GATE EC question library

The determinant of matrix $A$ is $5$ and the determinant of matrix B is $40$. The determinant of matrix $AB$ is ________

Let $X$ be a random variable which is uniformly chosen from the set of positive odd numbers less than $100$. The expectation, $E[X]$, is ________.

For $0 \leq t < \infty ,$ the maximum value of the function $f(t)= e^{-t}-2e^{-2t}$ occurs at

The value of $$\lim_{x\rightarrow \infty }(1 +\tfrac{1}{x})^{x}$$ is

If the characteristic equation of the differential equation $$\frac{\mathrm{d}^2 y}{\mathrm{dx}^2}+2\alpha \frac{\mathrm{d}y}{\mathrm{d} x}+y= 0$$ has two equal roots, then the value of $\alpha$ are

Norton’s theorem states that a complex network connected to a load can be replaced with an equivalent impedance

In the figure shown, the ideal switch has been open for a long time. If it is closed at t = 0, then the magnitude of the current (in mA) through the $4k \Omega$ resistor at $t= 0^{+}$ is ________.

A silicon bar is doped with donor impurities $N_{D}= 2.25 \times 10^{15} \text{atoms} / cm^{3}$. Given the intrinsic carrier concentration of silicon at $T = 300 \: K$ is $n_{i}= 1.5 \times 10^{10} cm^{-3}.$ Assuming complete impurity ionization, the equilibrium electron and hole concentrations are

An increase in the base recombination of a BJT will increase

In CMOS technology, shallow P-well or N-well regions can be formed using

The feedback topology in the amplifier circuit ( the base bias circuit is not shown for simplicity) in the figure is

In the differential amplifier shown in the figure, the magnitude of the common-mode and differential-mode gains are $A_{CM}$ and $A_{d},$ respectively. If the resistance $R_{E}$ is increased, then

A cascade connection of two voltage amplifier $A1$ and $A2$ is shown in the figure. The open-loop gain $A_{V0}$, input resistance $R_{in}$, and output resistance $R_{o}$ for A1 and A2 are as follows: $A1: A_{V0} = 10, R_{in} = 10k \Omega, R_{o} = 1k\Omega$ $A2: A_{V0} = 5, R_{in} = 5k \Omega, R_{o} =200\Omega$ The approximate overall voltage …

For an $n$-variable Boolean function, the maximum number of prime implicants is

The number of bytes required to represent the decimal number $1856357$ in packed BCD (Binary Coded Decimal) form is ___________.

In a half-subtractor circuit with $X$ and $Y$ as inputs, the Borrow $(M)$ and Difference $(N = X – Y)$ are given by

As FIR system is described by the system function $$H(z) = 1 + \frac{7}{2} z^{-1} + \frac{3}{2}z^{-2}$$. The system is

Let $x[n] = x[-n]$. Let $X(z)$ be the $z$-transform of $x[n]$. If $0.5 + j 0.25$ is a zero of $X(z)$, which one of the following must also be a zero of $x(z)$

Consider the periodic square wave in the figure shown. The ratio of the power in the $7^{th}$ harmonic to the power in the $5^{th}$ harmonic for this waveform is closest in value to ________.

The natural frequency of an undamped second-order system is $40$ rad/s. If the system is damped with a damping ratio $0.3$, the damped natural frequency in $rad/s$ is ___________.