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1
GATE IN 2024 | GA Question: 1
If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words [drizzle $\rightarrow$ rain $\rightarrow$ downpour] is analogous to [ $\rightarrow$ quarrel $\rightarrow$ feud]. Which one of the given options is appropriate to fill the blank? bicker bog dither dodge
If ' $\rightarrow$ ' denotes increasing order of intensity, then the meaning of the words[drizzle $\rightarrow$ rain $\rightarrow$ downpour] is analogous to [ $\rightarro...
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GATE IN 2024 | GA Question: 2
Statements: 1. All heroes are winners. 2. All winners are lucky people. Inferences: I. All lucky people are heroes. II. Some lucky people are heroes. III. Some winners are heroes. Which of the above inferences can be logically deduced from statements 1 and 2 ? Only I and II Only II and III Only I and III Only III
Statements:1. All heroes are winners.2. All winners are lucky people.Inferences:I. All lucky people are heroes.II. Some lucky people are heroes.III. Some winners are hero...
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GATE IN 2024 | GA Question: 3
A student was supposed to multiply a positive real number $p$ with another positive real number $q$. Instead, the student divided $p$ by $q$. If the percentage error in the student's answer is $80 \%$, the value of $q$ is $5$ $\sqrt{2}$ $2$ $\sqrt{5}$
A student was supposed to multiply a positive real number $p$ with another positive real number $q$. Instead, the student divided $p$ by $q$. If the percentage error in t...
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GATE IN 2024 | GA Question: 4
If the sum of the first 20 consecutive positive odd numbers is divided by $20^{2}$, the result is $1$ $20$ $2$ $1 / 2$
If the sum of the first 20 consecutive positive odd numbers is divided by $20^{2}$, the result is$1$$20$$2$$1 / 2$
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GATE IN 2024 | GA Question: 5
The ratio of the number of girls to boys in class VIII is the same as the ratio of the number of boys to girls in class IX. The total number of students (boys and girls) in classes VIII and IX is 450 and 360 , respectively. If the number of girls in classes VIII and IX is the same, then the number of girls in each class is $150$ $200$ $250$ $175$
The ratio of the number of girls to boys in class VIII is the same as the ratio of the number of boys to girls in class IX. The total number of students (boys and girls) ...
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GATE IN 2024 | GA Question: 6
In the given text, the blanks are numbered (i)-(iv). Select the best match for all the blanks. Yoko Roi stands (i) as an author for standing (ii) as an honorary fellow, after she stood (iii) her writings that stand (iv) the freedom of speech. (i) out (ii) down (iii) in (iv) for (i) down (ii) out (iii) by (iv) in (i) down (ii) out (iii) for (iv) in (i) out (ii) down (iii) by (iv) for
In the given text, the blanks are numbered (i)-(iv). Select the best match for all the blanks.Yoko Roi stands (i) as an author for standing (ii) as an honorary fellow, af...
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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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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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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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GATE IN 2024 | GA Question: 10
Visualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about this axis such that its view remains unchanged. The ...
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GATE IN 2024 | Question: 1
Let $\boldsymbol{z}=x+i y$ be a complex variable and $\overline{\boldsymbol{z}}$ be its complex conjugate. The equation $\bar{z}^{2}+z^{2}=2$ represents a parabola hyperbola ellipse circle
Let $\boldsymbol{z}=x+i y$ be a complex variable and $\overline{\boldsymbol{z}}$ be its complex conjugate. The equation $\bar{z}^{2}+z^{2}=2$ represents aparabolahyperbol...
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GATE IN 2024 | Question: 2
The pressure drop across a control valve is constant. The control valve with inherent characteristic has decreasing sensitivity. If $x$ represents the fraction of maximum stem position of the control valve, then the function $f(x)$ representing the fraction of maximum flow is $\alpha^{x-1}$, where $\alpha$ is constant $\sqrt{x}$ $x$ $x^{2}$
The pressure drop across a control valve is constant. The control valve with inherent characteristic has decreasing sensitivity. If $x$ represents the fraction of maximum...
