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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...

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gatecse asked Feb 20, 2018

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2

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...

2.9k points

Arjun asked Feb 16

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3

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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Arjun asked Feb 16

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4

GATE2018-GA-3
For $0\leq{x}\leq{2\pi}$, $\sin x \text{ and } \cos x$ are both decreasing functions in the interval _________ . $\left(0,\dfrac{\pi}{2}\right)$ $\left(\dfrac{\pi}{2},\pi\right)$ $\left(\pi,\dfrac{3\pi}{2}\right)$ $\left(\dfrac{3\pi}{2},2\pi\right)$

For $0\leq{x}\leq{2\pi}$, $\sin x \text{ and } \cos x$ are both decreasing functions in the interval _________ .$\left(0,\dfrac{\pi}{2}\right)$$\left(\dfrac{\pi}{2},\pi\r...

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gatecse asked Feb 20, 2018

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5

GATE IN 2023 | GA Question: 4
Which one among the following statements must be $\text{TRUE}$ about the mean and the median of the scores of all candidates appearing for $\text{GATE }2023?$ The median is at least as large as the mean. The mean is at least as large as the median. At most half the candidates have a score that is larger than the median At most half the candidates have a score that is larger than the mean.

Which one among the following statements must be $\text{TRUE}$ about the mean and the median of the scores of all candidates appearing for $\text{GATE }2023?$The median i...

2.7k points

admin asked May 22, 2023

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6

GATE IN 2023 | GA Question: 3
A 'frabjous' number is defined as a $3$ digit number with all digits odd, and no two adjacent digits being the same. For example, $137$ is a frabjous number, while $133$ is not. How many such frabjous numbers exist? $125$ $720$ $60$ $80$

A 'frabjous' number is defined as a $3$ digit number with all digits odd, and no two adjacent digits being the same. For example, $137$ is a frabjous number, while $133$ ...

2.7k points

admin asked May 22, 2023

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7

GATE2018-GA-2
"In spite of being warned repeatedly, he failed to correct his _________ behaviour ." The word that best fills the blank in the above sentence is rational reasonable errant good

"In spite of being warned repeatedly, he failed to correct his _________ behaviour ."The word that best fills the blank in the above sentence isrationalreasonableerrantgo...

1.4k points

gatecse asked Feb 20, 2018

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8

GATE2017: 61
Bhaichung was observing the pattern of people entering and leaving a car service centre. There was a single window where customers were being served. He saw that people inevitably came out of the centre in the order that they went in. However, the time they spent inside seemed to vary a lot: some people came out in ... likely to operate on a last-come-first-served basis. Entering the centre early ensured that one would have shorter service times and most people attempted to do this.

Bhaichung was observing the pattern of people entering and leaving a car service centre. There was a single window where customers were being served. He saw that people i...

soujanyareddy13

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soujanyareddy13 asked Nov 2, 2020

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9

GATE IN 2021 | GA Question: 7
Consider two rectangular sheets, Sheet $\text{M}$ and Sheet $\text{N}$ of dimensions $6\:cm \times 4\:cm$ each. $\text{Folding operation 1}$ : The sheet is folded into half by joining the short edges of the current shape. $\text{Folding operation 2}$ : The sheet is folded into half by joining the long edges of the current shape. ... of the final folded shape of Sheet $\text{N}$ to the final folded shape of Sheet $\text{M}$ is _____________. $13:7$ $3:2$ $7:5$ $5:13$

Consider two rectangular sheets, Sheet $\text{M}$ and Sheet $\text{N}$ of dimensions $6\:cm \times 4\:cm$ each.$\text{Folding operation 1}$ : The sheet is folded into hal...

2.9k points

Arjun asked Feb 19, 2021

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10

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...

