GATE EC question library

The circuit shown is a

Let $y[n]$ denote the convolution of $h[n]$ and $g[n]$, where $h[n]=(\frac{1}{2})^nu[n]$ and $g[n]$ is a casual sequence. If $y[0]=1$ and $y[1]=\frac{1}{2}$, then $g[1]$ equals

The state transition diagram for the logic circuit shown is

The voltage gain $A_v$ of the circuit shown below is

If $V_A-V_B=6\:V$, then $V_C-V_D$ is

The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1,6]$ is

Given that $A=\begin{bmatrix} -5 &-3 \\ 2 &0\end{bmatrix}$ and $I=\begin{bmatrix} 1 & 0 \\ 0 &1\end{bmatrix}$, the value of $A^3$ is

With $10\:V$ dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed: $1\: \Omega$ connected at port B draws a current of $3\:A$ $2.5\: \Omega$ connected at port B draws a current of $2\:A$ With $10\: V$ dc connected at port A, the current drawn by $7\:\Omega$ connected at port B is

With $10\:V$ dc connected at port A in the linear nonreciprocal two-port network shown below, the following were observed: $1\: \Omega$ connected at port B draws a current of $3\:A$ $2.5\: \Omega$ connected at port B draws a current of $2\:A$ For the same network, with $6\: V$ dc connected at port A, $1\:\Omega$ connected at port B draws …

In the three dimensional view of a silicon n-channel MOS transistor shown below, $\delta=20\:nm$. The transistor is of width $1\: \mu m$. The depletion width formed at every p-n junction is $10\:nm$. The relative permittivities of $Si$ and $SiO_2$, respectively, are $11.7$ and $3.9$, and $\varepsilon_0=8.9 \times 10^{-12} \: F/m$. The …

In the three dimensional view of a silicon n-channel MOS transistor shown below, $\delta=20\:nm$. The transistor is of width $1\: \mu m$. The depletion width formed at every p-n junction is $10\:nm$. The relative permittivities of $Si$ and $SiO_2$, respectively, are $11.7$ and $3.9$, and $\varepsilon_0=8.9 \times 10^{-12} \: F/m$. The …

An infinitely long uniform solid wire of radius $a$ carries a uniform dc current of density $\overrightarrow{j}$. The magnetic field at a distance $r$ from the center of the wire is proportional to

An infinitely long uniform solid wire of radius $a$ carries a uniform dc current of density $\overrightarrow{j}$. A hole of radius $b$ (b < a) ia now drilled along the length of the wire at a distance $d$ from the center of the wire as shown below. The magnetic field inside the hole is

The transfer function of a compensator is given as $$G_c(s)=\frac{s+a}{s+b}$$ $G_c(s)$ is a lead compensator if

The transfer function of a compensator is given as $$G_c(s)=\frac{s+a}{s+b}$$ The phase of the above lead compensator is maximum at

The logic function implemented by the circuit below is (ground implies a logic $\text{“0”})$

The output $\mathrm{Y}$ in the circuit below is always $\text{“1"}$ when

Which of the following options is the closest in meaning to the word below: Circuitous

Choose the most appropriate word from the options given below to complete the following sentence: His rather casual remarks on politics ____________ his lack of seriousness about the subject.

Hari (H), Gita (G), Irfan (I), and Saira (S) are siblings (i.e. brothers and sisters). All were born on $1^{st}$ January. The age difference between any two successive siblings (that is born one after another) is less than $3$ years. Given the following facts: Hari's age $+$ Gita's age $>$ Irfan's age $+$ Saira's age. The age difference between …