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1
GATE201361
$X$ and $Y$ are two positive real numbers such that $2X+Y \leq 6$ and $X + 2Y \leq 8$. For which of the following values of $(X,Y)$ the function $f(X,Y)=3X + 6Y$ will give maximum value ? $\left(\dfrac{4}{3} , \dfrac{10}{3}\right) \\$ $\left(\dfrac{8}{3} , \dfrac{20}{3}\right) \\$ $\left(\dfrac{8}{3} , \dfrac{10}{3}\right) \\$ $\left(\dfrac{4}{3} , \dfrac{20}{3}\right)$
edited
Jul 28
in
Numerical Ability
gate2013ce
0
answers
2
GATE20152GA4
Mr. Vivek walks $6$ meters Northeast, then turns and walks $6$ meters Southeast, both at $60$ degrees to east. He further moves $2$ meters South and $4$ meters West. What is the straight distance in meters between the point he started from and the point he finally reached? $2\sqrt{2}$ $2$ $\sqrt{2}$ $\dfrac{1}{\sqrt{2}}$
edited
Jul 27
in
Numerical Ability
gate2015ce2
0
answers
3
GATE20152GA5
Four cards are randomly selected from a pack of $52$ cards. If the first two cards are kings, what is the probability that the third card is a king? $\dfrac{4}{52} \\$ $\dfrac{2}{50} \\$ $\left ( \dfrac{1}{52}\right )\times\left ( \dfrac{1}{52}\right ) \\$ $\left ( \dfrac{1}{52}\right )\times\left ( \dfrac{1}{51}\right )\times\left ( \dfrac{1}{50}\right )$
edited
Jul 27
in
Numerical Ability
gate2015ce2
0
answers
4
GATE201524
$\underset{x \to \infty}{\lim} \bigg( 1+ \dfrac{1}{x} \bigg)^{2x} $ is equal to $e^{2}$ $e$ $1$ $e^2$
edited
Jul 27
in
Calculus
gate2015ce2
engineeringmathematics
0
answers
5
GATE20152GA9
Read the following table giving sales data of five types of batteries for years $2006$ to $2012$ ... the following, which type of battery achieved highest growth between the years $2006$ and $2012$? Type $V$ Type $III$ Type $II$ Type $I$
edited
Jul 27
in
Numerical Ability
gate2015ce2
0
answers
6
GATE2015128
Consider the following differential equation: $x(y\:dx +x\:dy) \cos \dfrac{y}{x}=y(x\:dyy\:dx) \sin \dfrac{y}{x}$ Which of the following is the solution of the above equation ($c$ is an arbitrary constant)? $\dfrac{x}{y} \cos \dfrac{y}{x} = c \\$ $\dfrac{x}{y} \sin \dfrac{y}{x} = c \\$ $xy \cos \dfrac{y}{x} = c \\$ $xy \sin \dfrac{y}{x} = c$
edited
Jul 26
in
Ordinary Differential Equation (ODE)
gate2015ce1
ordinarydifferentialequation
engineeringmathematics
0
answers
7
GATE2016227
If $f(x)$ and $g(x)$ are two probability density functions, $f(x) = \begin{cases} \dfrac{x}{a}+1 & :a \leq x < 0 \\ \dfrac{x}{a}+1 & : 0 \leq x \leq a \\ 0 & :\text{otherwise} \end{cases}$ ... different; Variance of $f(x)$ and $g(x)$ are same Mean of $f(x)$ and $g(x)$ are different; Variance of $f(x)$ and $g(x)$ are different
edited
Jul 25
in
Probability and Statistics
gate2016ce2
probabilitydensityfunction
engineeringmathematics
0
answers
8
GATE201625
What is the value of $\underset{x \rightarrow 0 \\ y \rightarrow 0}{\lim} \dfrac{xy}{x^2+y^2}$? $1$ $1$ $0$ Limit does not exist
edited
Jul 25
in
Calculus
gate2016ce2
limit
calculus
engineeringmathematics
0
answers
9
