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User Lakshman Patel RJIT
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Recent activity by Lakshman Patel RJIT
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1
GATE ECE 2022 | Question: 39
Consider a Boolean gate $\text{(D)}$ where the output $Y$ is related to the inputs $A$ and $B$ as, $Y = A + \overline{B},$ where $+$ denotes logical $\text{OR}$ operation. The Boolean inputs $'0'$ and $'1'$ are also ... $\text{OR}$ logic cannot be implemented $\text{NOR}$ logic can be implemented $\text{AND}$ logic cannot be implemented
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Others
Mar 21
16
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gateece-2022
multiple-selects
0
answers
2
GATE ECE 2022 | Question: 37
Select the $\text{CORRECT}$ statement(s) regarding semiconductor devices. Electrons and holes are of equal density in an intrinsic semiconductor at equilibrium. Collector region is generally more heavily doped than Base region in a $\text{BJT}.$ ... under steady state condition. Mobility of electrons always increases with temperature in Silicon beyond $300 \; \text{K}.$
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Others
Mar 21
27
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gateece-2022
multiple-selects
0
answers
3
GATE ECE 2022 | Question: 35
Consider the following series: $ \sum_{n=1}^{\infty} \frac{n^{d}}{c^{n}}$ For which of the following combinations of $c, d$ values does this series converge? $ c= 1, d = – 1$ $ c= 2, d = 1$ $ c= 0.5, d = – 10$ $ c= 1, d = – 2$
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Others
Mar 21
13
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gateece-2022
multiple-selects
0
answers
4
GATE ECE 2022 | Question: 20
Consider the following wave equation, $\frac{\partial^{2}f(x, t)}{\partial t^{2}} = 10000 \frac{\partial^{2}f(x, t)}{\partial x^{2}} $ Which of the given options is/are solution(s) to the given wave equation? $f(x, t) = e^{ - (x-100t)^{2}} + e^{ - (x+100t)^{2}}$ ... $f(x, t) = e^{ j 100 \pi (- 100x + t)} + e^{ j 100 \pi (100x + t)}$
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Others
Mar 21
40
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gateece-2022
multiple-selects
0
answers
5
GATE ECE 2022 | Question: 19
Let $H(X)$ denote the entropy of a discrete random variable $X$ taking $K$ possible distinct real values. Which of the following statements is/are necessarily true? $H(X) \leq \log_{2} K \; \text{bits}$ $H(X) \leq H (2X)$ $H(X) \leq H (X^{2})$ $H(X) \leq H (2^{X})$
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Others
Mar 21
53
views
gateece-2022
multiple-selects
0
answers
6
GATE ECE 2022 | Question: 17
Select the Boolean function(s) equivalent to $x+yz,$ where $x, y,$ and $z$ are Boolean variables, and $+$ denotes logical $\text{OR}$ operation. $x + z + xy$ $(x + y)(x + z)$ $x + xy + yz$ $x + xz + xy$
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Others
Mar 21
43
views
gateece-2022
multiple-selects
0
answers
7
GATE ECE 2022 | Question: 15
Consider the following partial differential equation $\text{(PDE)}$ $a \frac{ \partial^{2} f(x ,y)}{\partial x^{2}} + b \frac{ \partial^{2} f(x ,y)}{\partial y^{2}} = f(x, y),$ where $a$ and $b$ are distinct positive real numbers. Select the combination(s) of values of the ... $\xi = 0, \eta = 0$ $\xi = \frac{1}{\sqrt{a}}, \eta = \frac{1}{\sqrt{b}}$
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Others
Mar 21
39
views
gateece-2022
multiple-selects
1
answer
8
GATE ECE 2022 | GA Question: 5
