GATE EC question library

If $(1.001)^{1259}=3.52$ and $(1.001)^{2062}=7.85,$ then $(1.001)^{3321}=?$

Choose the most appropriate alternative from the options given below to complete the following sentence: If the tired soldier wanted to lie down, he _______ the mattress out on the balcony.

Choose the most appropriate word from the options given below to complete the following sentence: Given the seriousness of the situation that he had to face, his ___ was impressive.

Which one of the following options is the closest in meaning to the word given below? Latitude

One of the parts $(A, B, C, D)$ in the sentence given below contains an ERROR. Which one of the following is INCORRECT? I requested that he should be given the driving test today instead of tomorrow.

One of the legacies of the Roman legions was discipline. In the legions, military law prevailed and discipline was brutal. Discipline on the battlefield kept units obedient, intact and fighting, even when the odds and conditions were against them. Which one of the following statements best sums up the meaning of the above passage?

Raju has $14$ currency notes in his pocket consisting of only Rs. $20$ notes and Rs. $10$ notes. The total money value of the notes is Rs. $230$. The number of Rs. $10$ notes that Raju has is

There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number of weighings required to identify the heavier bag is

The data given in the following table summarizes the monthly budget of an average household. …

$A$ and $B$ are friends. They decide to meet between $1:00$pm and $2:00$ pm on a given day. There is a condition that whoever arrives first will not wait for the other for more than $15$ minutes. The probability that they will meet on that day is

The current $i_b$ through the base of a silicon $npn$ transistor is $1+0.1\cos(10000\pi t)\:mA$. At $300\:K$, the $r_\pi$ in the small signal model of the transistor is

The power spectral density of a real process $X(t)$ for positive frequencies is shown below. The values of $E[X^2(t)]$ and $\mid E[X(t)] \mid$, respectively, are

In a baseband communications link, frequencies upto $3500\:Hz$ are used for signaling. Using a raised cosine pulse with $75\%$ excess bandwidth and for no inter-symbol interference, the maximum possible signaling rate in the symbols per second is

A plane wave propagating in air with $\overrightarrow{E}=(8\hat{a}_x+6\hat{a}_y+5\hat{a}_z)e^{j(\omega t+3x-4y)}\:V/m$ is incident on a perfectly conducting slab positioned at $x\le0$ . The $\overrightarrow{E}$ field of the reflected wave is

The electric field of a uniform plane electromagnetic wave in free space, along the positive $x$ direction, is given by $\overrightarrow{E}=10(\hat{a}_y+j\hat{a}_z)e^{-j\:25x}$. The frequency and polarization of the wave, respectively, are

Consider the given circuit. In the circuit, the race around

The output $Y$ of a $2-\text{bit}$ comparator is logic $1$ whenever the $2-\text{bit}$ input $A$ is greater than the $2-\text{bit}$ input $B$. The number of combinations for which the output is logic $1$, is

The $i-v$ characteristics of the diode in the circuit given below are $$i = \begin{cases} \frac{v-0.07}{500}\:A, & v\ge0.7\:V \\ \:\:\:\:\:\:\:\:0\:A, & v \lt 0.7\:V \end{cases}$$ The current in the circuit is

In the following figure, $C_1$ and $C_2$ are ideal capacitors. $C_1$ has been charged to $12\:V$ before the ideal switch $S$ is closed at $t=0$. The current $i(t)$ for all $t$ is

The average power delivered to an impedance $(4-j3)\:\Omega$ by a current $5\cos(100\pi t+100)\:A$ is