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Questions by gatecse
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votes
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81
GATE2018 CE-2: 40
A prismatic propped cantilever beam of span $L$ and plastic moment capacity $M_p$ is subjected to a concentrated load at its mid-span. If the collapse load of the beam is $\alpha \dfrac{M_p}{L}$, the value of $\alpha$ is ______
A prismatic propped cantilever beam of span $L$ and plastic moment capacity $M_p$ is subjected to a concentrated load at its mid-span. If the collapse load of the beam is...
asked
Feb 17, 2018
Structural Analysis
gate2018-ce-2
numerical-answers
structural-engineering
structural-analysis
analysis-of-beams
cantilever-beam
+
–
0
votes
1
answer
82
GATE2018 CE-2: 39
A prismatic beam P-Q-R of flexural rigidity $EI = 1 \times 10^4 kNm^2$ is subjected to a momemnt of $180 kNm$ at Q as shown in the figure The rotation at Q (in rad. up to two decimal places is_____
A prismatic beam P-Q-R of flexural rigidity $EI = 1 \times 10^4 kNm^2$ is subjected to a momemnt of $180 kNm$ at Q as shown in the figureThe rotation at Q (in rad. up to ...
asked
Feb 17, 2018
Structural Analysis
gate2018-ce-2
numerical-answers
structural-engineering
structural-analysis
analysis-of-beams
prismatic-beam
+
–
0
votes
2
answers
83
GATE2018 CE-2: 38
An $8$ m long simply-supported elastic beam of rectangular cross-section ($100$ mm $\times 200 $mm) is subjected to a uniformly distributed load of $10$ kN/m over its entire span. The maximum principal stress (in MPa, up to two decimal places) at a point located at the extreme compression edge of a cross-section and at $2$ m from the support is _______
An $8$ m long simply-supported elastic beam of rectangular cross-section ($100$ mm $\times 200 $mm) is subjected to a uniformly distributed load of $10$ kN/m over its ent...
asked
Feb 17, 2018
Structural Analysis
gate2018-ce-2
numerical-answers
structural-engineering
structural-analysis
analysis-of-beams
simply-supported-elastic-beam
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–
0
votes
0
answers
84
GATE2018 CE-2: 37
The value (up to two decimal places) of a line integral $\int_C \overrightarrow{F}(\overrightarrow{r}) . d\overrightarrow{r}$, for $ \overrightarrow{F}(\overrightarrow{r}) = x^2 \hat{i} + y^2 \hat{j} $ along $C$ which is a straight line joining $(0, 0)$ to $(1, 1)$ is _________
The value (up to two decimal places) of a line integral $\int_C \overrightarrow{F}(\overrightarrow{r}) . d\overrightarrow{r}$, for $ \overrightarrow{F}(\overrightarrow{r...
asked
Feb 17, 2018
Calculus
gate2018-ce-2
numerical-answers
calculus
vector-calculus
line-integral
+
–
0
votes
0
answers
85
GATE2018 CE-2: 36
A level instrument at a height of $1.320$ m has been placed at a station having a Reduced Level (RL) of $112.565$ m. The instrument reads $-2.835$ m on a levelling staff held at the bottom of a bridge deck. The RL (in m) of the bottom of the bridge deck is $116.720$ $116.080$ $114.080$ $111.050$
A level instrument at a height of $1.320$ m has been placed at a station having a Reduced Level (RL) of $112.565$ m. The instrument reads $-2.835$ m on a levelling staff ...
asked
Feb 17, 2018
Geomatics Engineering
gate2018-ce-2
geomatics-engineering
total-station
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–
0
votes
0
answers
86
GATE2018 CE-2: 35
A car follows a slow moving truck (travelling at a speed of $10$ m/s) on a two-lane two-way highway. The car reduces its speed to $10$ m/s and follows the truck maintaining a distance of $16$m from the truck. On fining a clear gap in the opposite traffic ... ( from the time it leaves its lane and subsequently returns to its lane after overtaking) is $64$ m $72$ m $128$ m $144$ m
A car follows a slow moving truck (travelling at a speed of $10$ m/s) on a two-lane two-way highway. The car reduces its speed to $10$ m/s and follows the truck maintaini...