GATE2017 CE1: GA9
Two machines $M1$ and $M2$ are able to execute any of four jobs $P, Q, R$ and $S$. The machines can perform one job on one object at a time. Jobs $P, Q, R$ and $S$ take $30$ minutes, $20$ minutes, $60$ minutes and $15$ minutes each respectively. There ... $S$ on $4$ objects. What is the minimum time needed to complete all the jobs? $2$ hours $2.5$ hours $3$ hours $3.5$ hours
edited
Jul 25
in
Numerical Ability
gate2017ce1
generalaptitude
numericalability
worktime
0
answers
10
GATE2017 CE2: GA2
There was no doubt that their work was thorough. Which of the words below is closest in meaning to the underlined word above? pretty complete sloppy haphazard
edited
Jul 24
in
Verbal Ability
gate2017ce2
0
answers
11
GATE2017 CE227
Consider the following definite integral: $I= \int_0^1 \dfrac{(\sin ^{1}x)^2}{\sqrt{1x^2}} dx$. The value of the integral is $\dfrac{\pi ^3}{24} \\$ $\dfrac{\pi ^3}{12} \\$ $\dfrac{\pi ^3}{48} \\$ $\dfrac{\pi ^3}{64}$
edited
Jul 24
in
Calculus
gate2017ce2
definite
integral
calculus
engineeringmathematics
0
answers
12
GATE2017 CE2: GA5
Two dice are thrown simultaneously. The probability that the product of the numbers appearing on the top faces of the dice is a perfect square is $\dfrac{1}{9} \\$ $\dfrac{2}{9} \\$ $\dfrac{1}{3} \\$ $\dfrac{4}{9}$
edited
Jul 24
in
Numerical Ability
gate2017ce2
0
answers
13
GATE2017 CE2: GA4
What is the value of $x$ when $81\times\left (\dfrac{16}{25} \right )^{x+2}\div\left (\dfrac{3}{5} \right )^{2x+4}=144?$ $1$ $1$ $2$ $\text{Can not be determined}$
edited
Jul 24
in
Numerical Ability
gate2017ce2
0
answers
14
GATE2018 CE2: GA9
Given that $\dfrac{\log P}{yz} = \dfrac{\log Q}{zx} = \dfrac{\log R}{xy} = 10$ for $x \neq y \neq z$, what is the value of the product $PQR$? $0$ $1$ $xyz$ $10^{xyz}$
edited
Jul 23
in
Numerical Ability
gate2018ce2
generalaptitude
numericalability
logarithms
0
answers
15
GATE2018 CE1: GA3
Hema's age is $5$ years more than twice Hari's age. Suresh's age is $13$ years less than Hari's age. If Suresh is $3$ times as old as Hema, then how old is Hema? $14$ $17$ $18$ $19$
edited
Jul 21
in
Numerical Ability
gate2018ce1
generalaptitude
numericalability
agerelation
1
answer
16
GATE2018 CE1: 38
The solution (up to three decimal places) at $x=1$ of the differential equation $\dfrac{d^2y}{dx^2} + 2 \dfrac{dy}{dx} + y =0$ subject to boundary conditions $y(0) = 1$ and $\dfrac{dy}{dx}(0) = 1$ is _____
edited
Jul 21
in
Ordinary Differential Equation (ODE)
gate2018ce1
differentialequation
numericalanswers
ordinarydifferentialequation
engineeringmathematics
1
answer
17
GATE2018 CE1: 37
The solution at $x=1$, $t=1$ of the partial differential equation $\dfrac{\partial ^2 u}{\partial x^2} = 25 \dfrac{\partial ^2 u}{\partial t^2}$ subject to initial conditions of $u(0) = 3x$ and $\dfrac{\partial u}{\partial t}(0) =3$ is _______ $1$ $2$ $4$ $6$
edited
Jul 21
in
Partial Differential Equation (PDE)
gate2018ce1
partialdifferentialequation
engineeringmathematics
0
answers
18