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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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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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GATE IN 2024 | Question: 5
The capacitor shown in the figure has parallel plates, with each plate having an area $A$. The thickness of the dielectric materials are $d_{1}$ and $d_{2}$ and their relative permittivities are $\varepsilon_{1}$ and $\varepsilon_{2}$, respectively. Assume that the fringing field effects are negligible and $\varepsilon_{0}$ is the permittivity of free ... $\frac{\varepsilon_{0} \mathrm{~A}}{\mathrm{~d}_{1}+\delta \mathrm{d}_{1}+\frac{\mathrm{d}_{2}}{\varepsilon_{2}}}$
The capacitor shown in the figure has parallel plates, with each plate having an area $A$. The thickness of the dielectric materials are $d_{1}$ and $d_{2}$ and their rel...
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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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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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GATE IN 2024 | Question: 8
The sinusoidal transfer function corresponding to the polar plot shown in the figure, for $T>0$, is $1-j \omega T$ $\frac{1-j \omega T}{1+j \omega T}$ $1+j \omega T$ $\frac{1}{1+j \omega T}$
The sinusoidal transfer function corresponding to the polar plot shown in the figure, for $T>0$, is$1-j \omega T$$\frac{1-j \omega T}{1+j \omega T}$$1+j \omega T$$\frac{1...
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GATE IN 2024 | Question: 9
A matrix $M$ is constructed by stacking three column vectors $v_{1}, v_{2}, v_{3}$ as \[ M=\left[\begin{array}{lll} v_{1} & v_{2} & v_{3} \end{array}\right] \] Choose the set of vectors from the following options such that $\operatorname{rank}(M)=3$ ...
A matrix $M$ is constructed by stacking three column vectors $v_{1}, v_{2}, v_{3}$ as\[M=\left[\begin{array}{lll}v_{1} & v_{2} & v_{3}\end{array}\right]\]Choose the set o...
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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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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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GATE IN 2024 | Question: 12
Consider a filter defined by the difference equation \[ y[n]-0.5 y[n-2]=a x[n-4] \] where $x[n]$ and $y[n]$ represent the input and output, respectively. If the magnitude response of the filter at $\omega=\frac{\pi}{2}$ is $\left|H\left(\frac{\pi}{2}\right)\right|=0.5$, the value of $a$ is (rounded off to two decimal places).
Consider a filter defined by the difference equation\[y[n]-0.5 y[n-2]=a x[n-4]\]where $x[n]$ and $y[n]$ represent the input and output, respectively. If the magnitude res...
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GATE IN 2024 | Question: 13
Consider the circuit shown in the figure. The CMOS digital logic circuit has infinite input impedance. Assume the opamp is ideal. A 1.8 V Zener diode with a minimum Zener current of $2 \mathrm{~mA}$ is used. The corresponding maximum value of resistance $\mathrm{Rz}$ is $\mathrm{k} \Omega$. (rounded off to one decimal place).
Consider the circuit shown in the figure.The CMOS digital logic circuit has infinite input impedance. Assume the opamp is ideal. A 1.8 V Zener diode with a minimum Zener ...
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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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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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GATE IN 2024 | Question: 16
A $3 \times 3$ matrix $P$ with all real elements has eigenvalues $\frac{1}{4}, 1$, and -2 . The value of $\left|P^{-1}\right|$ is (rounded off to nearest integer).
A $3 \times 3$ matrix $P$ with all real elements has eigenvalues $\frac{1}{4}, 1$, and -2 . The value of $\left|P^{-1}\right|$ is (rounded off to nearest integer).
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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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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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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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GATE IN 2024 | Question: 20
The voltage applied and the current drawn by a circuit are \[ \begin{array}{c} v(t)=95+200 \cos (120 \pi t)+90 \cos \left(360 \pi t-60^{\circ}\right) \mathrm{V} \\ i(t)=4 \cos \left(120 \pi t-60^{\circ}\right)+1.5 \cos \left(240 \pi t-75^{\circ}\right) \mathrm{A} \end{array} \] The average power absorbed by the circuit is W (rounded off to nearest integer).
The voltage applied and the current drawn by a circuit are\[\begin{array}{c}v(t)=95+200 \cos (120 \pi t)+90 \cos \left(360 \pi t-60^{\circ}\right) \mathrm{V} \\i(t)=4 \co...
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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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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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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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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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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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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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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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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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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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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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