GATE EC question library

The first two rows in the Routh table for the characteristic equation of a certain closed-loop control system are given as $$\begin{array}{|c|cc} \hline s^3 & 1 &(2K+3) \\ s^2 & 2K & 4 \end{array}$$ The range of $K$ for which the system is stable is

A second-order linear time-invariant system is described by the following state equations $$\frac{d}{dt}x_1(t)+2x_1(t)=3u(t)$$ $$\frac{d}{dt}x_2(t)+x_2(t)=u(t)$$ where $x_1(t)$ and $x_2(t)$ are the two state variables and $u(t)$ denotes the input. If the output $c(t)=x_1(t)$, then the system is

The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as $$G(s)=\frac{K(s+2)}{s^2+2s+2}\;\text{and}\hspace{0.3cm}H(s)=1,$$ respectively. If the variable parameter $K$ is real positive, then the location of the breakaway point on the root locus diagram of the system is …

A wide sense stationary random process $X(t)$ passes through the LTI system shown in the figure. If the autocorrelation function of $X(t)$ is $R_X(\tau)$, then the autocorrelation function $R_Y(\tau)$ of the output $Y(t)$ is equal to

A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of $4.0\:kHz$ and two-sided noise power spectral density ${\large\frac{\eta}{2}}=2.5\times10^{-5}Watt\:per\:Hz$. If information at the rate of $52\:kbps$ is to be transmitted over this channel with arbitrarily small bit error rate, then the minimum bit-energy $E_b$ …

The bit error probability of a memoryless binary symmetric channel is $10^{-5}$. If $10^5$ bits are sent over this channel, then the probability that not more than one bit will be in error is _______

Consider an air-filled rectangular waveguide with dimensions $a=2.286\:cm$ and $b=1.016\:cm$. At $10 \:GHz$ operating frequency, the value of the propagation constant (per meter) of the corresponding propagation mode is _______

Consider an air-filled rectangular waveguide with dimensions $a=2.286\:cm$ and $b=1.016\:cm$. The increasing order of the cut-off frequencies for different modes is

A radar operating at $5\:GHz$ uses a common antenna for transmission and reception. The antenna has a gain of $150$ and is aligned for maximum directional radiation and reception to a target $1\:km$ away having radar cross-section of $3\:m^2$. If it transmits $100\:kW$, then the received power (in $\mu W)$ is _______

Consider the charge profile shown in the figure. The resultant potential distribution is best described by

Choose the most appropriate word from the options give below to complete the following sentence. The principal presented the chief guest with a __________, as token of appreciation.

Choose the appropriate word\phrase, out of the four options given below, to complete the following sentence : Frogs_______

Choose the word most similar in meaning to the given word: Educe

Operators $\square,$ $\Diamond$ and $\rightarrow$ are defined by: $a\,\square\,b=\frac{a+b}{a-b};\, a\,\Diamond, b=\frac{a+b}{a-b};$ $a\,\rightarrow\, b=ab.$ Find the value of $(66\,\square\, 6)\rightarrow(66\,\Diamond, 6).$

If $\log_{x}{(\frac{5}{7})}=\frac{-1}{3},$ then the value of $x$ is

The following question presents a sentence, part of which is underlined. Beneath the sentence, you find four ways of phrasing the underlined part. Following the requirements of the standard written English, select the answer that produces the most effective sentence. Tuberculosis, together with its effects, ranks one of the leading causes of death in India.

Read the following paragraph and choose the correct statement. Climate change has reduced human security and threatened human well being. An ignored reality of human progress is that human security largely depends upon environmental security. But on the contrary, human progress seems contradictory to environmental security. To keep up both at the required …

Fill in the missing value

A cube of side $3$ units is formed using a set of smaller cubes of side $1$ unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.

Humpty Dumpty sits on a wall every day while having lunch. The wall sometimes breaks. A person sitting in the wall falls if the wall breaks. Which one of the statement below is logically valid and can be inferred from the above sentences?