GATE2018 CE1: 2
For the given orthogonal matrix Q, $Q = \begin{bmatrix} 3/7 & 2/7 & 6/7 \\ 6/7 & 3/7 & 2/7 \\ 2/7 & 6/7 & 3/7 \end{bmatrix}$ ... $\begin{bmatrix} 3/7 & 6/7 & 2/7 \\ 2/7 & 3/7 & 6/7 \\ 6/7 & 2/7 & 3/7 \end{bmatrix}$
edited
Jul 21
in
Linear Algebra
gate2018ce1
matrixinverse
linearalgebra
engineeringmathematics
1
answer
19
GATE2018 CE1: 1
Which one of the following matrices is singular? $\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix} \\$ $\begin{bmatrix} 3 & 2 \\ 2 & 3 \end{bmatrix} \\$ $\begin{bmatrix} 2 & 4\\ 3 & 6 \end{bmatrix} \\$ $\begin{bmatrix} 4 & 3\\ 6 & 2 \end{bmatrix}$
edited
Jul 21
in
Linear Algebra
gate2018ce1
matrix
linearalgebra
engineeringmathematics
0
answers
20
GATE2018 CE1: GA10
Each of the letters arranged as below represents a unique integer from $1$ to $9$. The letters are positioned in the figure such that $(A \times B \times C), (B \times G \times E)$ and $(D \times E \times F)$ are equal. Which integer among the following choices cannot be ... $4$ $5$ $6$ $9$
edited
Jul 21
in
Numerical Ability
gate2018ce1
generalaptitude
numericalability
counting
0
answers
21
GATE2018 CE1: GA9
Consider a sequence of numbers $a_1, a_2, a_3, \dots , a_n$ where $a_n = \dfrac{1}{n}\dfrac{1}{n+2}$, for each integer $n>0$. Whart is the sum of the first $50$ terms? $\bigg( 1+ \dfrac{1}{2} \bigg)  \dfrac{1}{50} \\$ ... $1  \bigg( \dfrac{1}{51} + \dfrac{1}{52} \bigg)$
edited
Jul 21
in
Numerical Ability
gate2018ce1
generalaptitude
numericalability
summation
0
answers
22
GATE2019 CE2: 35
The inverse of the matrix $\begin{bmatrix} 2 & 3 & 4 \\ 4 & 3 & 1 \\ 1 & 2 & 4 \end{bmatrix}$ is $\begin{bmatrix} 10 & 4 & 9 \\ 15 & 4 & 14 \\ 5 & 1 & 6 \end{bmatrix} \\$ ...
edited
Jul 21
in
Linear Algebra
gate2019ce2
matrixinverse
linearalgebra
engineeringmathematics
1
answer
23
GATE2019 CE2: GA7
Population of state $X$ increased by $x\%$ and the population of state $Y$ increased by $y\%$ from $2001$ to $2011$. Assume that $x$ is greater than $y$. Let $P$ be the ratio of the population of state $X$ to state $Y$ in a given year. The percentage increase in $P$ ... $\dfrac{x}{y} \\$ $xy \\$ $\dfrac{100(xy)}{100+x} \\$ $\dfrac{100(xy)}{100+y}$
edited
Jul 21
in
Numerical Ability
gate2019ce2
generalaptitude
numericalability
percentages
0
answers
24
GATE2019 CE1: 4
For a small value of $h$, the Taylor series expansion for $f(x+h)$ is $f(x)+h{f}' (x) + \dfrac{h^2}{2!}{f}''(x) + \dfrac{h^3}{3!}{f}'''(x)+\dots \infty \\$ $f(x)h{f}' (x) + \dfrac{h^2}{2!}{f}''(x)  \dfrac{h^3}{3!}{f}'''(x)+ \dots \infty \\$ ... $f(x)h{f}' (x) + \dfrac{h^2}{2}{f}''(x)  \dfrac{h^3}{3}{f}'''(x)+ \dots \infty $
edited
Jul 20
in
Calculus
gate2019ce1
taylorseries
calculus
engineeringmathematics
0
answers
25
GATE2019 CE1: 2
Consider a twodimensional flow through isotropic soil along $x$ direction and $z$ direction. If $h$ is the hydraulic head, the Laplace's equation of continuity is expressed as $\dfrac{\partial h}{\partial x}+ \dfrac{\partial h}{\partial z} = 0 \\$ ...