asked
Feb 17, 2018
Traffic Engineering
gate2018-ce-2
traffic-engineering
transportation-engineering
traffic-stream
+
–
0
votes
0
answers
87
GATE2018 CE-2: 34
In a $5$ m wide rectangular channel, the velocity $u$ distribution in the vertical direction $y$ is given by $u=1.25 y^{\frac{1}{6}}$. The distance $y$ is measured from the channel bed. If the flow depth is $2$ m, the discharge per unit width of the channel is $2.40 \: m^3/s/m$ $2.80 \: m^3/s/m$ $3.27 \: m^3/s/m$ $12.02 \: m^3/s/m$
In a $5$ m wide rectangular channel, the velocity $u$ distribution in the vertical direction $y$ is given by $u=1.25 y^{\frac{1}{6}}$. The distance $y$ is measured from t...
asked
Feb 17, 2018
Hydraulics
gate2018-ce-2
water-resources-engineering
rectangular-channels
hydraulics
+
–
0
votes
0
answers
88
GATE2018 CE-2: 33
Three soil specimens (Soil $1$, Soil $2$ and Soil $3$), each $150$ mm long and $100$ mm diameter, are placed in series in a instant head flow set-up as shown in the figure. Suitable screens are provided at the boundaries of the specimens to keep them intact. The values of ... and $0.03$ cm/s, respectively. The value of $h$ in the set-up is $0$ mm $40$ mm $255$ mm $560$ mm
Three soil specimens (Soil $1$, Soil $2$ and Soil $3$), each $150$ mm long and $100$ mm diameter, are placed in series in a instant head flow set-up as shown in the figur...
asked
Feb 17, 2018
Soil Mechanics
gate2018-ce-2
soil-mechanics
geotechnical-engineering
permeability
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–
0
votes
0
answers
89
GATE2018 CE-2: 32
A $3$ m high vertical earth retaining wall retains a dry granular backfill with angle of internal friction of $30^{\circ}$ and unit weight of $20 \: kN/m^3$. If the wall is prevented from yielding (no movement), the total horizontal thrust (in kN per unit length) on the wall is $0$ $30$ $45$ $270$
A $3$ m high vertical earth retaining wall retains a dry granular backfill with angle of internal friction of $30^{\circ}$ and unit weight of $20 \: kN/m^3$. If the wall...
asked
Feb 17, 2018
Foundation Engineering
gate2018-ce-2
geotechnical-engineering
foundation-engineering
earth-pressure
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–
0
votes
0
answers
90
GATE2018 CE-2: 31
A singly-reinforced rectangular concrete beam of width $30$ mm and effective depth $400$ mm is to be designed using $M25$ grade concrete and $Fe500$ grade reinforcing steel. For the beam to be under-reinforced, the maximum number of $16$ mm diameter reinforcing bars that can be provided is, $3$ $4$ $5$ $6$
A singly-reinforced rectangular concrete beam of width $30$ mm and effective depth $400$ mm is to be designed using $M25$ grade concrete and $Fe500$ grade reinforcing ste...
asked
Feb 17, 2018
Concrete Structures
gate2018-ce-2
concrete-structures
structural-engineering
concrete-beam
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–
0
votes
0
answers
91
GATE2018 CE-2: 30
Four bolts P, Q, R and S of equal diameter are used for a bracket subjected to a load of $130$ kN as shown in the figure. The force in bolt P is $32.50$ kN $69.32$ kN $82.50$ kN $119.32$ kN
Four bolts P, Q, R and S of equal diameter are used for a bracket subjected to a load of $130$ kN as shown in the figure.The force in bolt P is$32.50$ kN$69.32$ kN$82.50$...
asked
Feb 17, 2018
Steel Structures
gate2018-ce-2
structural-engineering
force-in-bolt
steel-structures
bracket-connection
+
–
0
votes
0
answers
92
GATE2018 CE-2: 29
Two rigid bodies of mass $5$ kg and $4$ kg are at rest on a frictionless surface until acted upon by a force of $36$ N as shown in the figure. The contact force generated between the two bodies is $4.0$ N $7.2$ N $9.0$ N $16.0$ N
Two rigid bodies of mass $5$ kg and $4$ kg are at rest on a frictionless surface until acted upon by a force of $36$ N as shown in the figure. The contact force generated...
