: $C$ is the set of complex numbers, ܴ$R$ is the set of purely real numbers, and $P$ ܲis the set of purely imaginary numbers.