edited
Jul 20
in
Partial Differential Equation (PDE)
gate2019ce1
laplaceequation
continuity
partialdifferentialequation
engineeringmathematics
1
answer
26
GATE2019 CE1: 1
Which one of the following is correct? $\lim_{x\rightarrow 0} ( \dfrac{\sin4x}{\sin2x})=2 $ and $\lim_{x\rightarrow 0} ( \dfrac{\tan x}{x})=1 \\$ $\lim_{x\rightarrow 0} ( \dfrac{\sin4x}{\sin2x})=1$ and $\lim_{x\rightarrow 0} ( \dfrac{\tan x}{x})=1 \\$ ... $\lim_{x\rightarrow 0} ( \dfrac{\sin4x}{\sin2x})=2$ and $\lim_{x\rightarrow 0} ( \dfrac{\tan x}{x})= \infty$
edited
Jul 20
in
Calculus
gate2019ce1
calculus
limit
engineeringmathematics
1
answer
27
GATE2017 CE1: GA7
Students applying for hostel rooms are allotted rooms in order of seniority. Students already staying in a room will move if they get a room in their preferred list. Preferences of lower ranked applicants are ignored during allocation. Given the data below, which room will Ajit stay in ? ... $P$ $Q$ $R$ $S$
edited
Jul 20
in
Verbal Ability
gate2017ce1
generalaptitude
verbalability
verbalreasoning
0
answers
28
GATE2020CE1GA: 10
The total expenditure of a family, on different activities in a month, is shown in the piechart. The extra money spent on education as compared to transport (in percent) is ______. $5$ $33.3$ $50$ $100$
edited
Mar 6
in
Verbal Ability
gate2020ce1
0
answers
29
GATE2020CE1GA: 9
The unit’s place in $26591749^{110016}$ is ______. $1$ $3$ $6$ $9$
edited
Mar 6
in
Verbal Ability
gate2020ce1
0
answers
30
GATE2020CE1GA8
Insert seven numbers between $2$ and $34$, such that the resulting sequence including $2$ and $34$ is an arithmetic progression. The sum of these inserted seven numbers is ______. $120$ $124$ $126$ $130$
edited
Mar 6
in
Verbal Ability
gate2020ce1
0
answers
31
GATE2020CE1GA7
Five friends $P,Q,R,S$ and $T$ went camping. At night, they had to sleep in a row inside the tent.$P,Q$ and $T$ refused to sleep next to $R$ since he snored loudly. $P$ and $S$ wanted to avoid $Q$ as he usually hugged people in sleep. Assuming everyone was satisfied with the sleeping arrangements, what is the order in which they slept? $RSPTQ$ $SPRTQ$ $QRSPT$ $QTSPR$
edited
Mar 6
in
Verbal Ability
gate2020ce1
0
answers
32
GATE2020CE1GA6
The American psychologist Howard Gardner expounds that human intelligence can be subcategorized into multiple kinds, in such a way that individuals differ with respect to their relative competence in each kind. Based on this theory, modern ... theory of multiple intelligences. Modern educationists insist that the teaching curriculum and evaluation needs to be multidimensional.
edited
Mar 6
in
Verbal Ability
gate2020ce1
0
answers
33
GATE2020CE1GA5
The sum of two positive numbers is $100$. After subtracting $5$ from each number, the product of the resulting numbers is $0$. One of the original numbers is ______. $80$ $85$ $90$ $95$
edited
Mar 6
in
Verbal Ability
gate2020ce1
0
answers
34
GATE2020CE1GA4
If $0,1,2,\dots,7,8,9$ are coded as $O,P,Q,\dots,V,W,X$, then $45$ will be coded as ______. $TS$ $ST$ $SS$ $SU$
edited
Mar 6
in
Verbal Ability
gate2020ce1
0
answers
35
GATE2020CE1GA3
Select the word that fits the analogy: Fuse : Fusion :: Use : ______ Usage User Uses Usion
edited
Mar 6
in
Verbal Ability
gate2020ce1
0
answers
36
GATE2020CE1GA2
His hunger for reading is insatiable. He reads indiscriminately. He is most certainly a/an ______ reader. allround precocious voracious wise
edited
Mar 6
in
Verbal Ability
gate2020ce1
0
answers
37
GATE2020CE1GA1
It is a common criticism that most of the academicians live in their ________ , so, they are not aware of their real life challenges. homes ivory towers glass palaces big flats
edited
Mar 6
in
Verbal Ability
gate2020ce1
0
answers
38
GATE2020CE11
In the following partial differential equation, $\theta$ is a function of $t$ and $z$, and $D$ and $K$ are functions of $\theta$ ... The above equation is a second order linear equation a second degree linear equation a second order nonlinear equation a second degree nonlinear equation
asked
Feb 28
in
Engineering Mathematics
gate2020ce1
partialdifferentialequation
engineeringmathematics
0
answers
39
GATE2020CE12
The value of $\lim_{x\to\infty}\dfrac{x^25x+4}{4x^2+2x}$ is $0 \\$ $\dfrac{1}{4} \\$ $\dfrac{1}{2} \\$ $1$
