GATE EC question library

Common Data for Questions 71, 72,73: In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: $$\beta_{\mathrm{DC}}=60, \mathrm{~V}_{\mathrm{BE}}=0.7 \mathrm{~V}, h_{n^{c}} \longrightarrow \infty, h_{f \times} \longrightarrow \infty$$ The capacitance $\mathrm{C}_{\text{c }}$ can be assumed to be infinite. …

Common Data for Questions 71, 72,73: In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: $$\beta_{\mathrm{DC}}=60, \mathrm{~V}_{\mathrm{BE}}=0.7 \mathrm{~V}, h_{n^{c}} \longrightarrow \infty, h_{f c} \longrightarrow \infty$$ The capacitance $\mathrm{C}_{\text{c }}$ can be assumed to be infinite. In …

Common Data for Questions 71, 72,73: In the transistor amplifier circuit shown in the figure below, the transistor has the following parameters: $$\beta_{\mathrm{DC}}=60, \mathrm{~V}_{\mathrm{BE}}=0.7 \mathrm{~V}, h_{n^{c}} \longrightarrow \infty, h_{f c} \longrightarrow \infty$$ The capacitance $\mathrm{C}_{\text{c }}$ can be assumed to be infinite. In …

Common Data for Questions 74, 75: Let $g(t)=p(t)^{*} p(t)$, where * denotes convolution and $p(t)=u(t)-u(t-1)$ with $u(t)$ being the unit step function The impulse response of filter matched to the signal $s(t)=g(t)-\delta(t-2)^{*} g(t)$ is given as

Common Data for Questions 74, 75: Let $g(t)=p(t)^{*} p(t)$, where * denotes convolution and $p(t)=u(t)-u(t-1)$ with $u(t)$ being the unit step function An Amplitude Modulated signal is given as $$x_{\mathrm{AM}}(t)=100(p(t)+0.5 g(t)) \cos \omega_{c} t$$ in the interval $0 \leq t \leq 1$. One set of possible values of the modulating signal and …

statement for Linked Answer Questions 76 and 77 A regulated power supply, shown in figure below, has an unregulated input (UR) of $15$ Volts and generates a regulated output $V_{\text{out }}$. Use the component values shown in the figure. In the figure above, the ground has been shown by the symbol $\nabla$ The power dissipation across the transistor …

statement for Linked Answer Questions 76 and 77 A regulated power supply, shown in figure below, has an unregulated input (UR) of $15$ Volts and generates a regulated output $V_{\text{out }}$. Use the component values shown in the figure. In the figure above, the ground has been shown by the symbol $\nabla$ If the unregulated voltage increases by …

Statement for Linked Answer Questions 78 and 79 The following two questions refer to wide sense stationary stochastic processes It is desired to generate a stochastic process (as voltage process) with power spectral density $$S(\omega)=\frac{16}{16+\omega^{2}}$$ by driving a Linear-Time-Invariant system by zero mean white noise (as voltage process) with …

Statement for Linked Answer Questions 78 and 79 The following two questions refer to wide sense stationary stochastic processes The parameters of the system obtained in $\text{Q.78}$ would be

Statement for Linked Answer Questions 80 and 81 Consider the following Amplitude Modulated (AM) signal, where $f_{m}<\mathrm{B}$ $$x_{\mathrm{AM}}(t)=10\left(1+0.5 \sin 2 \pi f_{m} t\right) \cos 2 \pi f_{c} t$$ The average side-band power for the $\text{AM}$ signal given above is

Statement for Linked Answer Questions 80 and 81 Consider the following Amplitude Modulated (AM) signal, where $f_{m}<\mathrm{B}$ $$x_{\mathrm{AM}}(t)=10\left(1+0.5 \sin 2 \pi f_{m} t\right) \cos 2 \pi f_{c} t$$ The $\text{AM}$ signal gets added to a noise with Power Spectral Density $S_{n}(f)$ given in the figure below. The ratio of average …

Statement for Linked Answer Questions 82 and 83 Consider a unity-gain feedback control system whose open-loop transfer function is $$G(s)=\frac{as+1}{s^{2}}$$ The value of '$a$' so that the system has a phase-margin equal to $\frac{\pi}{4}$ is approximately equal to

Statement for Linked Answer Questions 82 and 83 Consider a unity-gain feedback control system whose open-loop transfer function is $$G(s)=\frac{as+1}{s^{2}}$$ With the value of '$a$' set for a phase-margin of $\frac{\pi}{4}$, the value of unit-impulse response of the open-loop system at $t=1$ second is equal to

Statement for Linked Answer Questions 84 and 85 A $30$-Volts battery with zero source resistance is connected to a coaxial line of characteristic impedance of $50$ Ohms at $t=0$ second and terminated in an unknown resistive load. The line length is such that it takes $400 \; \mu s$ for an electromagnetic wave to travel from source end to load end and …

Statement for Linked Answer Questions 84 and 85 A $30$-Volts battery with zero source resistance is connected to a coaxial line of characteristic impedance of $50$ Ohms at $t=0$ second and terminated in an unknown resistive load. The line length is such that it takes $400 \; \mu s$ for an electromagnetic wave to travel from source end to load end and …

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,