Hot questions / GO Instrumentation

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761

GATE2012-41
The double convex lens is used to couple a laser beam of diameter $5\;\text{mm}$ into an optical fiber with a numerical aperture of $0.5$. The minimum focal length of the lens that should be used in order to focus the entire beam into the fiber is $1.44\;\text{mm}$ $2.50\;\text{mm}$ $4.33\;\text{mm}$ $5.00\;\text{mm}$

The double convex lens is used to couple a laser beam of diameter $5\;\text{mm}$ into an optical fiber with a numerical aperture of $0.5$. The minimum focal length of the...

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762

GATE2012-49
With $\text{10 V}$ dc connected at port $\text{A}$ in the linear nonreciprocal two-port network shown below, the following were observed: $\text1\;\Omega$ connected at port $\text{B}$ draws a current of $\text{3 A}$ $\text2.5\;\Omega$ connected at port $\text{B}$ draws a current of $\text{2 A}$ For the same network, with $\text{6 V}$ dc connected ... $\text{A}$, the open circuit voltage at port $\text{B}$ is $\text{6 V}$ $\text{7 V}$ $\text{8 V}$ $\text{9 V}$

With $\text{10 V}$ dc connected at port $\text{A}$ in the linear nonreciprocal two-port network shown below, the following were observed:$\text1\;\Omega$ connected at por...

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763

GATE2012-18
A strain gauge is attached on a cantilever beam as shown. If the base of the cantilever vibrates according to the equation $x(t)=\sin\omega_1t+\sin\omega_2t,$ where $2\;\text{rad/s}<\omega_1,\;\omega_2<3\;\text{rad/s},$ then the output of the strain gauge is proportional to $x$ $\frac{dx}{dt}$ $\frac{d^2x}{dt^2}$ $\frac{d(x-y)}{dt}$

A strain gauge is attached on a cantilever beam as shown. If the base of the cantilever vibrates according to the equation $x(t)=\sin\omega_1t+\sin\omega_2t,$ where $2\;\...

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764

GATE2012-5
Given $f(z)=\frac{1}{z+1}-\frac{2}{z+3}.$ If $C$ is a counterclockwise path in the $z$-plane such that $|z+1|=1,$ the value of $\frac{1}{2\pi j}\oint_cf(z)dz$ is $-2$ $-1$ $1$ $2$

Given $f(z)=\frac{1}{z+1}-\frac{2}{z+3}.$ If $C$ is a counterclockwise path in the $z$-plane such that $|z+1|=1,$ the value of $\frac{1}{2\pi j}\oint_cf(z)dz$ is$-2$$-1$$...

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765

GATE2012-63
$\text{A}$ and $\text{B}$ are friends. They decide to meet between $\text{1 PM}$ and $\text{2 PM}$ 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 $\frac{1}{4}$ $\frac{1}{16}$ $\frac{7}{16}$ $\frac{9}{16}$

$\text{A}$ and $\text{B}$ are friends. They decide to meet between $\text{1 PM}$ and $\text{2 PM}$ on a given day. There is a condition that whoever arrives first will no...

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766

GATE2012-60
Choose the most appropriate word from the options given below to complete the following sentence: $\text{Given the seriousness of the situation that he had to face, his ___ was impressive}$. beggary nomenclature jealousy nonchalance

Choose the most appropriate word from the options given below to complete the following sentence:$\text{Given the seriousness of the situation that he had to face, his __...

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767

GATE2012-55
If $R_L=5\;\Omega,$ the approximate power consumption in the load is $700\;\text{W}$ $750\;\text{W}$ $800\;\text{W}$ $850\;\text{W}$

If $R_L=5\;\Omega,$ the approximate power consumption in the load is $700\;\text{W}$$750\;\text{W}$$800\;\text{W}$$850\;\text{W}$