asked
Feb 17, 2018
Engineering Mechanics
gate2018-ce-2
rigid-bodies
engineering-mechanics
structural-engineering
+
–
0
votes
0
answers
93
GATE2018 CE-2: 28
The rank of the following matrix is $\\ \begin{pmatrix} 1 & 1 & 0 & -2 \\ 2 & 0 & 2 & 2 \\ 4 & 1 & 3 & 1 \end{pmatrix}$ $1$ $2$ $3$ $4$
The rank of the following matrix is $\\ \begin{pmatrix} 1 & 1 & 0 & -2 \\ 2 & 0 & 2 & 2 \\ 4 & 1 & 3 & 1 \end{pmatrix}$$1$$2$$3$$4$
asked
Feb 17, 2018
Linear Algebra
gate2018-ce-2
linear-algebra
matrices
rank-of-matrix
+
–
0
votes
0
answers
94
GATE2018 CE-2: 27
The Laplace transform $F(s)$ of the exponential function, $f(t) = e^{at}$ when $t \geq 0$, where $a$ is a constant and $(s-a) >0$, is $\dfrac{1}{s+a} \\$ $\dfrac{1}{s-a} \\$ $\dfrac{1}{a-s} \\$ $\infty$
The Laplace transform $F(s)$ of the exponential function, $f(t) = e^{at}$ when $t \geq 0$, where $a$ is a constant and $(s-a) >0$, is$\dfrac{1}{s+a} \\$$\dfrac{1}{s-a} \\...
asked
Feb 17, 2018
Ordinary Differential Equation (ODE)
gate2018-ce-2
ordinary-differential-equation
laplace-transform
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–
0
votes
1
answer
95
GATE2018 CE-2: 26
The matrix $\begin{pmatrix} 2 & -4 \\ 4 & -2 \end{pmatrix}$ has real eigenvalues and eigenvectors real eigenvalues but complex eigenvectors complex eigenvalues but real eigenvectors complex eigenvalues and eigenvectors
The matrix $\begin{pmatrix} 2 & -4 \\ 4 & -2 \end{pmatrix}$ hasreal eigenvalues and eigenvectorsreal eigenvalues but complex eigenvectorscomplex eigenvalues but real eige...
asked
Feb 17, 2018
Linear Algebra
gate2018-ce-2
linear-algebra
matrices
eigen-values
eigen-vectors
+
–
0
votes
0
answers
96
GATE2018 CE-2: 25
A culvert is designed for a flood frequency of $100$ years and a useful life of $20$ years. The risk involved in the design of the culvert (in percentage, up to two decimal places) is _______
A culvert is designed for a flood frequency of $100$ years and a useful life of $20$ years. The risk involved in the design of the culvert (in percentage, up to two decim...
asked
Feb 17, 2018
Hydrology
gate2018-ce-2
numerical-answers
flood-estimation-and-routing
hydrology
water-resources-engineering
+
–
0
votes
0
answers
97
GATE2018 CE-2: 24
The intensity of irrigation for the $\textit{kharif}$ season is $50 \%$ for an irrigation project with culturable command area of $50,000 $ hectares. The duty for the $\textit{kharif}$ season is $1000$ hectare/cumec. Assuming transmission loss of $10 \%$, the required discharge (in cumec, up to two decimal places) at the head of the canal is _____
The intensity of irrigation for the $\textit{kharif}$ season is $50 \%$ for an irrigation project with culturable command area of $50,000 $ hectares. The duty for the $\t...
asked
Feb 17, 2018
Irrigation
gate2018-ce-2
numerical-answers
irrigation
water-resources-engineering
canal-regulatory-works
+
–
0
votes
0
answers
98
GATE2018 CE-2: 23
A fillet weld is simultaneously subjected to factored normal and shear stresses of $120$ MPa and $50$ MPa, respectively. As per $\text{ IS }800:2007$, the equivalent stress (in MPa, up to two decimal places) is _____
A fillet weld is simultaneously subjected to factored normal and shear stresses of $120$ MPa and $50$ MPa, respectively. As per $\text{ IS }800:2007$, the equivalent stre...