asked
Feb 28
in
Engineering Mathematics
gate2020ce1
engineeringmathematics
limit
calculus
0
answers
40
GATE2020CE13
The true value of $\ln(2)$ is $0.69$. If the value of $\ln(2)$ is obtained by linear interpolation between $\ln(1)$ and $\ln(6)$, the percentage of absolute error (round off to the nearest integer), is $35$ $48$ $69$ $84$
asked
Feb 28
in
Engineering Mathematics
gate2020ce1
engineeringmathematics
linearalgebra
linearinterpolation
0
answers
41
GATE2020CE14
The area of an ellipse represented by an equation $\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$ is $\dfrac{\pi ab}{4} \\$ $\dfrac{\pi ab}{2} \\$ $\pi ab \\$ $\dfrac{4\pi ab}{3}$
asked
Feb 28
in
Engineering Mathematics
gate2020ce1
engineeringmathematics
0
answers
42
GATE2020CE15
Consider the planar truss shown in the figure (not drawn to the scale) Neglecting self weight of the numbers, the number of zeroforce members in the truss under the action of the load $P$, is $6$ $7$ $8$ $9$
asked
Feb 28
in
Structural Analysis
gate2020ce1
structuralanalysis
structuralengineering
trusses
0
answers
43
GATE2020CE16
A reinforcing steel bar, partially embedded in concrete, is subjected to a tensile force $P$. The figure that appropriately represents the distribution of the magnitude of bond stress (represented as hatched region), along the embedded length of the bar, is
asked
Feb 28
in
Steel Structures
gate2020ce1
steelstructures
structuralengineering
0
answers
44
GATE2020CE17
In a twodimensional stress analysis, the state of stress at a point $P$ is $\begin{bmatrix} \sigma \end{bmatrix} = \begin{bmatrix}\sigma_{xx} &\tau_{xy} \\ \tau_{xy} &\sigma_{yy} \end{bmatrix}$ The necessary and sufficient condition for existence of the state of pure shear at ... $\tau_{xy}=0$ $\sigma_{xx}+\sigma_{yy}=0$ $(\sigma_{xx}\sigma_{yy})^2+4\tau^2_{xy}=0$
asked
Feb 28
in
Geotechnical Engineering
gate2020ce1
matrix
twodimensionalflow
geotechnicalengineering
0
answers
45
GATE2020CE18
During the process of hydration of cement, due to increase in Dicalcium Silicate $(C_2S)$ content in cement clinker, the heat of hydration increases decreases initially decreases and then increases does not change
asked
Feb 28
in
Geotechnical Engineering
gate2020ce1
geotechnicalengineering
hydration
0
answers
46
GATE2020CE19
The Los Angeles test for stone aggregates is used to examine abrasion resistance crushing strength soundness specific gravity
asked
Feb 28
in
Foundation Engineering
gate2020ce1
foundationengineering
geotechnicalengineering
0
answers
47
GATE2020CE110
Which one of the following statements is. $\textbf{NOT}$ correct? A clay deposit with a liquidity index greater than unity is in a state of plastic consistency. The cohesion of normally consolidated clay is zero when triaxial test is conducted ... 's equation predicts higher value of vertical stress at a point directly beneath the load as compared to Westergaards's equation.
asked
Feb 28
in
Geotechnical Engineering
gate2020ce1
geotechnicalengineering
0
answers
48
GATE2020CE111
In a soil investigation work at a site, Standard Penetration Test (SPT) was conducted at every $1.5\:m$ interval upto $30\: m$ depth. At $3\:m$ depth, the observed number of hammer blows for three successive $150\:mm$ penetrations were $8,6$ and $9$,respectively. The SPT Nvalue at $3\:m$ depth, is $23$ $17$ $15$ $14$
asked
Feb 28
in
Soil Mechanics
gate2020ce1
soilmechanics
geotechnicalengineering
spt
0
answers
49
GATE2020CE112
Velocity of flow is proportional to the first power of hydraulic gradient in Darcy’s law. This law is applicable to laminar flow in porous media transitional flow in porous media turbulent flow in porous media laminar as well as turbulent flow in porous media
asked
Feb 28
in
Hydraulics
gate2020ce1
hydraulics
waterresourcesengineering
0
answers
50
GATE2020CE113
A body floating in a liquid is in a stable state of equilibrium if its metacentre lies above its centre of gravity metacentre lies below its centre of gravity metacentre coincides with its centre of gravity centre of gravity is below its centre of buoyancy
asked
Feb 28
in
Engineering Mechanics
gate2020ce1
engineeringmechanics
structuralengineering
equilibrium
1,042
questions
95
answers
26
comments
44,148
users