Most answered questions / GO Instrumentation

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41

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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42

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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43

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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44

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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45

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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46

GATE IN 2024 | Question: 26
A wire of circular cross section with radius $a$ is shown in the figure. The current density is given by $\mathbf{J}=k s^{2}$, where $k$ is a constant, $s$ is the radial distance from the axis and $0 \leq s \leq a$. The total current $I$ in the wire is $\frac{\pi k a^{4}}{2}$ $\frac{2 \pi k a^{3}}{3}$ $\frac{\pi k a^{3}}{2}$ $\frac{\pi k a^{4}}{4}$

A wire of circular cross section with radius $a$ is shown in the figure. The current density is given by $\mathbf{J}=k s^{2}$, where $k$ is a constant, $s$ is the radial ...

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47

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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48

GATE IN 2024 | Question: 28
Consider a discrete-time sequence \[ x[n]=\left\{\begin{array}{ll} (0.2)^{n}, & 0 \leq n \leq 7 \\ 0, & \text { otherwise } \end{array}\right. \] The region of convergence of $X(z)$, the $z$-transform of $x[n]$, consists of all values of $z$ except $z=0.2$ all values of $z$ all values of $z$ except $z=0$ all values of $z$ except $z=\infty$

Consider a discrete-time sequence\[x[n]=\left\{\begin{array}{ll}(0.2)^{n}, & 0 \leq n \leq 7 \\0, & \text { otherwise }\end{array}\right.\]The region of convergence of $X...

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49

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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50

GATE IN 2024 | Question: 30
Laplace transform of a signal $x(t)$ is \[ X(s)=\frac{1}{s^{2}+13 s+42} \] Let $u(t)$ be the unit step function. Choose the signal $x(t)$ from the following options if the region of convergence is $-7

Laplace transform of a signal $x(t)$ is\[X(s)=\frac{1}{s^{2}+13 s+42}\]Let $u(t)$ be the unit step function. Choose the signal $x(t)$ from the following options if the re...

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51

GATE IN 2024 | Question: 31
In the figure shown, both the opamps $\mathrm{A}_{1}$ and $\mathrm{A}_{2}$ are ideal, except that the opamp $\mathrm{A}_{1}$ has an offset voltage $\left(\mathrm{V}_{\text {os }}\right)$ of $1 \mathrm{mV}$. For $\mathrm{V}_{\text {in }}=0 \mathrm{~V}$, the values of the output voltages $V_{\text {out1 }}$ ... $-1 \mathrm{mV}$ $1 \mathrm{mV}$ and $0 \mathrm{mV}$ $1 \mathrm{mV}$ and $-1 \mathrm{mV}$ $2 \mathrm{mV}$ and $0 \mathrm{mV}$

In the figure shown, both the opamps $\mathrm{A}_{1}$ and $\mathrm{A}_{2}$ are ideal, except that the opamp $\mathrm{A}_{1}$ has an offset voltage $\left(\mathrm{V}_{\tex...

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52

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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53

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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54

GATE IN 2024 | Question: 34
Consider the feedback control system shown in the figure. The steady-state error $e_{s s}=\lim _{t \rightarrow \infty}(r(t)-y(t))$ due to unit step reference $r(t)$ is $\frac{K-1}{K}$ $\frac{1}{2}$ $0$ $\frac{1-K}{K}$

Consider the feedback control system shown in the figure. The steady-state error $e_{s s}=\lim _{t \rightarrow \infty}(r(t)-y(t))$ due to unit step reference $r(t)$ is$\f...

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55

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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56

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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57

GATE IN 2024 | Question: 37
In the figure shown, assume - $\alpha$ is the phase angle between the load current and the load voltage - $\quad \beta$ is the phase angle by which pressure coil current lags the pressure coil voltage of the wattmeter - $\quad \gamma$ ... $\alpha=\gamma \pm \delta \pm \theta+\beta$ $\alpha=\gamma \pm \delta \pm \theta-\beta$

In the figure shown, assume- $\alpha$ is the phase angle between the load current and the load voltage- $\quad \beta$ is the phase angle by which pressure coil current la...

