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Recent questions tagged numerical-answers

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282
GATE ECE 2014 Set 4 | GA Question: 5
In a sequence of $12$ consecutive odd numbers, the sum of the first $5$ numbers is $425$. What is the sum of the last $5$ numbers in the sequence?
In a sequence of $12$ consecutive odd numbers, the sum of the first $5$ numbers is $425$. What is the sum of the last $5$ numbers in the sequence?
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283
GATE ECE 2014 Set 4 | Question: 2
The magnitude of the gradient for the function $f(x,y,z) = x^2 +3y^2 +z^3$ at the point $(1,1,1)$ is ___________.
The magnitude of the gradient for the function $f(x,y,z) = x^2 +3y^2 +z^3$ at the point $(1,1,1)$ is ___________.
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284
GATE ECE 2014 Set 4 | Question: 3
Let $X$ be a zero mean unit variance Gaussian random variable. $E[ \mid X \mid ]$ is equal to __________
Let $X$ be a zero mean unit variance Gaussian random variable. $E[ \mid X \mid ]$ is equal to __________
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285
GATE ECE 2014 Set 4 | Question: 5
The directional derivative of $f(x,y)= \frac{xy}{\sqrt{2}} (x+y)$ at $(1,1)$ in the direction of the unit vector at an angle of $\frac{\pi}{4}$ with $y$-axis, is given by _________.
The directional derivative of $f(x,y)= \frac{xy}{\sqrt{2}} (x+y)$ at $(1,1)$ in the direction of the unit vector at an angle of $\frac{\pi}{4}$ with $y$-axis, is given by...
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286
GATE ECE 2014 Set 4 | Question: 7
The magnitude of current (in mA) through the resistor $R_2$ in the figure shown is __________
The magnitude of current (in mA) through the resistor $R_2$ in the figure shown is __________
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287
GATE ECE 2014 Set 4 | Question: 10
The cut-off wavelength (in $\mu m$) of light that can be used for intrinsic excitation of a semiconductor material of bandgap $E_g = 1.1 \: eV$ is ______________
The cut-off wavelength (in $\mu m$) of light that can be used for intrinsic excitation of a semiconductor material of bandgap $E_g = 1.1 \: eV$ is ______________
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289
GATE ECE 2014 Set 4 | Question: 19
The sequence $x[n] = 0.5^n \: u[n]$, where $u[n]$ is the unit step sequence, is convolved with itself to obtain $y[n]$. Then $\Sigma_{n= -\infty}^{+ \infty} y[n]$ is _________.
The sequence $x[n] = 0.5^n \: u[n]$, where $u[n]$ is the unit step sequence, is convolved with itself to obtain $y[n]$. Then $\Sigma_{n= -\infty}^{+ \infty} y[n]$ is ____...
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290
GATE ECE 2014 Set 4 | Question: 23
In a double side-band (DSB) full carrier AM transmission system, if the modulation index is doubled, then the ratio of total sideband power to the carrier power increases by a factor of __________.
In a double side-band (DSB) full carrier AM transmission system, if the modulation index is doubled, then the ratio of total sideband power to the carrier power increases...
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292
GATE ECE 2014 Set 4 | Question: 26
With initial values $y(0) =y’(0)=1$, the solution of the differential equation $\frac{d^2y}{dx^2}+4 \frac{dy}{dx}+4y=0$ at $x=1$ is ________
With initial values $y(0) =y’(0)=1$, the solution of the differential equation $$\frac{d^2y}{dx^2}+4 \frac{dy}{dx}+4y=0$$ at $x=1$ is ________
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294
GATE ECE 2014 Set 4 | Question: 31
In the circuit shown in the figure, the value of $v_0(t)$ (in Volts) for $t \to \infty$ is ___________
In the circuit shown in the figure, the value of $v_0(t)$ (in Volts) for $t \to \infty$ is ___________
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295
GATE ECE 2014 Set 4 | Question: 32
The equivalent resistance in the infinite ladder network shown in the figure, is $R_e$. The value of $R_e/R$ is __________
The equivalent resistance in the infinite ladder network shown in the figure, is $R_e$.The value of $R_e/R$ is __________
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299
GATE ECE 2014 Set 4 | Question: 39
For the common collector amplifier shown in the figure, the BJT has high $\beta$, negligible $V_{CE(sat)}$, and $V_{BE}=0.7 \: V$. The maximum undistorted peak-to-peak output voltage $v_o$ (in Volts) is __________
For the common collector amplifier shown in the figure, the BJT has high $\beta$, negligible $V_{CE(sat)}$, and $V_{BE}=0.7 \: V$. The maximum undistorted peak-to-peak ou...
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302
GATE ECE 2014 Set 4 | Question: 47
Consider a transfer function $G_p(s) = \frac{ps^2+3ps-2}{s^2+(3+p)s+(2-p)}$ with $p$ a positive real parameter. The maximum value of $p$ until which $G_p$ remains stable is ___________.
Consider a transfer function $G_p(s) = \frac{ps^2+3ps-2}{s^2+(3+p)s+(2-p)}$ with $p$ a positive real parameter. The maximum value of $p$ until which $G_p$ remains stable...