An art gallery engages a security guard to ensure that the items displayed are protected. The diagram below represents the plan of the gallery where the boundary walls are opaque. The location the security guard posted is identified such that all the inner space (shaded region in the plan) ... $\text{Q}$ $\text{Q}$ $\text{Q}$ and $\text{S}$ $\text{R}$ and $\text{S}$
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in
Spatial Aptitude
Feb 26
109
views
gateece-2022
spatial-aptitude
patterns-in-two-dimensions
1
answer
9
GATE ECE 2022 | GA Question: 9
In a class of five students $\text{P, Q, R, S}$ and $\text{T},$ ... given above, the person who has copied in the exam is $\text{R}$ $\text{P}$ $\text{Q}$ $\text{T}$
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Analytical Aptitude
Feb 26
150
views
gateece-2022
analytical-aptitude
logical-reasoning
statements-follow
1
answer
10
GATE ECE 2022 | GA Question: 10
Consider the following square with the four corners and the center marked as $\text{P, Q, R, S}$ and $\text{T}$ respectively. Let $\text{X, Y}$ and $\text{Z}$ represent the following operations: $\text{X:}$ rotation of the square by $180$ ... The sequence of operations $(2)$ and $(3)$ are equivalent The sequence of operations $(1), (2)$ and $(3)$ are equivalent
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in
Spatial Aptitude
Feb 26
107
views
gateece-2022
spatial-aptitude
rotation
1
answer
11
GATE ECE 2022 | GA Question: 1
Mr. $\text{X}$ speaks __________ Japanese ____________ Chinese. neither /or either / nor neither / nor also / but
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in
Verbal Aptitude
Feb 21
127
views
gateece-2022
verbal-aptitude
most-appropriate-word
1
answer
12
GATE ECE 2022 | GA Question: 4
The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole. What is the maximum number of squares without a “hole in the interior” that can be formed within the $4 \times 4$ grid using the unit squares as building blocks? $15$ $20$ $21$ $26$
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in
Spatial Aptitude
Feb 21
91
views
gateece-2022
spatial-aptitude
patterns-in-two-dimensions
counting-figure
1
answer
13
GATE ECE 2022 | GA Question: 3
A trapezium has vertices marked as $\text{P, Q, R}$ and $\text{S}$ (in that order anticlockwise). The side $\text{PQ}$ is parallel to side $\text{SR}.$ Further, it is given that, $\text{PQ = 11 cm, QR = 4 cm, RS = 6 cm}$ and $\text{SP = 3 cm.}$ What is the shortest distance between $\text{PQ}$ and $\text{SR (in cm)}?$ $1.80$ $2.40$ $4.20$ $5.76$
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Quantitative Aptitude
Feb 21
194
views
gateece-2022
quantitative-aptitude
geometry
1
answer
14
GATE ECE 2022 | GA Question: 8
Four points $\text{P(0, 1), Q(0, – 3), R( – 2, – 1),}$ and $\text{S(2, – 1)}$ represent the vertices of a quadrilateral. What is the area enclosed by the quadrilateral? $4$ $4 \sqrt{2}$ $8$ $8 \sqrt{2}$
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Quantitative Aptitude
Feb 21
70
views
gateece-2022
quantitative-aptitude
cartesian-coordinates
area
1
answer
15
GATE ECE 2022 | GA Question: 2
A sum of money is to be distributed among $\text{P, Q, R,}$ and $\text{S}$ in the proportion $5:2:4:3,$ respectively. If $\text{R}$ gets ₹ $ 1000$ more than $\text{S},$ what is the share of $\text{Q (in ₹)}?$ $500$ $1000$ $1500$ $2000$
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in
Quantitative Aptitude
Feb 21
100
views
gateece-2022
quantitative-aptitude
ratio-proportions
1
answer
16
GATE ECE 2022 | GA Question: 7
Consider the following inequalities. $2x – 1 > 7$ $2x – 9 < 1$ Which one of the following expressions below satisfies the above two inequalities? $x \leq – 4$ $ – 4 < x \leq 4$ $4 < x < 5$ $x \geq 5$
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in
Quantitative Aptitude
Feb 19
73
views
gateece-2022
quantitative-aptitude
inequality
1
answer
