GATE EC question library

In the circuit shown in the figure, the BJT has a current gain $(\beta)$ of $50.$ For an emitter-base voltage ܸ $V_{EB} = 600\: mV,$ the emitter-collector voltage $V_{EC}$ (in Volts) is _______.

In the circuit shown using an ideal opamp, the $3$-dB cut-off frequency (in Hz) is _______.

In the circuit shown, assume that diodes $D_{1}$ and $D_{2}$ are ideal. In the steady state condition, the average voltage $V_{ab}$ (in Volts) across the $0.5\: \mu F$ capacitor is ______.

The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset $(\overline{R_{d}}\:\text{input}).$ The counter corresponding to this circuit is

In the circuit shown, diodes $D_{1}, D_{2}$ and $D_{3}$ are ideal, and the inputs $E_{1} , E_{2}$ and $E_{3}$ are $“0\: V”$ for logic $‘0’$ and $“10\: V”$ for logic $‘1’$. What logic gate does the circuit represent?

Which one of the following $8085$ microprocessor programs correctly calculates the product of two $8$-bit numbers stored in registers $B$ and $C?$

The impulse response of an LTI system can be obtained by

Consider a four-point moving average filter defined by the equation $y[n] = \displaystyle{}\sum _{i=0}^{3}\alpha_{i}\:x[n-i].$ The condition on the filter coefficients that results in a null at zero frequency is

Consider the Bode plot shown in the figure. Assume that all the poles and zeros are real-valued. The value of $f_{H}\: – f_{L}\:( \text{in}\: Hz)$ is ___________.

The phase margin (in degrees) of the system $G(s) = \dfrac{10}{s(s+10)}$ is _______.

The transfer function of a first-order controller is given as $$G_{C}(s) = \dfrac{K(s+a)}{s+b}$$where $K,a$ and ܾ$b$ are positive real numbers. The condition for this controller to act as a phase lead compensator is

The modulation scheme commonly used for transmission from GSM mobile terminals is

A message signal $m(t) = A_{m} \sin(2πf_{m}t)$ is used to modulate the phase of a carrier $A_{c} \cos(2πf_{c}t)$ to get the modulated signal $y(t) = A_{c} \cos(2πf_{c}t + m(t)).$ The bandwidth of $y(t)$

The directivity of an antenna array can be increased by adding more antenna elements, as a larger number of elements

A coaxial cable is made of two brass conductors. The spacing between the conductors is filled with Teflon $(\varepsilon_{r} = 2.1, \tan \delta = 0).$ Which one of the following circuits can represent the lumped element model of a small piece of this cable having length $\Delta z$?

The Newton-Raphson method is used to solve the equation $f(x) = x^{3} – 5x^{2} + 6x – 8 = 0.$ Taking the initial guess as $x = 5,$ the solution obtained at the end of the first iteration is __________.

A fair die with faces $\{1, 2, 3, 4, 5, 6\}$ is thrown repeatedly till $’3’$ is observed for the first time. Let $X$ denote the number of times the die is thrown. The expected value of $X$ is _______.

Consider the differential equation $$\dfrac{\mathrm{d^{2}}x(t) }{\mathrm{d} t^{2}} +3\frac{\mathrm{d}x(t)}{\mathrm{d} t} + 2x(t) = 0.$$ Given $x(0) = 20$ and $x(1) = 10/e,$ where $e = 2.718,$ the value of $x(2)$ is ________.

A vector field $\textbf{D} = 2\rho^{2}\:\textbf{a}_{\rho} + z\: \textbf{a}_{z}$ exists inside a cylindrical region enclosed by the surfaces $\rho =1,z = 0$ and $z = 5.$ Let $S$ be the surface bounding this cylindrical region. The surface integral of this field on $S(∯_{S} \textbf{D.ds})$ is _______.

In the circuit shown, the current $I$ flowing through the $50\;\Omega$ resistor will be zero if the value of capacitor $C (\text{in}\: \mu F)$ is ______.