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41
GATE IN 2024 | Question: 4
Match the following measuring devices with their principle of measurement. \begin{tabular}{|l|l|} \hline Measuring Device & Principle of Measurement \\ \hline (P) Optical pyrometer & (I) Variation in mutual inductance \\ \hline (Q) Thermocouple & (II) Change in resistance \\ \hline (R) Strain gauge & (III) Wavelength of radiated energy \\ ... $(\mathrm{P})-(\mathrm{II}),(\mathrm{Q})-(\mathrm{IV}),(\mathrm{R})-(\mathrm{I}),(\mathrm{S})-(\mathrm{III})$
Match the following measuring devices with their principle of measurement.\begin{tabular}{|l|l|}\hline Measuring Device & Principle of Measurement \\\hline (P) Optical py...
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42
GATE IN 2024 | Question: 21
The current $i(t)$ drawn by a circuit is given as \[ i(t)=4+30 \cos (t)-20 \sin (t)+15 \cos (3 t)-10 \sin (3 t) \mathrm{A} \] The root-mean-square value of $i(t)$ is A (rounded off to one decimal place).
The current $i(t)$ drawn by a circuit is given as\[i(t)=4+30 \cos (t)-20 \sin (t)+15 \cos (3 t)-10 \sin (3 t) \mathrm{A}\]The root-mean-square value of $i(t)$ is A (round...
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43
GATE IN 2024 | Question: 29
In the bridge circuit shown in the figure, under balanced condition, the values of $R$ and $C$ respectively, are $1.010 \Omega$ and $19.802 \mu \mathrm{F}$ $9.901 \Omega$ and $0.505 \mu \mathrm{F}$ $19.802 \Omega$ and $1.01 \mu \mathrm{F}$ $39.604 \Omega$ and $2.02 \mu \mathrm{F}$
In the bridge circuit shown in the figure, under balanced condition, the values of $R$ and $C$ respectively, are$1.010 \Omega$ and $19.802 \mu \mathrm{F}$$9.901 \Omega$ a...
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44
GATE2019 IN: 10
In the circuit shown below, the input voltage V${_i}{_n}$ is positive. The current (I) – voltage(V) characteristics of the diode can be assumed to be I = I${_0}$e$^{v/vr}$ under the forward bias condition, where V${_T}$ is the thermal voltage and I${_0}$ is the reverse saturation current. Assuming an ideal op-amp, the output voltage v${_o}{_u}{_t}$ of the circuit is proportional to log${_e}$(V${_i}{_n}/V{_T}$) 2V${_i}{_n}$ e$^{V}{_i}{_n}/^{V}{T}$ V$^{2}{_i}{_n}$
In the circuit shown below, the input voltage V${_i}{_n}$ is positive. The current (I) – voltage(V) characteristics of the diode can be assumed to be I = I${_0}$e$^{v/v...
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45
GATE IN 2024 | Question: 18
The resistance of a $20 \mathrm{k} \Omega$ resistor is measured six consecutive times using an LCR meter. The first five readings are $19 \mathrm{k} \Omega, 18 \mathrm{k} \Omega, 23 \mathrm{k} \Omega, 21 \mathrm{k} \Omega$ and $17 \mathrm{k} \Omega$. If the mean of the measurements and the true value are equal, the last reading is $k \Omega$ (rounded off to nearest integer).
The resistance of a $20 \mathrm{k} \Omega$ resistor is measured six consecutive times using an LCR meter. The first five readings are $19 \mathrm{k} \Omega, 18 \mathrm{k}...
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46
GATE IN 2024 | Question: 15
The number of complex multiplications required for computing a 16-point DFT using the decimation-in-time radix-2 FFT is (in integer).
The number of complex multiplications required for computing a 16-point DFT using the decimation-in-time radix-2 FFT is (in integer).
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47
GATE IN 2024 | Question: 25
Indian Premier League has divided the sixteen cricket teams into two equal pools: Pool-A and Pool-B. Four teams of Pool-A have blue logo jerseys while the rest four have red logo jerseys. Five teams of Pool-B have blue logo jerseys while the rest three have red logo jerseys. If one team from each pool reaches the final, the probability that one team has a blue logo jersey and another has a red logo jersey is (rounded off to one decimal place).
Indian Premier League has divided the sixteen cricket teams into two equal pools: Pool-A and Pool-B. Four teams of Pool-A have blue logo jerseys while the rest four have ...