asked
Feb 17, 2018
Solid Mechanics
gate2018-ce-2
numerical-answers
solid-mechanics
structural-engineering
shear-stress
equivalent-stress
+
–
0
votes
0
answers
99
GATE2018 CE-2: 22
A reinforced-concrete slab with effective depth of $80$ mm is simply supported at two opposite ends on $230$ mm thick masonry walls. The centre-to-centre distance between the walls is $3.3$ m. As per $\text{IS }456:2000$, the effective span of the slab (in m, up to two decimal places) is ________
A reinforced-concrete slab with effective depth of $80$ mm is simply supported at two opposite ends on $230$ mm thick masonry walls. The centre-to-centre distance between...
asked
Feb 17, 2018
Concrete Structures
gate2018-ce-2
numerical-answers
concrete-structures
structural-engineering
concrete-slabs
+
–
0
votes
1
answer
100
GATE2018 CE-2: 21
As per $\text{IS }456:2000$, the minimum percentage of tension reinforcement (up to two decimal places) required in reinforced-concrete beams of rectangular cross-section (considering effective depth in the calculation of area) using $Fe500$ grade steel is _____
As per $\text{IS }456:2000$, the minimum percentage of tension reinforcement (up to two decimal places) required in reinforced-concrete beams of rectangular cross-section...
asked
Feb 17, 2018
Steel Structures
gate2018-ce-2
numerical-answers
steel-structures
structural-engineering
reinforced-concrete-beam
+
–
0
votes
1
answer
101
GATE2018 CE-2: 20
The quadratic equation $2x^2 - 3x +3=0$ is to be solved numerically starting with an initial guess as $x_0=2$. The new estimate of $x$ after the first iteration using Newton-Raphson method is _________
The quadratic equation $2x^2 - 3x +3=0$ is to be solved numerically starting with an initial guess as $x_0=2$. The new estimate of $x$ after the first iteration using New...
asked
Feb 17, 2018
Numerical Methods
gate2018-ce-2
numerical-methods
newton-raphson-method
numerical-answers
+
–
0
votes
0
answers
102
GATE2018 CE-2: 19
Probability (up to one decimal place) of consecutively picking $3$ red balls without replacement from a box containing $5$ red balls and $1$ white ball is ___________
Probability (up to one decimal place) of consecutively picking $3$ red balls without replacement from a box containing $5$ red balls and $1$ white ball is ___________
asked
Feb 17, 2018
Probability and Statistics
gate2018-ce-2
probability-and-statistics
probability
conditional-probability
numerical-answers
+
–
0
votes
0
answers
103
GATE2018 CE-2: 18
The initial concavity in the load-penetration curve of a CBR test is NOT due to uneven top surface high impact at start of loading inclined penetration plunger soft top layer of soaked soil
The initial concavity in the load-penetration curve of a CBR test is NOT due touneven top surfacehigh impact at start of loadinginclined penetration plungersoft top layer...
asked
Feb 17, 2018
Foundation Engineering
gate2018-ce-2
foundation-engineering
geotechnical-engineering
load-penetration-curve
standard-penetration-test
+
–
0
votes
0
answers
104
GATE2018 CE-2: 17
As per $\text{IRC:}37-2012$, in order to control subgrade rutting in flexible pavements, the parameter to be considered is horizontal tensile strain at the bottom of bituminous layer vertical compressive strain on top of subgrade vertical compressive stress on top of granular layer vertical deflection at the surface of the pavement
As per $\text{IRC:}37-2012$, in order to control subgrade rutting in flexible pavements, the parameter to be considered ishorizontal tensile strain at the bottom of bitum...
asked
Feb 17, 2018
Highway Pavements
gate2018-ce-2
highway-pavements
transportation-engineering
design-of-flexible-and-rigid-pavement-using-irc-codes
+
–
0
votes
0
answers
105
GATE2018 CE-2: 16
Peak Hour Factor (PHF) is used to represent the proportion of peak sub-hourly traffic flow within the peak hour. If $15$-minute sub-hours are considered, the theoretically possible range of PHF will be $0$ to $1.0$ $0.25$ to $0.75$ $0.25$ to $1.0$ $0.5$ to $1.0$
Peak Hour Factor (PHF) is used to represent the proportion of peak sub-hourly traffic flow within the peak hour. If $15$-minute sub-hours are considered, the theoreticall...
