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Recent questions tagged gate2012-in
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GATE2012-65
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 $2$ $3$ $4$ $8$
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 balanc...
Milicevic3306
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Milicevic3306
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Quantitative Aptitude
gate2012-in
numerical-ability
numerical-computation
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2
GATE2012-64
The data given in the following table summarizes the monthly budget of an average household. ... $\text{NOT}$ spent on savings is $10\%$ $14\%$ $81\%$ $86\%$
The data given in the following table summarizes the monthly budget of an average household.$$\begin{array}{|l|c|}\hline \textbf{Category} & \textbf{Amount (Rs.)} \\\hlin...
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Milicevic3306
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Quantitative Aptitude
gate2012-in
numerical-ability
percentage
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3
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...
Milicevic3306
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Quantitative Aptitude
gate2012-in
numerical-ability
probability
conditional-probability
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4
GATE2012-62
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 ... Discipline was the armies' inheritance from their seniors The harsh discipline to which the legions were subjected to led to the odds and conditions being against them
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 obedie...
Milicevic3306
7.9k
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Milicevic3306
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Verbal Aptitude
gate2012-in
verbal-ability
verbal-reasoning
passage-reading
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5
GATE2012-61
Raju has $14$ currency notes in his pocket consisting of only $\text{Rs. 20}$ notes and $\text{Rs. 10}$ notes. The total money value of the notes is $\text{Rs. 230}$. The number of $\text{Rs. 10}$ notes that Raju has is $5$ $6$ $9$ $10$
Raju has $14$ currency notes in his pocket consisting of only $\text{Rs. 20}$ notes and $\text{Rs. 10}$ notes. The total money value of the notes is $\text{Rs. 230}$. The...
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Milicevic3306
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Quantitative Aptitude
gate2012-in
numerical-ability
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6
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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Verbal Aptitude
gate2012-in
verbal-ability
most-appropriate-word
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7
GATE2012-59
Which one of the following options is the closest in meaning to the word given below? $\text{Latitude}$ Eligibility Freedom Coercion Meticulousness
Which one of the following options is the closest in meaning to the word given below?$\text{Latitude}$EligibilityFreedomCoercionMeticulousness
Milicevic3306
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Verbal Aptitude
gate2012-in
verbal-ability
word-meaning
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8
GATE2012-58
One of the parts $\text{(A, B, C, D)}$ in the sentence given below contains an $\text{ERROR}$. Which one of the following is $\text{INCORRECT}$? $\text{I requested that he should be given the driving test today instead of tomorrow.}$ requested that should be given the driving test instead of tomorrow
One of the parts $\text{(A, B, C, D)}$ in the sentence given below contains an $\text{ERROR}$. Which one of the following is $\text{INCORRECT}$?$\text{I requested that he...
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Verbal Aptitude
gate2012-in
verbal-ability
english-grammar
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9
GATE2012-57
If $(1.001)^{1259}=3.52$ and $(1.001)^{2062}=7.85,$ then $(1.001)^{3321}=$ $2.23$ $4.33$ $11.37$ $27.64$
If $(1.001)^{1259}=3.52$ and $(1.001)^{2062}=7.85,$ then $(1.001)^{3321}=$$2.23$$4.33$$11.37$$27.64$
Milicevic3306
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Quantitative Aptitude
gate2012-in
numerical-ability
numerical-computation
unit-digit
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10
GATE2012-56
Choose the most appropriate alternative from the options given below to complete the following sentence: $\text{If the tired soldier wanted to lie down, he___ the mattress out on the balcony.}$ should take shall take should have taken will have taken
Choose the most appropriate alternative from the options given below to complete the following sentence:$\text{If the tired soldier wanted to lie down, he___ the mattress...
Milicevic3306
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Milicevic3306
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Verbal Aptitude
gate2012-in
verbal-ability
most-appropriate-word
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11
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...
Milicevic3306
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Milicevic3306
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Others
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12
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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13
GATE2012-50
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)=0.001F\;x^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 in the ... light on the photodetector when a force of $F=\text{1 N}$ is applied to the cantilever is $\text{1 mm}$ $\text{3 mm}$ $\text{6 mm}$ $\text{12 mm}$
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...
