GATE EC question library

The equivalent inductance measured between the terminals $1$ and $2$ for the circuit shown in the figure is

The circuit shown in in the figure, with $R=\frac{1}{3} \Omega$, $\mathrm{L}=\frac{1}{4} \mathrm{H}, \mathrm{C}=3 \mathrm{~F}$ has input voltage $v(t)=\sin 2 t$. The resulting current $i(t)$ is

For the circuit shown in in the figure, the time constant $\text{RC}=1 \mathrm{~ms}$. The input voltage is $v_{i}(t)=\sqrt{2}$ $\sin 10^{3} t$. The output voltage $v_{0}(t)$ is equal to

The impurity commonly used for realizing the base region of a silicon $n-p-n$ transistor is

If for a silicon $n-p-n$ transistor, the base-to-emitter voltage $\left(\mathrm{V}_{\mathrm{KE}}\right)$ is $0.7 \mathrm{~V}$ and the collector-to-base voltage $\left(\mathrm{V}_{\text{CB}}\right)$ is $0.2 \mathrm{~V}$, then the transistor is operating in the

Consider the following statements $\mathrm{S} 1$ and $\mathrm{S} 2$. $\text{S1 :}$ The $\beta$ of a bipolar transistor reduces if the base width is increased. $\text{S2 :}$ The $\beta$ of a bipolar transistor increases if the doping concentration in the base is increased. Which one of the following is correct?

An ideal $\text{op-amp}$ is an ideal

Voltage series feedback (also called series-shunt feedback) results in

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