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304
GATE ECE 2014 Set 4 | Question: 50
Consider the $Z$-channel given in the figure. The input is $0$ or $1$ with equal probability. If the output is $0$, the probability that the input is also $0$ equals ___________
Consider the $Z$-channel given in the figure. The input is $0$ or $1$ with equal probability.If the output is $0$, the probability that the input is also $0$ equals _____...
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306
GATE ECE 2014 Set 4 | Question: 53
The electric field (assumed to be one-dimensional) between two points $A$ and $B$ is shown. Let $\psi _A$ and $\psi _B$ be the electrostatic potentials at $A$ and $B$, respectively. The value of $\psi _B – \psi _A$ in Volts is ____________
The electric field (assumed to be one-dimensional) between two points $A$ and $B$ is shown. Let $\psi _A$ and $\psi _B$ be the electrostatic potentials at $A$ and $B$, re...
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307
GATE ECE 2014 Set 4 | Question: 54
Gven $\overrightarrow{F} = z \hat{a}_x + x \hat{a}_y + y \hat{a}_z$. If $S$ represents the portion of the sphere $x^2 +y^2+z^2=1$ for $z \geq 0$, then $\int _s \nabla \times \overrightarrow{F} \cdot \overrightarrow{ds}$ is __________.
Gven $\overrightarrow{F} = z \hat{a}_x + x \hat{a}_y + y \hat{a}_z$. If $S$ represents the portion of the sphere $x^2 +y^2+z^2=1$ for $z \geq 0$, then $\int _s \nabla \ti...
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309
GATE ECE 2014 Set 3 | GA Question: 8
A man can row at $8$ $km$ per hour in still water. If it takes him thrice as long to row upstream, as to row downstream, then find the stream velocity in $km$ per hour.
A man can row at $8$ $km$ per hour in still water. If it takes him thrice as long to row upstream, as to row downstream, then find the stream velocity in $km$ per hour.
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312
GATE ECE 2014 Set 3 | Question: 1
The maximum value of the function $f(x) = \text{ln } (1+x) – x $ (where $x >-1$) occurs at $x=$_______.
The maximum value of the function $f(x) = \text{ln } (1+x) – x $ (where $x >-1$) occurs at $x=$_______.
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313
GATE ECE 2014 Set 3 | Question: 7
In the figure shown, the value of the current $I$ (in Amperes) is __________.
In the figure shown, the value of the current $I$ (in Amperes) is __________.
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314
GATE ECE 2014 Set 3 | Question: 10
At $T= 300 \: K$, the hole mobility of a semiconductor $\mu _{p}= 500$ $cm^{2}$/V-s$ and $\frac{kT}{q}= 26$ $mV$. The hole diffusion constant $D_{p}$ in $cm^{2}$/s$ is _________
At $T= 300 \: K$, the hole mobility of a semiconductor $\mu _{p}= 500$ $cm^{2}$$/V-s$ and $\frac{kT}{q}= 26$ $mV$. The hole diffusion constant $D_{p}$ in $cm^{2}$$/s$ is ...
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315
GATE ECE 2014 Set 3 | Question: 12
In the circuit shown, the $PNP$ transistor has $\mid V_{BE} \mid = 0.7 \:V$ and $\beta = 50$. Assume that $R_{B}= 100 \: k \Omega$. For $V_{0}$ to be $5 \: V$, the value of $R_{C}$ (in $k \Omega$) is ________
In the circuit shown, the $PNP$ transistor has $\mid V_{BE} \mid = 0.7 \:V$ and $\beta = 50$. Assume that $R_{B}= 100 \: k \Omega$. For $V_{0}$ to be $5 \: V$, the value...
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316
GATE ECE 2014 Set 3 | Question: 13
The figure shows a half-wave rectifier. The diode $D$ is ideal. The average steady-state current (in Amperes) through the diode is approximately ___________.
The figure shows a half-wave rectifier. The diode $D$ is ideal. The average steady-state current (in Amperes) through the diode is approximately ___________.
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317
GATE ECE 2014 Set 3 | Question: 14
An analog voltage in the range $0$ to $8$ V is divided in $16$ equal intervals for conversion to $4$-bit digital output. The maximum quantization error (in V) is __________
An analog voltage in the range $0$ to $8$ V is divided in $16$ equal intervals for conversion to $4$-bit digital output. The maximum quantization error (in V) is ________...
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318
GATE ECE 2014 Set 3 | Question: 19
A modulated signal is $y(t)= m(t)\cos(40000\pi t)$, where the baseband signal $m(t)$ has frequency components less than $5$ KHz only. The minimum required rate (in KHz) at which $y(t)$ should be sampled to recover $m(t)$ is _______.
A modulated signal is $y(t)= m(t)\cos(40000\pi t)$, where the baseband signal $m(t)$ has frequency components less than $5$ KHz only. The minimum required rate (in KHz) a...
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320
GATE ECE 2014 Set 3 | Question: 28
A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is _______ .
A fair coin is tossed repeatedly till both head and tail appear at least once. The average number of tosses required is _______ .
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