Milicevic3306
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Others
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14
GATE2012-53
The transfer function of a compensator is given as $G_c(s)=\frac{s+a}{s+b}$ The phase of the above lead compensator is maximum at $\sqrt{2}\;\text{rad/s}$ $\sqrt{3}\;\text{rad/s}$ $\sqrt{6}\;\text{rad/s}$ $\frac{1}{\sqrt{3}}\;\text{rad/s}$
The transfer function of a compensator is given as $$G_c(s)=\frac{s+a}{s+b}$$The phase of the above lead compensator is maximum at $\sqrt{2}\;\text{rad/s}$$\sqrt{3}\;\tex...
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15
GATE2012-52
The transfer function of a compensator is given as $G_c(s)=\frac{s+a}{s+b}$ $G_c(s)$ is a lead compensator if $\text{a=1, b=2}$ $\text{a=3, b=2}$ $\text{a=-3, b=-1}$ $\text{a=3, b=1}$
The transfer function of a compensator is given as $$G_c(s)=\frac{s+a}{s+b}$$$G_c(s)$ is a lead compensator if $\text{a=1, b=2}$$\text{a=3, b=2}$$\text{a=-3, b=-1}$$\text...
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Milicevic3306
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Others
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16
GATE2012-54
The power factor of the load is $0.45$ $0.50$ $0.55$ $0.60$
The power factor of the load is$0.45$$0.50$$0.55$$0.60$
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17
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}$
Milicevic3306
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Milicevic3306
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Others
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18
GATE2012-44
A dynamometer arm makes contact with the piezoelectric load cell as shown. The $g-$constant of the piezoelectric material is $50\times10^{-3}\;\text {Vm/N}$ and the surface area of the load cell is $4\;{cm^2}$. If a torque $\tau=20 \;\text{Nm}$ is applied to the dynamometer, the output voltage $\text{V}_\circ$ of the load cell is $\text{4 V}$ $\text{5 V}$ $\text{10 V}$ $\text{16 V}$
A dynamometer arm makes contact with the piezoelectric load cell as shown. The $g-$constant of the piezoelectric material is $50\times10^{-3}\;\text {Vm/N}$ and the surf...
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Milicevic3306
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19
GATE2012-43
The open loop transfer function of a unity negative feedback control system is given by $G(s)=\frac{150}{s(s+9)(s+25)}$. The gain margin of the system is $10.8\;\text{dB}$ $22.3\;\text{dB}$ $34.1\;\text{dB}$ $45.6\;\text{dB}$
The open loop transfer function of a unity negative feedback control system is given by $G(s)=\frac{150}{s(s+9)(s+25)}$. The gain margin of the system is $10.8\;\text{dB}...
Milicevic3306
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20
GATE2012-42
An analog voltmeter uses external multiplier settings. With a multiplier setting of $20\;\text{k}\Omega$, it reads $400\;\text{V}$ and with a multiplier setting of $80\;\text{k}\Omega$, it reads $352\;\text{V}$. For a multiplier setting of $40\;\text{k}\Omega$, the voltmeter reads $371\;\text{V}$ $383\;\text{V}$ $394\;\text{V}$ $406\;\text{V}$
An analog voltmeter uses external multiplier settings. With a multiplier setting of $20\;\text{k}\Omega$, it reads $400\;\text{V}$ and with a multiplier setting of $80\;\...
Milicevic3306
7.9k
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Milicevic3306
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21
GATE2012-45
Water $\text{(density:}\;1000\;\text{kgm}^{-3})$ stored in a cylindrical drum of diameter $1\;\text{m}$ is emptied through a horizontal pipe of diameter $0.05\;\text{m}$. A pitot-static tube is placed inside the pipe facing the flow. At the time when the difference between the stagnation and static pressure measured by the pitot-static tube is $10\;\text{kPa}$, the ... $\frac{1}{75\sqrt{10}}\text{ms}^{-1}$ $\frac{1}{50\sqrt{10}}\text{ms}^{-1}$ $\frac{1}{40\sqrt5}\text{ms}^{-1}$
Water $\text{(density:}\;1000\;\text{kgm}^{-3})$ stored in a cylindrical drum of diameter $1\;\text{m}$ is emptied through a horizontal pipe of diameter $0.05\;\text{m}$....