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48
GATE IN 2024 | Question: 32
In the figure shown, the positive edge triggered $\mathrm{D}$ flip-flops are initially reset to $Q=0$. The logic gates and the multiplexers have no propagation delay. After reset, a train of clock pulses (CLK) are applied. The logic-states of the inputs DIN, $\mathrm{S}$ and the clock pulses are also shown in the figure. Assuming no timing violations, the ... clock to the $5^{\text {th }}$ clock, $\mathrm{Y}_{3} \mathrm{Y}_{4} \mathrm{Y}_{5}$ is $001$ $010$ $000$ $011$
In the figure shown, the positive edge triggered $\mathrm{D}$ flip-flops are initially reset to $Q=0$. The logic gates and the multiplexers have no propagation delay. Aft...
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49
GATE IN 2024 | GA Question: 9
Five cubes of identical size and another smaller cube are assembled as shown in Figure A. If viewed from direction $X$, the planar image of the assembly appears as Figure B. Figure $\mathrm{A}$ Figure B If viewed from direction $Y$, the planar image of the assembly (Figure A) will appear as \begin{tabular}{|l|l|} \hline & \\ \hline & \\ \hline \end{tabular}
Five cubes of identical size and another smaller cube are assembled as shown in Figure A. If viewed from direction $X$, the planar image of the assembly appears as Figure...
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50
GATE IN 2024 | Question: 33
In the figure shown, $R=1 \mathrm{k} \Omega$ and $C=0.1 \mu \mathrm{F}$. For a dc gain of -10 , the $3 \mathrm{~dB}$ cut-off frequency (rounded off to one decimal place) is Assume the opamp is ideal. $159.1 \mathrm{~Hz}$ $1591.5 \mathrm{~Hz}$ $1750.7 \mathrm{~Hz}$ $175.0 \mathrm{~Hz}$
In the figure shown, $R=1 \mathrm{k} \Omega$ and $C=0.1 \mu \mathrm{F}$. For a dc gain of -10 , the $3 \mathrm{~dB}$ cut-off frequency (rounded off to one decimal place) ...
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51
GATE IN 2024 | GA Question: 7
Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container. The figure below shows the arrangement of the chalk-sticks inside the cylinder. The length of the container is equal to the length of the chalk-sticks. The ratio of the occupied space to the empty space of the container is $5 / 2$ $7 / 2$ $9 / 2$ $3$
Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container. The figure below shows the arrangement of the chalk-sticks inside the cylinder.The...
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52
GATE IN 2024 | Question: 38
Consider an ultrasonic measurement system shown in the figure. The ultrasonic transmitter $(T)$ sends a continuous wave signal $x(t)=\cos \left(2 \pi f_{1} t\right)$ volts towards an object whose vibration is modeled as $m(t)=0.5 \sin \left(2 \pi f_{2} t\right)$ volts. Neglecting the phase shift due to any other effect, the received signal at ... 25 and $\pm 250 \mathrm{~Hz}$ 0.5 and $\pm 500 \mathrm{~Hz}$ 1 and $\pm 1000 \mathrm{~Hz}$ 0.75 and $\pm 1000 \mathrm{~Hz}$
Consider an ultrasonic measurement system shown in the figure. The ultrasonic transmitter $(T)$ sends a continuous wave signal $x(t)=\cos \left(2 \pi f_{1} t\right)$ volt...
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53
GATE IN 2024 | Question: 45
Consider a unity negative feedback system with its open-loop pole-zero map as shown in the figure. If the point $s=j \alpha, \alpha>0$, lies on the root locus, the value of $\alpha$ is (rounded off to nearest integer). Note: The poles are marked with $x$ in the figure.
Consider a unity negative feedback system with its open-loop pole-zero map as shown in the figure. If the point $s=j \alpha, \alpha>0$, lies on the root locus, the value ...
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54
GATE IN 2024 | Question: 49
In the circuit shown, assume the opamp is ideal and the initial charge on the capacitor is zero. The output voltage at time $t=2 \mathrm{~ms}$ is $\mathrm{V}$ (rounded off to one decimal place).
In the circuit shown, assume the opamp is ideal and the initial charge on the capacitor is zero. The output voltage at time $t=2 \mathrm{~ms}$ is $\mathrm{V}$ (rounded of...
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55
GATE IN 2024 | Question: 14
Figure shows an amplifier using an NMOS transistor. Assume that the transistor is in saturation with device parameters, $\mu_{n} C_{o x}=250 \mu \mathrm{A} / \mathrm{V}^{2}$, threshold voltage $\mathrm{VT}_{\mathrm{T}}=0.65 \mathrm{~V}$ and $\mathrm{W} / \mathrm{L}=4$. Ignore the channel length modulation effect. The drain current of the transistor at the operating point is $\mu \mathrm{A}$ (rounded off to nearest integer).