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58

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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59

GATE IN 2024 | Question: 39
The complex functions $f(z)=u(x, y)+i v(x, y)$ and $\overline{f(z)}=u(x, y)-i v(x, y)$ are both analytic in a given domain. Choose the correct option(s) from the following. $\frac{\partial u}{\partial x}=\frac{\partial v}{\partial y}=0$ $\frac{\partial u}{\partial y}=-\frac{\partial v}{\partial x} \neq 0$ $\frac{d f(z)}{d z}=0$ $\frac{d f(z)}{d z} \neq 0$

The complex functions $f(z)=u(x, y)+i v(x, y)$ and $\overline{f(z)}=u(x, y)-i v(x, y)$ are both analytic in a given domain. Choose the correct option(s) from the followin...

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60

GATE IN 2024 | Question: 40
The readings recorded from a 20 -psig pressure gauge are given in the Table. The regression line obtained for the data is $y=0.04 x+10.32$. The regression coefficient of determination, $R^{2}=$ (rounded off to three decimal places). \begin{tabular}{|c|c|c|c|c|c|} \hline$x$ & 1 & 2 & 3 & 4 & 5 \\ \hline$y$ (psig) & 10.3 & 10.5 & 10.4 & 10.5 & 10.5 \\ \hline \end{tabular}

The readings recorded from a 20 -psig pressure gauge are given in the Table. The regression line obtained for the data is $y=0.04 x+10.32$. The regression coefficient of ...

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61

GATE IN 2024 | Question: 41
In the figure shown, $\mathrm{R}=4.5 \mathrm{k} \Omega, \Delta \mathrm{R}=1.5 \mathrm{k} \Omega$, and $\mathrm{INA}$ is assumed to be ideal. The equivalent resistance between $\mathrm{A}$ and $\mathrm{B}$ is $\mathrm{k} \Omega$ (rounded off to nearest integer).

In the figure shown, $\mathrm{R}=4.5 \mathrm{k} \Omega, \Delta \mathrm{R}=1.5 \mathrm{k} \Omega$, and $\mathrm{INA}$ is assumed to be ideal. The equivalent resistance bet...

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62

GATE IN 2024 | Question: 42
Consider the capacitive sensor circuit and its output voltage shown in the figure. The circuit is switched $\mathrm{ON}$ at $\mathrm{t}=0$. Assuming the opamp to be ideal, the frequency of the output voltage $\mathrm{V}_{0}$ is $\mathrm{kHz}$ (rounded off to two decimal places).

Consider the capacitive sensor circuit and its output voltage shown in the figure. The circuit is switched $\mathrm{ON}$ at $\mathrm{t}=0$. Assuming the opamp to be ideal...

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63

GATE IN 2024 | Question: 43
The 4-point DFTs of two sequences $x[n]$ and $y[n]$ are $X[k]=[1,-j, 1, j]$ and $Y[k]=[1,3 j, 1,-3 j]$, respectively. Assuming $z[n]$ represents the 4 -point circular convolution of $x[n]$ and $y[n]$, the value of $z[0]$ is (rounded off to nearest integer). Note: The DFT of a $N$-point sequence $x[n]$ is defined as \[ X[k]=\sum_{n=0}^{N-1} x[n] e^{\frac{-j 2 \pi n k}{N}} \]

The 4-point DFTs of two sequences $x[n]$ and $y[n]$ are $X[k]=[1,-j, 1, j]$ and $Y[k]=[1,3 j, 1,-3 j]$, respectively. Assuming $z[n]$ represents the 4 -point circular con...

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64

GATE IN 2024 | Question: 44
Consider the figure shown. For zero deflection in the galvanometer, the required value of resistor $R_{x}$ is $\Omega$ (rounded off to nearest integer).

Consider the figure shown. For zero deflection in the galvanometer, the required value of resistor $R_{x}$ is $\Omega$ (rounded off to nearest integer).

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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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66

GATE IN 2024 | Question: 46
A shielded cable with $\mathrm{C}_{\text {stray }}=20 \mathrm{pF}$ and $\mathrm{R}_{\text {wire }}=10 \Omega$ is used to connect the inductive sensors as shown in the figure. The RMS value of $V_{\text {out }}$ is $\mathrm{V}$ (rounded off to two decimal places). Note: Assume all components are ideal, and sensors are not magnetically coupled.

A shielded cable with $\mathrm{C}_{\text {stray }}=20 \mathrm{pF}$ and $\mathrm{R}_{\text {wire }}=10 \Omega$ is used to connect the inductive sensors as shown in the fig...

