GATE EC question library

In the circuit shown below, the silicon $npn$ transistor $Q$ has a very high value of $\beta.$ The required value of $R_{2}$ in $k\Omega$ to produce $I_{C} = 1\: mA$ is

Let $U$ and $V$ be two independent and identically distributed random variables such that $P(U=+1)=P(U=-1) = \dfrac{1}{2}.$ The entropy $H(U + V)$ in bits is

Bits $1$ and $0$ are transmitted with equal probability. At the receiver, the pdf of the respective received signals for both bits are as shown below. If the detection threshold is $1,$ the $BER$ will be

Bits $1$ and $0$ are transmitted with equal probability. At the receiver, the pdf of the respective received signals for both bits are as shown below. The optimum threshold to achieve minimum bit error rate $(BER)$ is

Consider the following figure The current $I_{S}$ in $\text{Amps}$ in the voltage source, and voltage $V_{S}$ in Volts across the current source respectively, are

Consider the following figure The current in the $1\Omega$ resistor in $\text{Amps}$ is

A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ denote incident, reflected, and transmitted electric field vectors associated with the wave. The angle of incidence $\theta_{i}$ and the expression for $\vec{E_{i}}$ are

A monochromatic plane wave of wavelength $\lambda = 600 \mu m$ is propagating in the direction as shown in the figure below. $\vec{E_{i}},\vec{E_{r}},$ and $\vec{E_{t}}$ denote incident, reflected, and transmitted electric field vectors associated with the wave. The expression for $\vec{E_{r}}$ is

The state diagram of a system is shown below. A system is described by the state-variable equations $$\dot{X}= AX+Bu;\:\: y = CX+Du$$ The state-variable equations of the system shown in the figure above are

The state diagram of a system is shown below. A system is described by the state-variable equations $$\dot{X}= AX+Bu;\:\: y = CX+Du$$ The state transition matrix $e^{At}$ of the system shown in the figure above is

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