Figure shows an amplifier using an NMOS transistor. Assume that the transistor is in saturation with device parameters, $\mu_{n} C_{o x}=250 \mu \mathrm{A} / \mathrm{V}^{...
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56
GATE IN 2024 | Question: 11
A linear transducer is calibrated for the ranges shown in the figure. The gain of the transducer is $\mathrm{mA} /{ }^{\circ} \mathrm{C}$ (rounded off to two decimal places).
A linear transducer is calibrated for the ranges shown in the figure. The gain of the transducer is $\mathrm{mA} /{ }^{\circ} \mathrm{C}$ (rounded off to two decimal plac...
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57
GATE IN 2024 | Question: 3
A discrete-time sequence is given by $x[n]=[1,2,3,4]$ for $0 \leq n \leq 3$. The zero lag auto-correlation value of $x[n]$ is $1$ $10$ $20$ $30$
A discrete-time sequence is given by $x[n]=[1,2,3,4]$ for $0 \leq n \leq 3$. The zero lag auto-correlation value of $x[n]$ is$1$$10$$20$$30$
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58
GATE IN 2024 | Question: 23
The switch in the following figure has been closed for a long time $(t
The switch in the following figure has been closed for a long time $(t
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59
GATE IN 2024 | Question: 36
Let $C$ be the closed curve in the $x y$-plane, traversed in the counterclockwise direction along the boundary of the rectangle with vertices at $(0,0),(2,0),(2,1),(0,1)$. The value of the line integral \[ \oint_{C}\left(-e^{y} d x+e^{x} d y\right) \] is $e^{2}+2 e-3$ $e^{2}-2 e-3$ $e^{2}+e-1$ $e^{2}+e+1$
Let $C$ be the closed curve in the $x y$-plane, traversed in the counterclockwise direction along the boundary of the rectangle with vertices at $(0,0),(2,0),(2,1),(0,1)$...
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60
GATE IN 2024 | Question: 50
In the figure shown, $\mathrm{Sw}$ is a switch whose position changes from 1 to 0 when $\mathrm{Vc}$ changes from logic HIGH to LOW and vice versa. The bandwidth of the permanent magnet moving coil (PMMC) type voltmeter is $1 \mathrm{~Hz}$ ... $\mathrm{V}$ (rounded off to nearest integer). Note: Assume all components are ideal.
In the figure shown, $\mathrm{Sw}$ is a switch whose position changes from 1 to 0 when $\mathrm{Vc}$ changes from logic HIGH to LOW and vice versa. The bandwidth of the p...
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61
GATE IN 2024 | Question: 24
Consider a system given by the following first order differential equation: \[ \frac{d y}{d t}=y+2 t-t^{2} \] where, $y(0)=1$ and $0 \leq t
Consider a system given by the following first order differential equation:\[\frac{d y}{d t}=y+2 t-t^{2}\]where, $y(0)=1$ and $0 \leq t
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62
GATE IN 2024 | Question: 27
The measured values from a flow instrument, whose range is between 0 and 2 flow units, are shown in the histogram. The systematic error (bias) and the maximum error (in flow units), respectively are 0.12 and 0.14 0.01 and 0.10 0.10 and 0.14 0.04 and 0.12
The measured values from a flow instrument, whose range is between 0 and 2 flow units, are shown in the histogram. The systematic error (bias) and the maximum error (in f...
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63
GATE IN 2024 | Question: 19
Consider the readout circuit of a piezoelectric sensor shown in the figure. When the piezoelectric sensor generates a charge $q_{p}$, the resulting change in voltage $\mathrm{V}_{\mathrm{X}}$ is $-2 \mathrm{~V}$. Then the corresponding change in the voltage $\mathrm{V}_{\text {out }}$ is V (rounded off to nearest integer). Note: Assume all components are ideal.
Consider the readout circuit of a piezoelectric sensor shown in the figure.When the piezoelectric sensor generates a charge $q_{p}$, the resulting change in voltage $\mat...
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64
GATE IN 2024 | Question: 22
A linear potentiometer $(0-10 \mathrm{k} \Omega)$ is used to measure the water level as shown in the figure. The resistance between $\mathrm{A}$ and $\mathrm{C}$ varies linearly from 0 to $10 \mathrm{k} \Omega$ for a change in water level from 0 to $20 \mathrm{~cm}$ ... $\mathrm{V}_{\text {out }}=5 \mathrm{~V}$, the water level is $\mathrm{cm}$ (rounded off to one decimal place).