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67

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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68

GATE IN 2024 | Question: 48
An ADC has a full scale voltage of $1.4 \mathrm{~V}$, resolution of $200 \mathrm{mV}$, and produces binary output data. The input signal of the ADC has a bandwidth of $500 \mathrm{MHz}$, and it samples the data at the Nyquist rate. The parallel data output is converted to a serial bit stream using a parallel-to-serial converter. The data rate at the output of the parallel-to-serial converter is Gbps (rounded off to nearest integer).

An ADC has a full scale voltage of $1.4 \mathrm{~V}$, resolution of $200 \mathrm{mV}$, and produces binary output data. The input signal of the ADC has a bandwidth of $50...

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69

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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70

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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71

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

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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73

GATE IN 2024 | Question: 53
Two magnetically coupled coils, when connected in series-aiding configuration, have a total inductance of $500 \mathrm{mH}$. When connected in series-opposing configuration, the coils have a total inductance of $300 \mathrm{mH}$. If the self-inductance of both the coils are equal, then the coupling coefficient is (rounded off to two decimal places).

Two magnetically coupled coils, when connected in series-aiding configuration, have a total inductance of $500 \mathrm{mH}$. When connected in series-opposing configurati...

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74

GATE IN 2024 | Question: 54
The solution of an ordinary differential equation $y^{\prime \prime \prime}+3 y^{\prime \prime}+3 y^{\prime}+y=30 e^{-t}$ is \[ y(t)=\left(c_{0}+c_{1} t-c_{2} t^{2}+c_{3} t^{3}\right) e^{-t} \] Given $y(0)=3, y^{\prime}(0)=-3$ and $y^{\prime \prime}(0)=-47$, the value of $\left(c_{0}+c_{1}+c_{2}+c_{3}\right)$ is (rounded off ... $c_{0}, c_{1}, c_{2}, c_{3}$ are constants.

The solution of an ordinary differential equation $y^{\prime \prime \prime}+3 y^{\prime \prime}+3 y^{\prime}+y=30 e^{-t}$ is\[y(t)=\left(c_{0}+c_{1} t-c_{2} t^{2}+c_{3} t...

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75

GATE IN 2024 | Question: 55
A random variable $X$ has a probability density function \[ f_{X}(x)=\left\{\begin{array}{cc} e^{-x}, & x \geq 0 \\ 0, & \text { otherwise } \end{array}\right. \] The probability of $X>2$ is (rounded off to three decimal places).

A random variable $X$ has a probability density function\[f_{X}(x)=\left\{\begin{array}{cc}e^{-x}, & x \geq 0 \\0, & \text { otherwise }\end{array}\right.\]The probabilit...

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76

GATE IN 2023 | GA Question: 5
In the given diagram, ovals are marked at different heights $(h)$ of a hill. Which one of the following options $\mathbf{P}, \mathbf{Q}, \mathbf{R}$, and $\mathbf{S}$ depicts the top view of the hill? $\mathbf{P}$ $\mathbf{Q}$ $\mathbf{R}$ $\mathbf{S}$

In the given diagram, ovals are marked at different heights $(h)$ of a hill. Which one of the following options $\mathbf{P}, \mathbf{Q}, \mathbf{R}$, and $\mathbf{S}$ dep...

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77

GATE IN 2023 | GA Question: 6
Residency is a famous housing complex with many well-established individuals among its residents. A recent survey conducted among the residents of the complex revealed that all of those residents who are well established in their respective fields happen to be academicians. The survey also revealed that most of ... are residents of the complex who are well established in their fields. Some academicians residing in the complex are well established in their fields.

Residency is a famous housing complex with many well-established individuals among its residents. A recent survey conducted among the residents of the complex revealed th...

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78

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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79

GATE IN 2023 | GA Question: 9
Which one of the given figures $\text{P, Q, R}$ and $\text{S}$ represents the graph of the following function? $f(x)=|| x+2|-| x-1||$ $\text{P}$ $\text{Q}$ $\text{R}$ $\text{S}$

Which one of the given figures $\text{P, Q, R}$ and $\text{S}$ represents the graph of the following function?$$f(x)=|| x+2|-| x-1||$$ $\text{P}$$\text{Q}$$\text{R}$$\te...

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80

GATE IN 2023 | GA Question: 10

An opaque cylinder (shown below) is suspended in the path of a parallel beam of light, such that its shadow is cast on a screen oriented perpendicular to the direction of...

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