17
GATE ECE 2021 | GA Question: 9
The number of minutes spent by two students, $X$ and $Y$, exercising every day in a given week are shown in the bar chart above. The number of days in the given week in which one of the students spent a minimum of $10\%$ more than the other student, on a given day, is $4$ $5$ $6$ $7$
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in
Quantitative Aptitude
Apr 23, 2021
416
views
gateec-2021
numerical-ability
data-interpretation
bar-graph
2
answers
18
GATE ECE 2020 | GA Question: 10
The following figure shows the data of students enrolled in $5$ years $(2014\;\text{to}\; 2018)$ for two schools $P$ and $Q$. During this period, the ratio of the average number of the students enrolled in school $P$ to the average of the difference of the number of students enrolled in schools $P$ and $Q$ is _______. $8 : 23$ $23 : 8$ $23 : 31$ $31 : 23$
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Quantitative Aptitude
Apr 22, 2021
1.2k
views
gate2020-ec
numerical-ability
data-interpretation
bar-graph
1
answer
19
GATE ECE 2021 | GA Question: 5
Consider the following sentences: I woke up from sleep. I woked up from sleep. I was woken up from sleep. I was wokened up from sleep. Which of the above sentences are grammatically $\text{CORRECT}$? $\text{(i) and (ii)}$ $\text{(i) and (iii)}$ $\text{(ii) and (iii)}$ $\text{(i) and (iv)}$
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Verbal Aptitude
Apr 11, 2021
383
views
gateec-2021
verbal-ability
english-grammar
tense
1
answer
20
GATE ECE 2021 | GA Question: 7
Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence $\text{(AI)}$ is currently a hot topic. $\text{Al}$ enables computers to learn, given enough training data. For humans, sitting in front of a ... $\text{(ii) and (iv)}$ $\text{(i), (iii) and (iv)}$ $\text{(i) and (iii)}$
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in
Verbal Aptitude
Apr 11, 2021
256
views
gateec-2021
verbal-ability
verbal-reasoning
passage-reading
1
answer
21
GATE ECE 2021 | GA Question: 4
$\textit{Nostalgia}$ is to $\textit{anticipation}$ as ____________ is to _____________ Which one of the following options maintains a similar logical relation in the above sentence? Present, past Future, past Past, future Future, present
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in
Verbal Aptitude
Apr 11, 2021
397
views
gateec-2021
verbal-ability
word-pairs
1
answer
22
GATE ECE 2021 | GA Question: 3
The least number of squares that must be added so that the line $P-Q$ becomes the line of symmetry is ____________ $4$ $3$ $6$ $7$
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Spatial Aptitude
Apr 11, 2021
334
views
gateec-2021
spatial-aptitude
patterns-in-two-dimensions
2
answers
23
GATE ECE 2021 | GA Question: 2
$p$ and $q$ are positive integers and $\dfrac{p}{q}+\dfrac{q}{p}=3,$ then, $\dfrac{p^{2}}{q^{2}}+\dfrac{q^{2}}{p^{2}}=$ $3$ $7$ $9$ $11$
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in
Quantitative Aptitude
Apr 11, 2021
286
views
gateec-2021
numerical-ability
algebra
1
answer
24
GATE ECE 2021 | GA Question: 1
The current population of a city is $11,02,500$ . If it has been increasing at the rate of $5\%$ per annum, what was its population $2$ years ago? $9,92,500$ $9,95,006$ $10,00,000$ $12,51,506$
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in
Quantitative Aptitude
Apr 11, 2021
268
views
gateec-2021
numerical-ability
simple-compound-interest
1
answer
25
GATE ECE 2021 | GA Question: 6
Given below are two statements and two conclusions. $\text{Statement 1}$: All purple are green. $\text{Statement 2}$: All black are green. $\text{Conclusion I}$: Some black are purple. $\text{Conclusion II}$: No black is purple. Based on the above ... correct Either conclusion $\text{I}$ or $\text{II}$ is correct Both conclusion $\text{I}$ and $\text{II}$ are correct