A linear potentiometer $(0-10 \mathrm{k} \Omega)$ is used to measure the water level as shown in the figure. The resistance between $\mathrm{A}$ and $\mathrm{C}$ varies l...
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65
GATE IN 2024 | Question: 17
The Nyquist sampling frequency for $x(t)=10 \sin ^{2}(200 \pi t)$ is $\mathrm{Hz}$ (rounded off to nearest integer).
The Nyquist sampling frequency for $x(t)=10 \sin ^{2}(200 \pi t)$ is $\mathrm{Hz}$ (rounded off to nearest integer).
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66
GATE IN 2024 | Question: 35
The transfer function of a system is \[ G(s)=\frac{\omega_{n}^{2}}{s^{2}+2 \xi \omega_{n} s+\omega_{n}^{2}} \] Choose the range of $\xi$ and $\omega_{n}$ (in $\mathrm{rad} / \mathrm{s}$ ) from the following options such that the poles lie on the shaded region of the $s$-plane as shown in the figure. $\xi \geq \frac{1}{2}$ ... $\omega_{n} \geq 2$ $\xi \geq \frac{1}{2}$ and $\omega_{n} \geq \sqrt{3}$ $\xi \geq \frac{1}{4}$ and $\omega_{n} \geq \sqrt{3}$
The transfer function of a system is\[G(s)=\frac{\omega_{n}^{2}}{s^{2}+2 \xi \omega_{n} s+\omega_{n}^{2}}\]Choose the range of $\xi$ and $\omega_{n}$ (in $\mathrm{rad} / ...
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GATE IN 2024 | GA Question: 8
The plot below shows the relationship between the mortality risk of cardiovascular disease and the number of steps a person walks per day. Based on the data, which one of the following options is true? The risk reduction on increasing the steps/day from 0 to 10000 is less than the risk reduction on increasing the ... risk reduction occurs on going from 0 to 5000 . For any 5000 increment in steps/day the largest risk reduction occurs on going from 15000 to 20000 .
The plot below shows the relationship between the mortality risk of cardiovascular disease and the number of steps a person walks per day. Based on the data, which one of...
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68
GATE IN 2024 | Question: 6
Among the given options, the simplified form of the Boolean function $F=(A+\bar{A} \cdot B)+\bar{A} \cdot(A+\bar{B}) \cdot C$ is $A+B+C$ A.B.C $B+\bar{A} \cdot C$ $\bar{A}+B . C$
Among the given options, the simplified form of the Boolean function $F=(A+\bar{A} \cdot B)+\bar{A} \cdot(A+\bar{B}) \cdot C$ is$A+B+C$A.B.C$B+\bar{A} \cdot C$$\bar{A}+B ...
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69
GATE IN 2024 | Question: 47
In the figure shown, the diode current is given by $I_{D}=I_{S} e^{\frac{\alpha V_{D}}{T}} \cdot V_{D}$ is the diode voltage in volts, $T$ is the absolute temperature in Kelvin, $\alpha=1.16 \times 10^{4} \mathrm{~K} / \mathrm{V}$, and $I_{S}=10^{-15} \mathrm{~A}$ is the saturation ... independent. The change in the output voltage $\left(\mathrm{V}_{\text {out }}\right.$ ) per Kelvin change in temperature is $\mathrm{mV}$ (rounded off to one decimal place).
In the figure shown, the diode current is given by $I_{D}=I_{S} e^{\frac{\alpha V_{D}}{T}} \cdot V_{D}$ is the diode voltage in volts, $T$ is the absolute temperature in ...
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70
GATE2018IN: 55
A multi-mode optical fiber with a large core diameter has a core refractive index $n_1 = 1.5$ and cladding refractive index $n_2 = 1.4142.$ The maximum value of $\theta_A$ (in degrees) for which the incident light from air will be guided in the optical fiber is $\pm$ _______________.
A multi-mode optical fiber with a large core diameter has a core refractive index $n_1 = 1.5$ and cladding refractive index $n_2 = 1.4142.$ The maximum value of $\theta_A...
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GATE IN 2024 | Question: 51
A $50 \mathrm{kVA}$ transformer has an efficiency of $95 \%$ at full load and unity power factor. Assume the core losses are negligible. The efficiency of the transformer at $75 \%$ of the full load and 0.8 power factor is $\%$ (rounded off to one decimal place).
A $50 \mathrm{kVA}$ transformer has an efficiency of $95 \%$ at full load and unity power factor. Assume the core losses are negligible. The efficiency of the transformer...
