List of top Questions asked in GATE IN

A Zener diode is used as a 4 V voltage regulator in the circuit shown. Given that the diode requires a minimum current of 4 mA for voltage regulation, the maximum current (in milliamperes) permitted to flow through the load \( R_L \) is _________ (round off to one decimal place)
A signal \( V_{\text{in}}(t) \) shown is applied from \( t = 0 \) ms to \( t = 6 \) ms to the circuit shown. Given the initial voltage across the capacitor is 0.3 V, and that the diode is ideal, the open circuit voltage \( V_{\text{out}}(t) \) at \( t = 5 \) ms is _________
The transfer function of a system is: \[ \frac{(s + 1)(s + 3)}{(s + 5)(s + 7)(s + 9)}. \] In the state-space representation of the system, the minimum number of state variables (in integer) necessary is _________.
A photodiode is made of a semiconductor with a bandgap of 1.42 eV. Given that Planck’s constant is \(6.626 \times 10^{-34}\) J·s, the speed of light in vacuum is \(3 \times 10^8\) m/s, and \(1 \, \text{eV} = 1.6 \times 10^{-19}\) J, the cut-off wavelength (in nanometers) of the photodiode is _________ (round off to one decimal place).
The logic block shown has an output \( F \) given by _________
The output F of the digital circuit shown can be written in the form _________
Given \( M = \begin{bmatrix} 2 & 3 & 7 \\ 6 & 4 & 7 \\ 4 & 6 & 14 \end{bmatrix} \), which of the following statement(s) is/are correct?
In which of the following bridge(s) is the balancing condition frequency-independent?
Consider 24 voice signals being transmitted without latency using time-division multiplexing. If each signal is sampled at 12 kHz and represented by an 8-bit word, the bit-duration (in microseconds) is _________ (round off to two decimal places)
An analog-to-digital converter with resolution 0.01 V converts analog signals between 0 V to +10 V to an unsigned binary output. The minimum number of bits (in integer) in the output is _________
The figure shows a Chromel-Alumel thermocouple, where the junction A is held at temperature \( T_A \), and a thermal emf \( E_1 \) is measured using an ideal voltmeter between the open ends B1 and B2, both held at temperature \( T_B \). Two identical copper wires are introduced between B1-C1 and B2-C2 as shown in the figure. When C1 and C2 are held at temperature \( T_C \), the voltmeter reads a thermal emf \( E_2 \). Then, _________
A unity-gain negative-feedback control system has a loop-gain \( L(s) \) given by \[ L(s) = \frac{6}{s(s-5)} \] The closed-loop system is _________
The resistance of a pure copper wire of length 10 cm and diameter 1 mm is to be measured. The most suitable method from amongst the choices given below is _________.
A Hall sensor is based on the principle of _________
The output of a system \( y(t) \) is related to its input \( x(t) \) according to the relation \( y(t) = x(t) \sin(2\pi t) \). This system is _________
A signal \( x(t) \) is band-limited between 100 Hz and 200 Hz. A signal \( y(t) \) is related to \( x(t) \) as follows:
y(t) = x(2t - 5)
The statement that is always true is_________

A sinusoidal carrier wave with amplitude \( A_c \) and frequency \( f_c \) is amplitude modulated with a message signal \( m(t) \) having frequency \( 0<f_m \ll f_c \) to generate the modulated wave \( s(t) \) given by \[ s(t) = A_c[1 + m(t)]\cos(2\pi f_c t) \] The message signal that can be retrieved completely using envelope detection is _________

A periodic function \( f(x) \), with period 2, is defined as \[ f(x) = \begin{cases} -1 - x & \text{for } -1 \leq x&t;0 \\ 1 - x & \text{for } 0 \leq x \leq 1 \end{cases} \] The Fourier series of this function contains _________

A pneumatic nozzle-flapper system is conventionally used to convert _________
The input \( x(t) \) to a system is related to its output \( y(t) \) as
\[ \frac{d y(t)}{dt} + y(t) = 3x(t - 3)u(t - 3) \] \text{Here \( u(t) \) represents a unit-step function.}
\text{The transfer function of this system is _________}

The input-output relationship of an LTI system is given below. 

\( \text{For an input } x[n] \text{ shown below,} \) 

\( \text{the peak value of the output when } x[n] \text{ passes through } h \text{ is:} \)

Taking \( N \) as positive for clockwise encirclement, otherwise negative, the number of encirclements \( N \) of \( (-1, 0) \) in the Nyquist plot of \( G(s) = \frac{3}{s-1} \) is \(\underline{\hspace{2cm}}\).
 

The diode used in the circuit has a fixed voltage drop of 0.6 V when forward biased. A signal \( v_s \) is given to the ideal OpAmp as shown. When \( v_s \) is at its positive peak, the output \( (v_{OA}) \) of the OpAmp in volts is \(\underline{\hspace{2cm}}\). 

The transistor Q1 has a current gain \( \beta_1 = 99 \) and the transistor Q2 has a current gain \( \beta_2 = 49 \). The current \( I_{B2} \) in microampere is \(\underline{\hspace{2cm}}\). 

Let \( f(z) = \dfrac{1}{z^2 + 6z + 9} \) defined in the complex plane. The integral \( \oint_{c} f(z) \, dz \) over the contour of a circle \( c \) with center at the origin and unit radius is \(\underline{\hspace{2cm}}\).