GATE EC question library

The complex envelope of the bandpass signal $x(t)=-\sqrt{2}\left(\dfrac{\sin (\pi t/5)}{\pi t/5}\right)\sin (\pi t – \dfrac{\pi}{4}),$ centered about $f=\dfrac{1}{2}\:Hz,$ is

A random binary wave $y(t)$ is given by $$y(t) = \sum_{n = -\infty}^{\infty}X_{n}\:p(t-nT-\phi)$$ where $p(t)=u(t)-u(t-T),u(t)$ is the unit step function and $\phi$ is an independent random variable with uniform distribution in $[0,T].$The sequence $\{X_{n}\}$ consist of independent and identically distributed binary valued random variables with …

Consider the $3\:m$ long lossless air-filled transmission line shown in the figure. It has a characteristic impedance of $120\pi\: \Omega,$ is terminated by a short circuit, and is excited with a frequency of $37.5\: MHz.$ What is the nature of the input impedance $(Z_{in})?$

A $200\: m$ long transmission line having parameters shown in the figure is terminated into a load ܴ$R_{L}$. The line is connected to a $400\: V$ source having source resistance $R_{S}$ through a switch, which is closed at $t = 0.$ The transient response of the circuit at the input of the line $(z = 0)$ is also drawn in the figure. The value of …

A coaxial capacitor of inner radius $1\: mm$ and outer radius $5\: mm$ has a capacitance per unit length of $172\: pF/m.$ If the ratio of outer radius to inner radius is doubled, the capacitance per unit length $\text{(in}\: pF/m)$ is ________.

Choose the most appropriate phrase from the options given below to complete the following sentence. The aircraft _________ take off as soon as its flight plan was filed.

Read the statements: All women are entrepreneurs. Some women are doctors. Which of the following conclusions can be logically inferred from the above statements?

Choose the most appropriate word from the options given below to complete the following sentence. Many ancient cultures attributed disease to supernatural causes. However, modern science has largely helped _________ such notions.

The statistics of runs scored in a series by four batsmen are provided in the following table. Who is the most consistent batsman of these four? …

What is the next number in the series? $12$ $35$ $81$ $173$ $357$ ________,

Find the odd one from the following group: $W,E,K,O \qquad I,Q,W,A \qquad F,N,T,X \qquad N,V,B,D$

For submitting tax returns, all resident males with annual income below $Rs$ $10$ lakh should fill up Form $P$ and all resident females with income below $Rs$ $8$ lakh should fill up Form $Q.$ All people with incomes above $Rs$ $10$ lakh should fill up Form $R,$ except non residents with income above $Rs$ $15$ lakhs, who should fill up …

A train that is $280$ meters long, traveling at a uniform speed, crosses a platform in $60$ seconds and passes a man standing on the platform in $20$ seconds. What is the length of the platform in meters?

The exports and imports (in crores of $Rs$.) of a country from $2000$ to $2007$ are given in the following bar chart. If the trade deficit is defined as excess of imports over exports, in which year is the trade deficit $\frac{1}{5}$th of the exports?

You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is

For matrices of same dimension $M, N$ and scalar $c$, which one of these properties DOES NOT ALWAYS hold?

In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has a sibling is ________.

$C$ is a closed path in the $z$-plane given by $\mid z \mid = 3.$ The value of the integral $\displaystyle{}\oint_{C}\bigg(\dfrac{z^{2}-z+4j}{z+2j}\bigg)dz$ is

A real $(4 \times 4)$ matrix $A$ satisfies the equation $A^{2} = I$, where $I$ is the $(4 \times 4)$ identity matrix. The positive eigen value of $A$ is ______.

Let $X_{1},X_{2},$ and $X_{3}$ be independent and identically distributed random variables with the uniform distribution on $[0,1].$ The probability $P\{X_{1}\: \text{is the largest}\}$ is ________.