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Analytical Aptitude
Apr 11, 2021
620
views
gateec-2021
analytical-aptitude
logical-reasoning
statements-follow
0
answers
26
GATE ECE 2021 | Question: 12
Addressing of a $32K\:\times\:16$ memory is realized using a single decoder. The minimum number of $\text{AND}$ gates required for the decoder is $2^{8}$ $2^{32}$ $2^{15}$ $2^{19}$
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Digital Circuits
Apr 11, 2021
103
views
gateec-2021
digital-circuits
combinational-circuits
decoders
0
answers
27
GATE ECE 2021 | Question: 11
If $(1235)_{x}\:=\:(3033)_{y}$, where $x$ and $y$ indicate the bases of the corresponding numbers, then $x\:=\:7$ and $y\:=\:5$ $x\:=\:8$ and $y\:=\:6$ $x\:=\:6$ and $y\:=\:4$ $x\:=\:9$ and $y\:=\:7$
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Digital Circuits
Apr 11, 2021
237
views
gateec-2021
digital-circuits
number-system
number-representation
0
answers
28
GATE ECE 2021 | Question: 13
The block diagram of a feedback control system is shown in the figure The transfer function $\dfrac{Y{\left ( s \right )}}{X {\left ( s \right )}}$ of the system is $\frac{G_{1}+G_{2}+G_{1}G_{2}H}{1+G_{1}H}$ $\frac{G_{1}+G_{2}}{1+G_{1}H+G_{2}H}$ $\frac{G_{1}+G_{2}}{1+G_{1}H}$ $\frac{G_{1}+G_{2}+G_{1}G_{2}H}{1+G_{1}H+G_{2}H}$
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Control Systems
Apr 11, 2021
90
views
gateec-2021
control-systems
0
answers
29
GATE ECE 2021 | Question: 37
For a vector field $D=\rho\cos^{2}\:\varphi \:a_{\rho }+z^{2}\sin^{2}\:\varphi \:a_{\varphi }$ in a cylindrical coordinate system $\left ( \rho ,\varphi ,z \right )$ with unit vectors $a_{\rho },a_{\varphi }$ and $a_{z}$, the ... $\left ( \rho =3, 0\leq z\leq 2 \right )$ (rounded off to two decimal places) is ________________
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Vector Analysis
Apr 11, 2021
55
views
gateec-2021
numerical-answers
vector-analysis
1
answer
30
GATE ECE 2021 | Question: 1
The vector function $F\left ( r \right )=-x\hat{i}+y\hat{j}$ is defined over a circular arc $C$ shown in the figure. The line integral of $\int _{C} F\left ( r \right ).dr$ is $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{6}$ $\frac{1}{3}$
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Vector Analysis
Apr 11, 2021
347
views
gateec-2021
vector-analysis
vector-in-planes
0
answers
31
GATE ECE 2021 | Question: 16
If the vectors $(1.0,\:-1.0,\:2.0)$, $(7.0,\:3.0,\:x)$ and $(2.0,\:3.0,\:1.0)$ in $\mathbb{R}^{3}$ are linearly dependent, the value of $x$ is __________
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in
Vector Analysis
Apr 11, 2021
147
views
gateec-2021
numerical-answers
vector-analysis
vector-in-planes
0
answers
32
GATE ECE 2021 | Question: 17
Consider the vector field $F\:=\:a_{x}\left ( 4y-c_{1}z \right )+a_y\left ( 4x + 2z\right )+a_{z}\left ( 2y +z\right )$ in a rectangular coordinate system $(x,y,z)$ with unit vectors $a_{x},\:a_{y}$ and $a_{z}$. If the field $F$ is irrotational (conservative), then the constant $c_{1}$ (in integer) is _________________
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in
Vector Analysis
Apr 11, 2021
125
views
gateec-2021
numerical-answers
vector-analysis
vector-in-planes
0
answers
33
GATE ECE 2021 | Question: 26
Consider the integral $\oint _{c}\frac{sin\left ( x \right )}{x^{2}\left ( x^{2}+4 \right )}dx$ where $C$ is a counter-clockwise oriented circle defined as $\left | x-i \right |=2$. The value of the integral is $-\frac{\pi }{8}\sin\left ( 2i \right )$ $\frac{\pi }{8}\sin\left ( 2i \right )$ $-\frac{\pi }{4}\sin\left ( 2i \right )$ $\frac{\pi }{4}\sin\left ( 2i \right )$