2.9k points

Arjun asked Feb 16

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11

GATE2018IN: 44
A 2-bit synchronous counter using two $J-K$ flip flops is shown. The expressions for the inputs to the $J-K$ flip flops are also shown in the figure. The output sequence of the counter starting from $Q_1Q_2 = 00$ is $00 \rightarrow 11 \rightarrow 10 \rightarrow 01 \rightarrow 00 …$ $00 \rightarrow 01 \rightarrow 10 \rightarrow 11 \rightarrow 00…$ $00 \rightarrow 01 \rightarrow 11 \rightarrow 10 \rightarrow 00…$ $00 \rightarrow 10 \rightarrow 11 \rightarrow 01 \rightarrow 00 ...$

A 2-bit synchronous counter using two $J-K$ flip flops is shown. The expressions for the inputs to the $J-K$ flip flops are also shown in the figure. The output sequence ...

1.4k points

gatecse asked Feb 20, 2018

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12

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...

2.7k points

admin asked Feb 16

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13

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...

2.7k points

admin asked Feb 16

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14

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...

2.9k points

Arjun asked Feb 16

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15

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...

2.7k points

admin asked Feb 16

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16

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...

2.7k points

admin asked Feb 16

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17

GATE2020 IN: 24
The capacitance $C_x$ of a capacitive type sensor is $(1000x) pF,$ where x is the input to the sensor. As shown in the figure, the sensor is excited by a voltage $\text{10 sin(100}\pi\: t) V$. The other terminal of the sensor is tied to the input of a high input impedance amplifier through a shielded cable, with shield connected ... . The cable capacitance is $\text{100 pF}$. The peak of the voltage $V_A$ at the input of the amplifier when $\text{x=0.1 (in volts)}$ is _________.

The capacitance $C_x$ of a capacitive type sensor is $(1000x) pF,$ where x is the input to the sensor. As shown in the figure, the sensor is excited by a voltage $\text{...

soujanyareddy13

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soujanyareddy13 asked Nov 3, 2020

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18

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...

2.7k points

admin asked May 22, 2023

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19

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...

2.9k points

Arjun asked Feb 16

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20

GATE2019 IN: GA-7
In a country of $1400$ million population, $70\%$ own mobile phones. Among the mobile phone owners, only $294$ million access the Internet. Among these Internet users, only half buy goods from e-commerce portals. What is the percentage of these buyers in the country? $10.50$ $14.70$ $15.00$ $50.00$

In a country of $1400$ million population, $70\%$ own mobile phones. Among the mobile phone owners, only $294$ million access the Internet. Among these Internet users, on...

2.9k points

Arjun asked Feb 10, 2019

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21

GATE2018-GA-1
"When she fell down the ________ , she received many _________ but little help." The words that best fill the blanks in the above sentence are stairs, stares stairs, stairs stares, stairs stares, stares

"When she fell down the ________ , she received many _________ but little help."The words that best fill the blanks in the above sentence arestairs, staresstairs, stairss...

1.4k points

gatecse asked Feb 20, 2018

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22

GATE2018IN: 14
Consider the transfer function G(s) = $\frac{2}{(s+1)(s+2)}$. The phase margin of G(s) in degrees is $\_\_\_\_\_$

Consider the transfer function G(s) = $\frac{2}{(s+1)(s+2)}$. The phase margin of G(s) in degrees is $\_\_\_\_\_$

1.4k points

gatecse asked Feb 20, 2018

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23

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...

2.7k points

admin asked Feb 16

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24

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 ...

2.7k points

admin asked Feb 16

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25

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...

2.7k points

admin asked Feb 16

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26

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...

2.7k points

admin asked Feb 16

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27

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).

2.7k points

admin asked Feb 16

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28

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...

2.7k points

admin asked Feb 16

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29

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...

2.7k points

admin asked Feb 16

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30

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).

2.7k points

admin asked Feb 16

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31

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...

2.7k points

admin asked Feb 16

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32

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...

2.7k points

admin asked Feb 16

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33

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...

2.7k points

admin asked May 22, 2023

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34

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...

2.7k points

admin asked Feb 16

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35

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...

2.7k points

admin asked Feb 16

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36

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...

2.7k points

admin asked Feb 16

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37

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...

2.9k points

Arjun asked Feb 16

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38

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 ...

2.7k points

admin asked Feb 16

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39

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...

2.7k points

admin asked Feb 16

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40

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...

2.7k points

admin asked Feb 16

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