Recent questions tagged gate2013-ec

What is the chance that a leap year, selected at random, will contain $53$ Saturdays?$2/7$$3/7$$1/7$$5/7$

Statement: There were different streams of freedom movements in colonial India carried out by the moderates, liberals, radicals, socialists, and so on.Which one of the fo...

Find the sum to $n$ terms of the series $10+84+ 734 +\dots $$\frac{9(9^n+1)}{10}+1$$\frac{9(9^n-1)}{8}+1$$\frac{9(9^n-1)}{8}+n$$\frac{9(9^n-1)}{8}+n^2$

The set of values of $p$ for which the roots of the equation $3x^2+2x+p(p-1)=0$ are of opposite sign is$(-\infty ,0)$$(0,1)$$(1,\infty )$$(0,\infty )$

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 $e^{At}$ ...

They were requested not to $\textbf{quarrel}$ with others.Which one of the following options is the closest in meaning to the word $\textbf{quarrel}$?make outcall outdig ...

Complete the sentence:Dare _______________ mistakes.committo commitcommittedcommitting

Statement: You can always give me a ring whenever you need.Which one of the following is the best inference from the above statement?Because I have a nice caller tune.Bec...

Choose the grammatically CORRECT sentence:Two and two add four.Two and two become four.Two and two are four.Two and two make four.

A car travels $8 \: km$ in the first quarter of an hour, $6\: km$ in the second quarter and $16\: km$ in the thirdquarter. The average speed of the car in $km$ per hour ...

In the summer of $2012,$ in New Delhi, the mean temperature of Monday to Wednesday was $41^{\circ}C$ and of Tuesday to Thursday was $43^{\circ}C$. If the temperature on T...

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 threshol...

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 sy...

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$13, − 2...

Consider the following figure The current in the $1\Omega$ resistor in $\text{Amps}$ is$2$$3.33$ $10$ $12$

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 $\vec{E_{t}}$ ...

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 $\vec{E_{t}}$ ...

A voltage $1000 \sin\omega t\:\: \text{Volts}$ is applied across $YZ.$ Assuming ideal diodes, the voltage measured across $WX$ in $\text{Volts},$ is $\sin \omega t$$(\sin...

In the circuit shown below, $Q_{1}$ has negligible collector-to-emitter saturation voltage and the diode drops negligible voltage across it under forward bias. If $V_{cc}...

Bits $1$ and $0$ are transmitted with equal probability. At the receiver, the pdf of the respective receivedsignals for both bits are as shown below.If the detection thre...

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$\frac{3}{4} ...

There are four chips each of $1024\:\text{bytes}$ connected to a $16\:\text{bit}$ address bus as shown in the figure below. $RAMs\: 1, 2, 3$ and $4$ respectively are mapp...

Three capacitors $C_{1}, C_{2}$ and $C_{3}$ whose values are $10\mu F, 5\mu F,$ and $2\mu F$ respectively, have breakdown voltages of $10V, 5V,$ and $2V$ respectively. Fo...

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$2...

Consider two identically distributed zero-mean random variables $U$ and $V.$ Let the cumulative distribution functions of $U$ and $2V$ be $F(x)$ and $G(x)$ respectively. ...

A system is described by the differential equation $\dfrac{\mathrm{d}^{2} y}{\mathrm{d} x} + 5\dfrac{\mathrm{d}y }{\mathrm{d} x} + 6y(t) = x(t).$Let $x(t)$ be a rectangul...

The signal flow graph for a system is given below. The transfer function $\dfrac{Y(s)}{U(s)}$ for this system is $\frac{s+1}{5s^{2}+6s+2} \\$$\frac{s+1}{s^{2}+6s+2} \\$$\...

A system described by a linear, constant coefficient, ordinary, first order differential equation has an exact solution given by $y(t)$ for $t>0,$ when the forcing functi...

In the circuit shown below the $\text{op-amps}$ are ideal. Then $V_{\text{out}}$ in $\text{Volts}$ is$4$$6$$8$$10$

The ac schematic of an $NMOS$ common-source stage is shown in the figure below, where part of the biasing circuits has been omitted for simplicity. For the $n$-channel $...