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768

GATE2012-54
The power factor of the load is $0.45$ $0.50$ $0.55$ $0.60$

The power factor of the load is$0.45$$0.50$$0.55$$0.60$

Milicevic3306

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769

GATE2012-51
The deflection profile $y(x)$ of a cantilever beam due to application of a point force $F$ (in Newton), as a function of distance $x$ from its base, is given by $y(x)=0.001Fx^2[1-\frac{x}{3}]m.$ The angular deformation $\theta$ at the end of the cantilever is measured by reflecting a laser beam off a mirror $\text{M}$ as shown ... the cantilever to measure the effect of time varying forces, the ratio of their output is $\frac{12}{7}$ $\frac{40}{11}$ $\frac{176}{23}$ $\frac{112}{15}$

The deflection profile $y(x)$ of a cantilever beam due to application of a point force $F$ (in Newton), as a function of distance $x$ from its base, is given by $y(x)=0.0...

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770

GATE2012-21
Light of wavelength $630\;\text{nm}$ in vacuum, falling normally on a biological specimen of thickness $10\;\mu\text{m}$, splits into two beams that are polarized at right angles. The refractive index of the tissue for the two polarizations are $1.32$ and $1.333$. When the two beams emerge, they are out of phase by $0.13^\circ$ $74.3^\circ$ $90.0^\circ$ $128.6^\circ$

Light of wavelength $630\;\text{nm}$ in vacuum, falling normally on a biological specimen of thickness $10\;\mu\text{m}$, splits into two beams that are polarized at righ...

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771

GATE2012-28
The direction of vector $\text{A}$ is radially outward from the origin, with $|A|=kr^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\nabla.$ $\text{A=0}$ is $-2$ $2$ $1$ $0$

The direction of vector $\text{A}$ is radially outward from the origin, with $|A|=kr^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\nabla....

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772

GATE2012-31
If $\text{V}_\text{A}-\text{V}_\text{B}=6\;\text{V}$, then $\text{V}_\text{C}-\text{V}_\text{D}$ is $-5\;\text{V}$ $2\;\text{V}$ $3\;\text{V}$ $6\;\text{V}$

If $\text{V}_\text{A}-\text{V}_\text{B}=6\;\text{V}$, then $\text{V}_\text{C}-\text{V}_\text{D}$ is $-5\;\text{V}$$2\;\text{V}$$3\;\text{V}$$6\;\text{V}$

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773

GATE2012-20
An $\text{LED}$ emitting at $1\;\mu\text{m}$ with a spectral width of $50\;\text{nm}$ is used in a Michelson interferometer. To obtain a sustained interference, the maximum optical path difference between the two arms of the interferometer is $200\;\mu\text{m}$ $20\;\mu\text{m}$ $1\;\mu\text{m}$ $50\;\text{nm}$

An $\text{LED}$ emitting at $1\;\mu\text{m}$ with a spectral width of $50\;\text{nm}$ is used in a Michelson interferometer. To obtain a sustained interference, the maxim...

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774

GATE2012-13
In the sum of products function $f(X,\;Y,\;Z)=\sum(2,\;3,\;4,\;5),$ the prime implicants are $\overline{X}Y,\;X\overline{Y}$ $\overline{X}Y,\;X\overline{Y}\;\overline{Z},\;X\overline{Y}Z$ $\overline{X}Y\overline{Z},\;\overline{X}YZ,\;X\overline{Y}$ $\overline{X}Y\overline{Z},\;\overline{X}YZ,\;X\overline{Y}\;\overline{Z},\;X\overline{Y}Z$

In the sum of products function $f(X,\;Y,\;Z)=\sum(2,\;3,\;4,\;5),$ the prime implicants are $\overline{X}Y,\;X\overline{Y}$$\overline{X}Y,\;X\overline{Y}\;\overline{Z},\...

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775

GATE2012-8
In the following figure, $\text{C}_1$ and $\text{C}_2$ are ideal capacitors. $\text{C}_1$ has been charged to $12\;\text{V}$ before the ideal switch $\text{S}$ is closed at $t=0$. The current $i(t)$ for all $t$ is $\text{zero}$ $\text{a step function}$ $\text{an exponentially decaying function}$ $\text{an impulse function}$

In the following figure, $\text{C}_1$ and $\text{C}_2$ are ideal capacitors. $\text{C}_1$ has been charged to $12\;\text{V}$ before the ideal switch $\text{S}$ is closed ...

