GATE EC question library

The outputs of the two flip-flops $Q1$, $Q2$ in the figure shown are initialized to $0,0$. The sequence generated at $Q1$ upon application of clock signal is

For the $8085$ microprocessor, the interfacing circuit to input $8$-bit digital data $( DI_{0}-DI_{7})$ from an external device is shown in the figure. The instruction for correct data transfer is

Consider a discrete-time signal $$x[n]= \begin{cases} n & \text{for } 0\leq n\leq 10 \\ 0 & \text{otherwise }\end{cases}$$ If $y[n]$ is the convolution of $x[n]$ with itself, the value of $y[4]$ is _______ .

The input-output relationship of a causal stable LTI system is given as $$y[n] = \alpha \: y[n-1] + \beta \: x[n]$$. If the impulse response $h[n]$ of this system satisfies the condition $\sum_{n=0}^{\infty}h[n]= 2$, the relationship between $\alpha$ and $\beta$ is

The value of the integral $\int_{-\infty }^{\infty } \text{sinc}^{2}(5t) \: dt$ is _______.

An unforced linear time invariant (LTI) system is represented by $$\begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} -1 & 0 \\ 0& -2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}$$ If the initial conditions are $x_1(0)= 1$ and $x_2(0)= -1$, the solution of the state equation is

The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure. If the system is connected in a unity negative feedback configuration, the steady state error of the closed loop system, to a unit ramp input, is _________.

Consider the state space system expressed by the signal flow diagram shown in the figure. The corresponding system is

The input to a $1$ – bit quantizer is a random variable $X$ with pdf $f_{X}( x )= 2e^{-2x}$ for $x\geq 0$ and $f_{X} (x )= 0$ for $x< 0$. For outputs to be of equal probability, the quantizer threshold should be ______.

Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms $s_{1}( t )= \alpha \cos 2\pi f_1 t$, and $s_2(t) = \alpha \cos 2 \pi f_2 t$ where $\alpha = 4$ mV. Assume an AWGN channel with two-sided noise power spectral density $\frac{N_o}{2}= 0.5 \times 10^{-12}$ W/Hz. Using an optimal receiver and the relation …

The power spectral density of a real stationary random process $X(t)$ is given by $$S_X (f) = \begin{cases} \frac{1}{W}, & \mid f \mid \leq W \\ 0, & \mid f \mid > W \end{cases}$$ The value of the expectation $E \left [ \pi X(t)X\left ( t-\frac{1}{4W} \right ) \right ]$ is __________.

In the figure, $M(f)$ is the Fourier transform of the message signal $m(t)$ where $A = 100$ Hz and $B = 40$ Hz. Given $v(t)= \cos (2\pi f_{c}t)$ and $w(t)= \cos (2\pi (f_{c}+A)t)$, where $f_{c}>A$. The cutoff frequencies of both the filters are $f_{c}$. The bandwidth of the signal at the output of the modulater (in Hz) is ______.

If the electric field of a plane wave is $$\overrightarrow{E}(z,t)= \hat{x}3 \cos(\omega t-kz+30^{\circ}) – \hat{y} 4 \sin(\omega t – kz+45^{\circ}) (mV/m),$$ the polarization state of the plane wave is

In the transmission line shown, the impedance $Z_{\text{in}}$ (in ohms) between node A and the ground is _________.

For a rectangular waveguide of internal dimension $a\times b \: (a> b)$, the cut-off frequency for the $TE_{11}$ mode is the arithmetic mean of the cut-off frequencies for $TE_{10}$ mode and $TE_{20}$ mode. If $a= \sqrt{5}$ cm, the value of $b$ (in cm) is ______.

“India is a country of rich heritage and cultural diversity.” Which one of the following facts best supports the claim made in the above sentence?

The value of one U.S. dollar is $65$ Indian Rupees today, compared to $60$ last year. The Indian Rupee has ____________.

'Advice' is ________________.

The next term in the series $81, 54, 36, 24, \dots$ is ________

In which of the following options will the expression $P < M$ be definitely true?