GATE EC question library

Consider a system of linear equations: $$x-2y+3z=-1, \\ x-3y+4z=1, \text{ and } \\ -2x+4y-6z=k.$$ The value of $k$ for which the system has infinitely many solutions is ___________

A function $f(x)=1-x^2+x^3$ is defined in the closed interval $[-1,1]$. The value of $x$, in the open interval $(-1,1)$ for which the mean value theorem is satisfied, is

Suppose $A$ and $B$ are two independent events with probabilities $P(A) \neq 0$ and $P(B) \neq 0$. Let $\overline{A}$ and $\overline{B}$ be their complements. Which one of the following statements is FALSE?

Let $z=x+iy$ be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction. Which one of the following statements is NOT TRUE?

The value of $p$ such that the vector $\begin{bmatrix} 1 \\ 2 \\ 3 \end{bmatrix}$ is an eigenvector of the matrix $\begin{bmatrix} 4 & 1 & 2 \\ p & 2 & 1 \\ 14 & -4 & 10 \end{bmatrix}$ is _________.

In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the capacitor is ____________.

In the network shown in the figure, all resistors are identical with $R = 300 \Omega$. The resistance $R_{ab}$ (in $\Omega$) of the network is __________.

In the given circuit, the values of $V_1$ and $V_2$ respectively are

A region of negative differential resistance is observed in the current voltage characteristics of a silicon PN junction if

A silicon sample is uniformly doped with donor type impurities with a concentration of $10^{16} / cm^3$. The electron and hole mobilities in the sample are $1200 \: cm^2/V-s$ and $400 \: cm^2/V-s$ respectively. Assume complete ionization of impurities. The charge of an electron is $1.6 \times 10^{-19} \:C$. The resistivity of the sample (in …

For the circuit with ideal diodes shown in the figure, the shape of the output $v_{\text{out}}$ for the given sine wave input $v_{\text{in}}$ will be

In the circuit shown below, the Zener diode is ideal and the Zener voltage is $6$ V. The output voltage $V_o$ (in volts) is ________.

In the circuit shown, the switch SW is thrown from position $A$ to position $B$ at time $t=0$. The energy (in $\mu J$) taken from the $3$ V source to charge the $0.1 \: \mu F$ capacitor from $0$ V t $3$ V is

In an 8085 microprocessor, the shift registers which store the result of an addition and the overflow bit are, respectively

A $16$ Kb ($=16,384$ bits) memory array is designed as a square with an aspect ratio of one (number of rows is equal to the number of columns). The minimum number of address lines needed for the row decoder is ___________

Consider a four bit $D$ to $A$ converter. The analog value corresponding to digital signals of values $0000$ and $0001$ are $0$ V and $0.0625$ V respectively. The analog value (in Volts) corresponding to the digital signal $1111$ is _________

The result of the convolution $x(-t) * \delta (-t-t_0)$ is

The waveform of a periodic signal $x(t)$ is shown in the figure. A signal $g(t)$ is defined by $g(t) = x \big( \frac{t-1}{2} \big)$. The average power of $g(t)$ is ________

Negative feedback in a closed-loop control system $\textbf{ DOES NOT}$

A unity negative feedback system has the open-loop transfer function $G(s) = \frac{K}{s(s+1)(s+3)}$. The value of the gain $K (>0)$ at which the root locus crosses the imaginary axis is ________