asked
Feb 17, 2018
Traffic Engineering
gate2018-ce-2
peak-hour-factor
traffic-engineering
transportation-engineering
+
–
0
votes
0
answers
106
GATE2018 CE-2: 15
In the figures, Group I represents the atmospheric temperature profiles (P, Q, R and S) and Group II represents dispersion of pollutants from a smoke stack $(1, 2, 3$ and $4)$. In the figures of Group I, the dashed line represents the dry adiabatic lapse rate, whereas the horizontal axis represents temperature and ... $P-1, Q-4, R-3, S-2$ $P-3, Q-1, R-2, S-4$
In the figures, Group I represents the atmospheric temperature profiles (P, Q, R and S) and Group II represents dispersion of pollutants from a smoke stack $(1, 2, 3$ and...
asked
Feb 17, 2018
Air Pollution
gate2018-ce-2
environmental-engineering
air-pollution
sources-and-impacts-of-pollutants
+
–
0
votes
1
answer
107
GATE2018 CE-2: 14
As per $\text{IS }10500:2012$, for drinking water in the absence of alternate source of water, the permissible limits for chloride and sulphate, in mg/L, respectively are $250$ and 200$ $1000$ and 400$ $200$ and 250$ $500$ and 1000$
As per $\text{IS }10500:2012$, for drinking water in the absence of alternate source of water, the permissible limits for chloride and sulphate, in mg/L, respectively are...
asked
Feb 17, 2018
Water and Waste Water Quality and Treatment
gate2018-ce-2
environmental-engineering
permissible-limits
water-and-waste-water-quality-and-treatment
physical-chemical-and-biological-parameters
+
–
0
votes
0
answers
108
GATE2018 CE-2: 13
For a given discharge in an open channel, there are two depths which have the same specific energy. These two depths are known as alternate depths critical depths normal depths sequent depths
For a given discharge in an open channel, there are two depths which have the same specific energy. These two depths are known asalternate depthscritical depthsnormal dep...
asked
Feb 17, 2018
Water Resources Engineering
gate2018-ce-2
water-resources-engineering
hydraulics
energy-depth-relationships
+
–
0
votes
0
answers
109
GATE2018 CE-2: 12
Dupuit's assumptions are valid for artesian aquifer confined aquifer leaky aquifer unconfined aquifer
Dupuit's assumptions are valid forartesian aquiferconfined aquiferleaky aquiferunconfined aquifer
asked
Feb 17, 2018
Water Resources Engineering
gate2018-ce-2
dupuit's-assumptions
aquifers
water-resources-engineering
hydrology
+
–
0
votes
0
answers
110
GATE2018 CE-2: 11
The clay mineral, whose structural units are held together by potassium bond is Halloysite Illite Kaolinite Smectite
The clay mineral, whose structural units are held together by potassium bond isHalloysiteIlliteKaoliniteSmectite
asked
Feb 17, 2018
Geotechnical Engineering
gate2018-ce-2
geotechnical-engineering
clay-mineral
characteristics-of-clay
+
–
1
votes
0
answers
111
GATE2018 CE-2: 10
Which one of the following statements is NOT correct? When the water content of soil lies between its liquid limit and plastic limit, the soil is said to be in plastic state. Boussinesq's theory is used for the analysis of stratified ... fine sand, after applying overburden correction, if the Standard Penetration Test value exceeds $15$, dilatancy correction is to be applied
Which one of the following statements is NOT correct?When the water content of soil lies between its liquid limit and plastic limit, the soil is said to be in plastic sta...
asked
Feb 17, 2018
Geotechnical Engineering
gate2018-ce-2
geotechnical-engineering
foundation-engineering
boussinesq's-theory
+
–
0
votes
0
answers
112
GATE2018 CE-2: 9
The contact pressure and settlement distribution for a footing are shown in the figure. The figure corresponds to a rigid footing on a granular soil flexible footing on a granular soil flexible footing on saturated clay rigid footing on cohesive soil
The contact pressure and settlement distribution for a footing are shown in the figure.The figure corresponds to arigid footing on a granular soilflexible footing on a g...
asked
Feb 17, 2018
Foundation Engineering
gate2018-ce-2
foundation-engineering
geotechnical-engineering
settlement-analysis
combined-footing
+
–
0
votes
0
answers
113
GATE2018 CE-2: 8
A flownet below a dam consists of $24$ equipotential drops and $7$ flow channels. The difference between the upstream the upstream and downstream water levels is $6$ m. The length of the flow line adjacent to the toe of the dam at exit is $1$ m. The specific gravity and void ... dam are $2.70$ and $0.70$, respectively. The factor of safety against piping is $1.67$ $2.5$ $3.4$ $4$
A flownet below a dam consists of $24$ equipotential drops and $7$ flow channels. The difference between the upstream the upstream and downstream water levels is $6$ m. T...