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776

GATE2012-3
Two independent random variables $\text{X}$ and $\text{Y}$ are uniformly distributed in the interval $[-1, 1]$. The probability that max$\text{[X, Y]}$ is less than $1/2$ is $3/4$ $9/16$ $1/4$ $2/3$

Two independent random variables $\text{X}$ and $\text{Y}$ are uniformly distributed in the interval $[-1, 1]$. The probability that max$\text{[X, Y]}$ is less than $1/2$...

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777

GATE2012-47
The open loop transfer function of a unity gain negative feedback control system is given by $G(s)=\frac{s^2+4s+8}{s(s+2)(s+8)}.$ The angle $\theta$ , at which the root locus approaches the zeros of the system, satisfies $|\theta|=\pi-\tan^{-1}[\frac{1}{4}]$ $|\theta|=\frac{3\pi}{4}-\tan^{-1}[\frac{1}{3}]$ $|\theta|=\frac{\pi}{2}-\tan^{-1}[\frac{1}{4}]$ $|\theta|=\frac{\pi}{4}-\tan^{-1}[\frac{1}{3}]$

The open loop transfer function of a unity gain negative feedback control system is given by $G(s)=\frac{s^2+4s+8}{s(s+2)(s+8)}.$ The angle $\theta$ , at which the root l...

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778

GATE2012-34
The state variable description of an $\text{LTI}$ system is given by $\begin{bmatrix}\dot{x_1}\\\dot{x_2\\\dot{x_3}}\end{bmatrix}=\begin{bmatrix}0 & a_1 & 0\\0 & 0 & a_2\\a_3 & 0 & 0\end{bmatrix}\begin{bmatrix}x_1\\x_2\\x_3\end{bmatrix}+\begin{bmatrix}0\\0\\1\end{bmatrix}u$ ... $a_2=0,$ $a_3\neq 0$ $a_1= 0,$ $a_2\neq 0,$ $a_3\neq 0$ $a_1=0,$ $a_2\neq 0,$ $a_3=0$ $a_1\neq 0,$ $a_2\neq 0,$ $a_3=0$

The state variable description of an $\text{LTI}$ system is given by $$\begin{bmatrix}\dot{x_1}\\\dot{x_2\\\dot{x_3}}\end{bmatrix}=\begin{bmatrix}0 & a_1 & 0\\0 & 0 & a_2...

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779

GATE2012-10
The $i-v$ characteristics of the diode in the circuit given below are $i=\left\{ \begin{array}{rcl} \frac{\text{v}-0.7}{500}\text{A},& \text{v}\geq0.7\text{v}\\ 0\;\text{A}, & \text{v}<0.7\text{v} \end{array}\right.$ $10\;\text{mA}$ $9.3\;\text{mA}$ $6.67\;\text{mA}$ $6.2\;\text{mA}$

The $i-v$ characteristics of the diode in the circuit given below are $$i=\left\{ \begin{array}{rcl} \frac{\text{v}-0.7}{500}\text{A},& \text{v}\geq0.7\text{v}\\ 0\;\text...

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780

GATE2012-26
A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is $1/3$ $1/2$ $2/3$ $3/4$

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is$1/3$$1/2$$2/3$$3/4$

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781

GATE2018-GA-8
To pass a test, a candidate needs to answer at least $2$ out of $3$ questions correctly. A total of $6,30,000$ candidates appeared for the test. Question $A$ was correctly answered by $3,30,000$ candidates. Question $B$ was answered correctly by $2,50,000$ candidates. Question $C$ was answered correctly by $2,60,000$ candidates ... all questions correctly is the same as the number answering none, how many candidates failed to clear the test? $30,000$ $2,70,000$ $3,90,000$ $4,20,000$

To pass a test, a candidate needs to answer at least $2$ out of $3$ questions correctly. A total of $6,30,000$ candidates appeared for the test. Question $A$ was correctl...