GATE EC question library

A binary communication system makes use of the symbols “zero” and “one”. There are channel errors. Consider the following events: …

The parallel-plate capacitor shown in the figure has movable plates. The capacitor is charged so that the energy stored in it is $E$ when the plate separation is $d$. The capacitor is then isolated electrically and the plate are moved such that the plate separation becomes $2d$. At this new plate separation, what is the energy stored in the capacitor, …

A lossless microstrip transmission line consists of a trace of width $w$. It is drawn over a pratically infinite ground plane and is separated by a dielectric slab of thickness $t$ and relative permittivity $\varepsilon _{r}> 1.$ The inductance per unit length and the characteristic impedance of this line are $L$ and $Z_{0}$, respectively. Which …

A microwave circuit consisting of lossless transmission lines $T_{1}$ and $T_{2}$ is shown in the figure. The plot shows the magnitude of the input reflection coefficient $\Gamma$ as a function of frequency $f$. The phase velocity of the signal in the transmission lines is $2\times 10^{8}$ $m/s$. The length $L$ (in meters) of $T_{2}$ is …

A positive charge $q$ is placed at $x=0$ between two infinte metal plates placed at $x=-d$ and at $x=+d$ respectively. The metal plates lie in the $yz$ plane. The charge is at rest at $t=0$, when a voltage $+V$ is applied to the plate at $-d$ and voltage $-V$ is applied to the plate at $x=+d$. Assume that the quantity of the charge $q$ …

An apple costs Rs.$10$. An onion costs Rs.$8$. Select the most suitable sentence with respect to grammar and usage.

The Buddha said, “Holding on to anger is like grasping a hot coal with the intent of throwing it at someone else; you are the one who gets burnt. ” Select the word below which is closest in meaning to the word underlined above.

$M$ has a son $Q$ and a daughter $R.$ He has no other children. $E$ is the mother of $P$ and daughter-in-law of $M.$ How is $P$ related to $M?$

The number that least fits this set$:(324,441,97$ and $64)$ is

It takes $10$s and $15$s, respectively, for two trains traveling at a different constant speeds to completely pass a telegraph post. The length of the first train is $120$ m and that of the second train is $150$ m. The magnitude of the difference in the speeds of the two trains (in m/s) is _________

The velocity $V$ of a vehicle along a straight line is measured in m/s and plotted as shown with respect to time in seconds. At the end of the $7$ seconds, how much will the odometer reading increase by (in m)?

The overwhelming number of people infected with rabies in India has been flagged by the World Health Organization as a source of concern. It is estimated that inoculating $70\%$ of pets and stray dogs against rabies can lead to a significant reduction in the number of people infected with rabies. Which of the following can be logically inferred from the …

A flat is shared by four first-year undergraduate students. They agreed to allow the oldest of them to enjoy some extra space in the flat. Manu is two months older than Sravan, who is three months younger than Trideep. Pavan is one month older than Sravan. Who should occupy the extra space in the flat?

Find the area bounded by the lines $3x+2y=14$, $2x-3y=5$ in the first quadrant.

A straight line is fit to a data set $(\text{ln }x,y).$ This line intercepts the abscissa at $\text{ln } x =0.1$ and has a slope of $-0.02$. What is the value of $y$ at $x=5$ from the fit?

Consider a $2\times2$ sqaure matrix $$\textbf{A}= \begin{bmatrix} \sigma &x\\ \omega &\sigma \end{bmatrix},$$ where $x$ is unknown. If the eigen values of the matrix $\textbf{A}$ are $(\sigma + j\omega)$ and $(\sigma - j\omega)$, then $x$ is equal to

For $f(z)= \large\frac{\sin(z)}{z^2}$, the residue of the pole at $z = 0$ is _______

The probability of getting a “head” in a single toss of a biased coin is $0.3$. The coin is tossed repeatedly till a head is obtained. If the tosses are independent, then the probability of getting “head” for the first time in the fifth toss is _______

The integral $\int\limits_{0}^{1}\large\frac{dx}{\sqrt{(1-x)}}$ is equal to _______

Consider the first order initial value problem $$y’= y+2x-x^2 ,\ y(0)=1,\ (0 \leq x < \infty)$$ with exact solution $y(x) = x^2 + e^x$. For $x = 0.1$, the percentage difference between the exact solution and the solution obtained using a single iteration of the second-order Runga-Kutta method with step-size $h=0.1$ is _______