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in
Complex Analysis
Apr 11, 2021
209
views
gateec-2021
complex-analysis
0
answers
34
GATE ECE 2021 | Question: 27
A box contains the following three coins. A fair coin with head on one face and tail on the other face. A coin with heads on both the faces. A coin with tails on both the faces. A coin is picked randomly from the box and tossed. Out of the two remaining coins in the box, one ... getting a head in the second toss is $\frac{2}{5}$ $\frac{1}{3}$ $\frac{1}{2}$ $\frac{2}{3}$
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Probability and Statistics
Apr 11, 2021
209
views
gateec-2021
probability-and-statistics
probability
conditional-probability
1
answer
35
GATE ECE 2021 | GA Question: 10
Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above. The ratio of the area of the regular convex hexagon to the area of the original equilateral triangle is $2:3$ $3:4$ $4:5$ $5:6$
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in
Quantitative Aptitude
Apr 11, 2021
367
views
gateec-2021
numerical-ability
geometry
triangles
area
0
answers
36
GATE ECE 2021 | Question: 3
Two continuous random variables $X$ and $Y$ are related as $Y=2X+3$ Let $\sigma ^{2}_{X}$ and $\sigma ^{2}_{Y}$denote the variances of $X$ and $Y$, respectively. The variances are related as $\sigma ^{2}_{Y}=2 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=4 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=5 \sigma ^{2}_{X}$ $\sigma ^{2}_{Y}=25 \sigma ^{2}_{X}$
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in
Probability and Statistics
Apr 11, 2021
111
views
gateec-2021
probability-and-statistics
random-variable
variance
0
answers
37
GATE ECE 2021 | Question: 2
Consider the differential equation given below. $\frac{dy}{dx}+\frac{x}{1-x^{2}}y=x\sqrt{y}$ The integrating factor of the differential equation is $\left ( 1-x^{2} \right )^{-3/4}$ $\left ( 1-x^{2} \right )^{-1/4}$ $\left ( 1-x^{2} \right )^{-3/2}$ $\left ( 1-x^{2} \right )^{-1/2}$
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in
Differential Equations
Apr 11, 2021
148
views
gateec-2021
differential-equations
first-order-differential-equation
1
answer
38
GATE ECE 2021 | GA Question: 8
Consider a square sheet of side $1$ unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step. one of the cut triangles is revolved about its short edge to form a solid cone. The volume of the resulting cone, in cubic units, is ____________ $\frac{\pi }{3}$ $\frac{2\pi }{3}$ $\frac{3\pi }{2}$ $3\pi$
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Quantitative Aptitude
Apr 11, 2021
1.6k
views
gateec-2021
numerical-ability
mensuration
cones
0
answers
39
GATE ECE 2021 | Question: 36
A real $2\times2$ non-singular matrix $A$ with repeated eigenvalue is given as $A=\begin{bmatrix} x & -3.0\\ 3.0 & 4.0 \end{bmatrix}$ where $x$ is a real positive number. The value of $x$ (rounded off to one decimal place) is ________________
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Linear Algebra
Apr 11, 2021
94
views
gateec-2021
numerical-answers
linear-algebra
eigen-values
0
answers
40
GATE ECE 2021 | Question: 46
The propagation delay of the exclusive$-\text{OR}$ ($\text{XOR}$) gate in the circuit in the figure is $3\:ns$. The propagation delay of all the flip-flops is assumed to be zero. The clock ($\text{Clk}$ ... of triggering clock edges after which the flip-flop outputs $Q_{2}Q_{1}Q_{0}$ becomes $1\; 0\; 0$ (in integer) is
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in
Digital Circuits
Apr 11, 2021
123
views
gateec-2021
numerical-answers
digital-circuits
sequential-circuit
counters
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