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72
GATE2019 IN: 14
Four strain gauges in a Wheatstone bridge configuration are connected to an instrumentation amplifier as shown in the figure. From the choices given below, the preferred value for the common mode rejection ratio(CMRR) of the amplifier, in dB, would be -20 0 3 100
Four strain gauges in a Wheatstone bridge configuration are connected to an instrumentation amplifier as shown in the figure. From the choices given below, the preferred ...
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73
GATE IN 2023 | GA Question: 2
Disagree : Protest: : Agree: __________ (By word meaning) Refuse Pretext Recommend Refute
Disagree : Protest: : Agree: __________(By word meaning)RefusePretextRecommendRefute
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Verbal Aptitude
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GATE IN 2024 | Question: 7
Consider the state-space representation of a system \[ \dot{x}=A x+B u \] where $x$ is the state vector, $u$ is the input, $A$ is the system matrix and $B$ is the input matrix. Choose the matrix $A$ ... $\left[\begin{array}{cc}1 & 1.5 \\ 2 & -3\end{array}\right]$ $\left[\begin{array}{rr}0 & 1 \\ -2 & 3\end{array}\right]$
Consider the state-space representation of a system\[\dot{x}=A x+B u\]where $x$ is the state vector, $u$ is the input, $A$ is the system matrix and $B$ is the input matri...
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75
GATE2019 IN: GA-4
Five numbers $10,7,5,4$ and $2$ are to be arranged in a sequence from left to right following the directions given below: No two odd or even numbers are next to each other. The second number from the left is exactly half of the left-most number. The middle number is exactly twice the right-most number. Which is the second number from the right? $2$ $4$ $7$ $10$
Five numbers $10,7,5,4$ and $2$ are to be arranged in a sequence from left to right following the directions given below:No two odd or even numbers are next to each other...
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Analytical Aptitude
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GATE2018IN: 15
In the given circuit, assume that the opamp is ideal and the transistor has a $\beta$ of 20. The current I${_0}$( in $\mu A$) flowing through the load Z${_L}$ is $\_\_\_\_\_\_$.
In the given circuit, assume that the opamp is ideal and the transistor has a $\beta$ of 20. The current I${_0}$( in $\mu A$) flowing through the load Z${_L}$ is $\_\_\_...
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GATE IN 2023 | GA Question: 8
The information contained in DNA is used to synthesize proteins that are necessary for the functioning of life. DNA is composed of four nucleotides: Adenine (A), Thymine (T), Cytosine (C), and Guanine (G). The information contained in DNA can then be thought of as a sequence of these four nucleotides: A, T, C, and G. DNA has coding ... of proteins. The function of about $98 \%$ of human DNA is not understood. only (i) only (ii) both (i) and (ii) neither (i) nor (ii)
The information contained in DNA is used to synthesize proteins that are necessary for the functioning of life. DNA is composed of four nucleotides: Adenine (A), Thymine ...
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Analytical Aptitude
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GATE IN 2022 | Question: 41
Monochromatic light of wavelength $532 \; \text{nm}$ is used to measure the absorption coefficient of a material in a $\text{UV}$-Visible Spectrophotometer. The measured light intensity after transmission through a $1 \; \text{cm}$ thick sample of the material is $0.414 \; \text{mW/cm}^{2}.$ ... $0.186 \; \text{mW/cm}^{2}.$ The absorption coefficient $(\text{in cm}^{-1})$ of the material is ____________ (round off to two decimal places)
Monochromatic light of wavelength $532 \; \text{nm}$ is used to measure the absorption coefficient of a material in a $\text{UV}$-Visible Spectrophotometer. The measured ...
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79
GATE IN 2024 | Question: 10
The capacitance formed between two concentric spherical metal shells having radii $x$ and $y$ with $y>x$ is Note: $\epsilon$ is the permittivity of the medium between the shells. $4 \pi \epsilon\left(\frac{x y}{y-x}\right)$ $4 \pi \epsilon\left(\frac{x^{2}}{y-x}\right)$ $4 \pi \epsilon\left(\frac{y^{2}}{y-x}\right)$ $4 \pi \epsilon\left(\frac{y^{2}-x y}{x}\right)$
The capacitance formed between two concentric spherical metal shells having radii $x$ and $y$ with $y>x$ isNote: $\epsilon$ is the permittivity of the medium between the ...
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80
GATE IN 2024 | Question: 52
A three-phase squirrel-cage induction motor has a starting torque of $100 \%$ of the full load torque and a maximum torque of $300 \%$ of the full load torque. Neglecting the stator impedance, the slip at the maximum torque is $\%$ (rounded off to two decimal places).
A three-phase squirrel-cage induction motor has a starting torque of $100 \%$ of the full load torque and a maximum torque of $300 \%$ of the full load torque. Neglecting...
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