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22
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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Milicevic3306
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23
GATE2012-46
A U-tube manometer of tube diameter $D$ is filled with a liquid of zero viscosity. If the volume of the liquid filled is $V$, the natural frequency of oscillations in the liquid level about its mean position, due to small perturbations, is $\frac{D}{2\sqrt{2\pi}}\sqrt{\frac{g}{V}}$ $\frac{2\sqrt2}{\sqrt\pi}$\frac{\sqrt{gV}}{D^2}$ $\frac{1}{2\sqrt\pi}$\frac{\sqrt{gD}}{V^{1/3}}$ $\frac{1}{\sqrt{\pi}}\sqrt{\frac{g}{D}}$
A U-tube manometer of tube diameter $D$ is filled with a liquid of zero viscosity. If the volume of the liquid filled is $V$, the natural frequency of oscillations in the...
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Milicevic3306
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24
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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Milicevic3306
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25
GATE2012-48
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}$ With $\text{10 V}$ dc connected at port $\text{A}$, the ... $\text{B}$ is $\frac{3}{7}\;\text{A}$ $\frac{5}{7}\;\text{A}$ $\text{1 A}$ $\frac{9}{7}\;\text{A}$
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...
Milicevic3306
7.9k
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Milicevic3306
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Others
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26
GATE2012-36
The Fourier transform of a signal $h(t)$ is $H(j\omega)=(2\cos\omega)(\sin2\omega)/\omega.$ The value of $h(0)$ is $1/4$ $1/2$ $1$ $2$
The Fourier transform of a signal $h(t)$ is $H(j\omega)=(2\cos\omega)(\sin2\omega)/\omega.$ The value of $h(0)$ is $1/4$$1/2$$1$$2$
Milicevic3306
7.9k
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Differential equations
gate2012-in
differential-equations
fourier-transform
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–
0
votes
0
answers
27
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 $$\begin{bmatrix}\dot{x_1}\\\dot{x_2\\\dot{x_3}}\end{bmatrix}=\begin{bmatrix}0 & a_1 & 0\\0 & 0 & a_2...
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28
GATE2012-35
The state transition diagram for the logic circuit shown is
The state transition diagram for the logic circuit shown is
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29
GATE2012-40
The input $x(t)$ and output $y(t)$ of a system are related as $y(t)=\int^{t}_{-\infty}x(\tau)\cos(3\tau)d\tau$. The system is time-invariant and stable stable and not time-invariant time-invariant and not stable not time-invariant and not stable
The input $x(t)$ and output $y(t)$ of a system are related as $y(t)=\int^{t}_{-\infty}x(\tau)\cos(3\tau)d\tau$. The system is time-invariant and stablestable and not time...
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30
GATE2012-39
The circuit shown is a low pass filter with $\text{f}_{3\text{dB}}=\frac{1}{(R_1+R_2)C}\;\text{rad/s}$ high pass filter with $\text{f}_{3\text{dB}}=\frac{1}{R_1C}\;\text{rad/s}$ low pass filter with $\text{f}_{3\text{dB}}=\frac{1}{R_1C}\;\text{rad/s}$ high pass filter with $\text{f}_{3\text{dB}}=\frac{1}{(R_1+R_2)C}{rad/s}$
The circuit shown is alow pass filter with $\text{f}_{3\text{dB}}=\frac{1}{(R_1+R_2)C}\;\text{rad/s}$high pass filter with $\text{f}_{3\text{dB}}=\frac{1}{R_1C}\;\text{ra...
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31
GATE2012-38
The feedback system shown below oscillates at $2\;\text{rad/s}$ when $K=2$ and $a=0.75$ $K=3$ and $a=0.75$ $K=4$ and $a=0.5$ $K=2$ and $a=0.5$
The feedback system shown below oscillates at $2\;\text{rad/s}$ when$K=2$ and $a=0.75$$K=3$ and $a=0.75$$K=4$ and $a=0.5$$K=2$ and $a=0.5$
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32
GATE2012-37
Let $y[n]$ denote the convolution of $h[n]$ and $g[n]$, where $h[n]=(1/2)^n\;u[n]$ and $g[n]$ is a causal sequence. If $y[0]=1$ and $y[1]=1/2$, then $g[1]$ equals $0$ $1/2$ $1$ $3/2$
Let $y[n]$ denote the convolution of $h[n]$ and $g[n]$, where $h[n]=(1/2)^n\;u[n]$ and $g[n]$ is a causal sequence. If $y[0]=1$ and $y =1/2$, then $g $ equals$0$$1/2$$1$$...
