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Hot questions in Engineering Mathematics
2
votes
1
answer
41
GATE2019 CE-1: 1
Which one of the following is correct? $\displaystyle{} \lim_{x\rightarrow 0} \left( \dfrac{\sin4x}{\sin2x}\right)=2\;\text{and}\: \lim_{x\rightarrow 0} \left( \dfrac{\tan x}{x}\right)=1$ ...
Which one of the following is correct?$\displaystyle{} \lim_{x\rightarrow 0} \left( \dfrac{\sin4x}{\sin2x}\right)=2\;\text{and}\: \lim_{x\rightarrow 0} \left( \dfrac{\tan...
Arjun
13.0k
points
Arjun
asked
Feb 14, 2019
Calculus
gate2019-ce-1
calculus
limits
+
–
0
votes
0
answers
42
GATE2017 CE-2-2
Let $w=f(x,y)$, where $x$ and $y$ are functions of $t$. Then, according to the chain rule, $\dfrac{dw}{dt}$ is equal to $\dfrac{dw}{dx} \dfrac{dx}{dt} + \dfrac{dw}{dy} \dfrac{dt}{dt} \\$ ... $\dfrac{d w}{dx} \dfrac{\partial x}{\partial t} + \dfrac{dw}{dy} \dfrac{\partial y}{ \partial t}$
Let $w=f(x,y)$, where $x$ and $y$ are functions of $t$. Then, according to the chain rule, $\dfrac{dw}{dt}$ is equal to$\dfrac{dw}{dx} \dfrac{dx}{dt} + \dfrac{dw}{dy} \df...
gatecse
4.0k
points
gatecse
asked
Aug 7, 2019
Calculus
gate2017-ce-2
calculus
partial-derivatives
+
–
0
votes
0
answers
43
GATE2017 CE-2-1
Consider the following simultaneous equations (with $c_1$ and $c_2$ being constants): $3x_1+2x_2=c_1$ $4x_1+x_2=c_2$ The characteristic equation for these simultaneous equation is $\lambda^2 – 4 \lambda – 5=0$ $\lambda^2 – 4 \lambda + 5=0$ $\lambda^2 + 4 \lambda – 5=0$ $\lambda^2 + 4 \lambda + 5=0$
Consider the following simultaneous equations (with $c_1$ and $c_2$ being constants):$3x_1+2x_2=c_1$$4x_1+x_2=c_2$The characteristic equation for these simultaneous equat...
gatecse
4.0k
points
gatecse
asked
Aug 7, 2019
Linear Algebra
gate2017-ce-2
linear-algebra
system-of-equations
+
–
0
votes
0
answers
44
GATE2017 CE-2-29
Consider the following second-order differential equation: $y’’ – 4y’+3y =2t -3t^2$. The particular solution of the differential solution equation is $ – 2 -2t-t^2$ $ – 2t-t^2$ $2t-3t^2$ $ – 2 -2t-3 t^2$
Consider the following second-order differential equation: $y’’ – 4y’+3y =2t -3t^2$. The particular solution of the differential solution equation is$ – 2 -2t-t...
gatecse
4.0k
points
gatecse
asked
Aug 7, 2019
Partial Differential Equation (PDE)
gate2017-ce-2
ordinary-differential-equation
second-order-differential-equation
+
–
0
votes
0
answers
45
GATE2017 CE-2-19
The divergence of the vector field $V=x^2 i + 2y^3 j + z^4 k$ at $x=1, \: y=2, \: z=3$ is ________
The divergence of the vector field $V=x^2 i + 2y^3 j + z^4 k$ at $x=1, \: y=2, \: z=3$ is ________
gatecse
4.0k
points
gatecse
asked
Aug 7, 2019
Calculus
gate2017-ce-2
calculus
vector-calculus
divergence
numerical-answers
+
–
0
votes
0
answers
46
GATE2017 CE-2-26
The tangent to the curve represented by $y=x \text{ ln }x$ is required to have $45^{\circ}$ inclination with the $x$-axis. The coordinates of the tangent point would be $(1,0)$ $(0, 1)$ $(1,1)$ $(\sqrt{2}, (\sqrt{2})$
The tangent to the curve represented by $y=x \text{ ln }x$ is required to have $45^{\circ}$ inclination with the $x$-axis. The coordinates of the tangent point would be$(...
gatecse
4.0k
points
gatecse
asked
Aug 7, 2019
Calculus
gate2017-ce-2
calculus
curves
+
–
0
votes
0
answers
47
GATE2017 CE-2-27
Consider the following definite integral: $I= \displaystyle{} \int_0^1 \dfrac{(\sin ^{-1}x)^2}{\sqrt{1-x^2}} dx$. The value of the integral is $\dfrac{\pi ^3}{24} \\$ $\dfrac{\pi ^3}{12} \\$ $\dfrac{\pi ^3}{48} \\$ $\dfrac{\pi ^3}{64}$
Consider the following definite integral: $I= \displaystyle{} \int_0^1 \dfrac{(\sin ^{-1}x)^2}{\sqrt{1-x^2}} dx$. The value of the integral is$\dfrac{\pi ^3}{24} \\$$\dfr...
