GATE EC question library

The circuit in the given figure is a

Assuming $\mathrm{V}_{\text{CEsat }}=0.2 \mathrm{~V}$ and $\beta=50$, the minimum base current $\left(I_{v}\right)$ required to drive the transistor in the given figure to saturation is

A master-slave flip-flop has the characteristic that

The range of signed decimal numbers that can be represented by $6$-bite $1$'s complement number is

A digital system is required to amplify a binary-encoded audio signal. The user should be able to control the gain of the amplifier from a minimum to a maximum in $100$ increments. The minimum number of bits required to encode, in straight binary, is

Choose the correct one from among the alternatives $\text{A, B, C, D}$ after matching an item from Group $1$ with the most appropriate item in Group $2.$ …

Figure given below shows the internal schematic of a $\text{TTL AND-OR}$ -Invert $\text{(AOI)}$ gate. For the inputs shown in the given figure, the output $\text{Y}$ is

Given figure is the voltage transfer characteristic of

The impulse response $h[n]$ of a linear time-invariant system is given by $$h[n]=u[n+3]+u[n-2]-2 u[n-7]$$ where $u[n]$ is the unit step sequence. The above system is

The distribution function $\mathrm{F}_{1}(x)$ of a random variable $\mathrm{X}$ is shown in the figure. The probability that $X=1$ is

The $z$-transform of a system is $H(z)=\frac{z}{z-0.2}.$ If the ROC is $|z|<0.2$, then the impulse response of the system is

The Fourier transform of a conjugate symmetric function is always

Given $\mathrm{G}(s) \mathrm{H}(z)=\frac{\mathrm{K}}{s(s+1)(s+3)}$, the point of intersection of the asymptotes of the root loci with the real axis is

In a $\text{PCM}$ system, if the code word length is increased from $6$ to $8$ bits, the signal to quantization noise ratio improves by the factor

An AM signal is detected using an envelope detector. The carrier frequency and modulating signal frequency are $1 \; \mathrm{MHz}$ and $2 \; \mathrm{kHz}$ respectively. An appropriate value for the time constant of the envelope detector is

An AM signal and a narrow-band FM signal with identical carriers, modulating signals and modulation indices of $0.1$ are added together. The resultant signal can be closely approximated by

In the output of a DM speech encoder, the consecutive pulses are of opposite polarity during time interval $t_{1} < t < t_{2}.$ This indicates that during this interval

The phase velocity of an electromagnetic wave propagating in a hollow metallic rectangular waveguide in the $\mathrm{TE}_{10}$ mode is

Consider a lossless antenna with a directive gain of $+6 \mathrm{~dB}$. If $1 \mathrm{~mW}$ of power is fed to it the total power radiated to the antenna will be

For the lattice circuit shown in the figure, $Z_{a}=j 2 \Omega$ and $Z_{b}=2 \Omega$. The values of the open circuit impedance parameters $Z=\left[\begin{array}{ll}z_{11} & z_{12} \\ z_{21} & z_{22}\end{array}\right]$ are