asked
Feb 17, 2018
Soil Mechanics
gate2018-ce-2
geotechnical-engineering
soil-mechanics
seepage-through-soils
+
–
0
votes
0
answers
114
GATE2018 CE-2: 7
A vertical load of $10$ kN acts on a hinge located at a distance of $L/4$ from the roller support Q of a beam of length $L$ (see figure). The vertical reaction at support Q is $0.0$ kN $2.5$ kN $7.5$ kN $10.0$ kN
A vertical load of $10$ kN acts on a hinge located at a distance of $L/4$ from the roller support Q of a beam of length $L$ (see figure).The vertical reaction at support ...
asked
Feb 17, 2018
Structural Analysis
gate2018-ce-2
structural-engineering
structural-analysis
analysis-of-beams
+
–
0
votes
0
answers
115
GATE2018 CE-2: 6
A structural member subjected to compression, has both translation and rotation restrained at one end, while only translation is restrained at the other end. As per $\text{IS }456:2000$, the effective length factor recommended for design is $0.50$ $0.65$ $0.70$ $0.80$
A structural member subjected to compression, has both translation and rotation restrained at one end, while only translation is restrained at the other end. As per $\tex...
asked
Feb 17, 2018
Structural Engineering
gate2018-ce-2
structural-engineering
steel-structures
design-of-compression-members
+
–
0
votes
0
answers
116
GATE2018 CE-2: 5
The setting time of cement is determined using Le Chatelier apparatus Briquette testing apparatus Vicat apparatus Casagrande's apparatus
The setting time of cement is determined usingLe Chatelier apparatusBriquette testing apparatusVicat apparatusCasagrande's apparatus
asked
Feb 17, 2018
Construction Materials and Management
gate2018-ce-2
structural-engineering
construction-materials-and-management
setting-time-of-cement
+
–
0
votes
0
answers
117
GATE2018 CE-2: 4
All the members of the planar truss (see figure), have the same properties in terms of area of cross-section (A) and modulus of elasticity (E). For the loads shown on the truss, the statement that correctly represents the nature of forces in the members of the ... and $1$ members in compression, and $2$ zero-force member There are $2$ members in tension, and $3$ zero-force member
All the members of the planar truss (see figure), have the same properties in terms of area of cross-section (A) and modulus of elasticity (E).For the loads shown on the ...
asked
Feb 17, 2018
Structural Analysis
gate2018-ce-2
structural-analysis
structural-engineering
trusses
+
–
0
votes
0
answers
118
GATE2018 CE-2: 3
A probability distribution with right skew is shown in the figure. The correct statement for the probability distribution is Mean is equal to mode Mean is greater than median but less than mode Mean is greater than median and mode Mode is greater than median
A probability distribution with right skew is shown in the figure.The correct statement for the probability distribution isMean is equal to modeMean is greater than media...
asked
Feb 17, 2018
Probability and Statistics
gate2018-ce-2
probability-and-statistics
statistics
probability-distribution
mean-median-mode
+
–
0
votes
0
answers
119
GATE2018 CE-2: 2
The graph of a function $f(x)$ is shown in the figure. For $f(x)$ to be a valid probability density function, the value of $h$ is $1/3$ $2/3$ $1$ $3$
The graph of a function $f(x)$ is shown in the figure.For $f(x)$ to be a valid probability density function, the value of $h$ is$1/3$$2/3$$1$$3$
asked
Feb 17, 2018
Probability and Statistics
gate2018-ce-2
probability-and-statistics
probability
probability-density-function
+
–
0
votes
0
answers
120
GATE2018 CE-2: 1
The solution of the equation $x \frac{dy}{dx} +y = 0$ passing through the point $(1,1)$ is $x$ $x^2$ $x^{-1}$ $x^{-2}$
The solution of the equation $x \frac{dy}{dx} +y = 0$ passing through the point $(1,1)$ is$x$$x^2$$x^{-1}$$x^{-2}$
asked
Feb 17, 2018
Ordinary Differential Equation (ODE)
gate2018-ce-2
ordinary-differential-equation
+
–
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