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33
GATE2012-28
The direction of vector $\text{A}$ is radially outward from the origin, with $|A|=kr^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\nabla.$ $\text{A=0}$ is $-2$ $2$ $1$ $0$
The direction of vector $\text{A}$ is radially outward from the origin, with $|A|=kr^n$ where $r^2=x^2+y^2+z^2$ and $k$ is a constant. The value of $n$ for which $\nabla....
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7.9k
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Calculus
gate2012-in
calculus
curl
divergence
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0
answers
34
GATE2012-30
Consider the differential equation $\frac{d^2y(t)}{dt^2}+2\frac{dy(t)}{dt}+y(t)=\delta(t)$ with $y(t)|_{t=0^-}=-2$ and $\frac{dy}{dt}|_{t=0^-}=0$. The numerical value of $\frac{dy}{dt}|_{t=0^+}$ is $-2$ $-1$ $0$ $1$
Consider the differential equation$\frac{d^2y(t)}{dt^2}+2\frac{dy(t)}{dt}+y(t)=\delta(t)$ with $y(t)|_{t=0^-}=-2$ and $\frac{dy}{dt}|_{t=0^-}=0$.The numerical value of $\...
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Differential equations
gate2012-in
differential-equations
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0
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0
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35
GATE2012-29
The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1, 6]$ is $21$ $25$ $41$ $46$
The maximum value of $f(x)=x^3-9x^2+24x+5$ in the interval $[1, 6]$ is $21$$25$$41$$46$
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7.9k
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Calculus
gate2012-in
calculus
maxima-minima
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36
GATE2012-27
Given that $A=\begin{bmatrix}-5 &-3\\2 &0\end{bmatrix}$ and $I=\begin{bmatrix}1 & 0\\0 &1\end{bmatrix}$, the value of $A^3$ is $15A+12I$ $19A+30I$ $17A+15I$ $17A+21I$
Given that$A=\begin{bmatrix}-5 &-3\\2 &0\end{bmatrix}$ and $I=\begin{bmatrix}1 & 0\\0 &1\end{bmatrix}$, the value of $A^3$ is$15A+12I$$19A+30I$$17A+15I$$17A+21I$
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Linear Algebra
gate2012-in
linear-algebra
matrices
matrix-algebra
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37
GATE2012-26
A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is $1/3$ $1/2$ $2/3$ $3/4$
A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is$1/3$$1/2$$2/3$$3/4$
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Milicevic3306
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Probability and Statistics
gate2012-in
probability-and-statistics
probability
conditional-probability
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38
GATE2012-33
The voltage gain $A_v$ of the circuit shown below is $|A_v|\approx 200$ $|A_v|\approx 100$ $|A_v|\approx 20$ $|A_v|\approx 10$
The voltage gain $A_v$ of the circuit shown below is$|A_v|\approx 200$$|A_v|\approx 100$$|A_v|\approx 20$$|A_v|\approx 10$
Milicevic3306
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Milicevic3306
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Others
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39
GATE2012-32
Assuming both the voltage sources are in phase, the value of $\text{R}$ for which maximum power transferred from circuit $\text{A}$ to circuit $\text{B}$ is $0.8\;\Omega$ $1.4\;\Omega$ $2\;\Omega$ $2.8\;\Omega$
Assuming both the voltage sources are in phase, the value of $\text{R}$ for which maximum power transferred from circuit $\text{A}$ to circuit $\text{B}$ is $0.8\;\Omega$...
Milicevic3306
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Milicevic3306
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Others
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40
GATE2012-31
If $\text{V}_\text{A}-\text{V}_\text{B}=6\;\text{V}$, then $\text{V}_\text{C}-\text{V}_\text{D}$ is $-5\;\text{V}$ $2\;\text{V}$ $3\;\text{V}$ $6\;\text{V}$
If $\text{V}_\text{A}-\text{V}_\text{B}=6\;\text{V}$, then $\text{V}_\text{C}-\text{V}_\text{D}$ is $-5\;\text{V}$$2\;\text{V}$$3\;\text{V}$$6\;\text{V}$
Milicevic3306
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Milicevic3306
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