gatecse
4.0k
points
gatecse
asked
Aug 7, 2019
Calculus
gate2017-ce-2
calculus
definite-integral
+
–
0
votes
2
answers
48
GATE2019 CE-2: 43
A series of perpendicular offsets taken from a curved boundary wall to a straight survey line at an interval of $6 \: m$ are $1.22, \: 1.67, \: 2.04, \: 2.34, \: 2.14, \: 1.87$, and $1.15 \:m$. The area (in $m^2$, round off to 2 decimal places) bounded by the survey line, curved boundary wall, the first and the last offsets, determined using Simpson’s rule, is ________
A series of perpendicular offsets taken from a curved boundary wall to a straight survey line at an interval of $6 \: m$ are $1.22, \: 1.67, \: 2.04, \: 2.34, \: 2.14, \:...
Arjun
13.0k
points
Arjun
asked
Feb 12, 2019
Numerical Methods
gate2019-ce-2
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
numerical-answers
+
–
0
votes
0
answers
49
GATE2019 CE-1: 30
Consider two functions: $x=\psi \text{ ln } \phi$ and $y= \phi \text{ ln } \psi$. Which one of the following is the correct expression for $\frac{\partial \psi}{\partial x}$? $\dfrac{x \: \text{ln } \psi}{\text{ln } \phi \text{ ln } \psi -1} \\$ ... $\dfrac{\: \text{ln } \psi}{\text{ln } \phi \text{ ln } \psi -1}$
Consider two functions: $x=\psi \text{ ln } \phi$ and $y= \phi \text{ ln } \psi$. Which one of the following is the correct expression for $\frac{\partial \psi}{\partial ...
Arjun
13.0k
points
Arjun
asked
Feb 14, 2019
Calculus
gate2019-ce-1
calculus
partial-derivatives
+
–
1
votes
0
answers
50
GATE2019 CE-1: 2
Consider a two-dimensional 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 $\dfrac{\partial h}{\partial x}+ \dfrac{\partial h}{\partial z} = 0 \\$ ...
Consider a two-dimensional flow through isotropic soil along $x$ direction and $z$ direction. If $h$ is the hydraulic head, the Laplace’s equation of continuity is exp...
Arjun
13.0k
points
Arjun
asked
Feb 14, 2019
Partial Differential Equation (PDE)
gate2019-ce-1
partial-differential-equation
laplace-equation
+
–
1
votes
0
answers
51
GATE2019 CE-1: 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 $
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)-...
Arjun
13.0k
points
Arjun
asked
Feb 14, 2019
Calculus
gate2019-ce-1
calculus
taylor-series
+
–
0
votes
0
answers
52
GATE2019 CE-1: 27
A one-dimensional domain is discretized into $N$ sub-domains of width $\Delta x$ with node numbers $i=0,1,2,3, \dots , N$. If the time scale is discretized in steps of $\Delta t$, the forward-time and centered-space finite difference approximation at i th node and n th time step, for the ...
A one-dimensional domain is discretized into $N$ sub-domains of width $\Delta x$ with node numbers $i=0,1,2,3, \dots , N$. If the time scale is discretized in steps of $\...
Arjun
13.0k
points
Arjun
asked
Feb 14, 2019
Partial Differential Equation (PDE)
gate2019-ce-1
partial-differential-equation
+
–
0
votes
0
answers
53
GATE2019 CE-1: 23
The probability that the annual maximum flood discharge will exceed $25000 \: m^3/s$, at least once in next $5$ years is found to be $0.25$. The return period of this flood event (in years, round off to $1$ decimal place is __________
The probability that the annual maximum flood discharge will exceed $25000 \: m^3/s$, at least once in next $5$ years is found to be $0.25$. The return period of this flo...
Arjun
13.0k
points
Arjun
asked
Feb 14, 2019
Probability and Statistics
gate2019-ce-1
numerical-answers
probability-and-statistics
probability
conditional-probability
+
–
2
votes
0
answers
54
GATE2019 CE-2: 35
The inverse of the matrix $\begin{bmatrix} 2 & 3 & 4 \\ 4 & 3 & 1 \\ 1 & 2 & 4 \end{bmatrix}$ is $\begin{bmatrix} 10 & -4 & -9 \\ -15 & 4 & 14 \\ 5 & -1 & -6 \end{bmatrix} \\$ ...
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...
Arjun
13.0k
points
Arjun
asked
Feb 12, 2019
Linear Algebra
gate2019-ce-2
linear-algebra
matrices
inverse-of-matrix
+
–
0
votes
0
answers
55
GATE2019 CE-2: 3
The following inequality is true for all $x$ close to $0$. $2-\dfrac{x^2}{3} < \dfrac{x \sin x}{1- \cos x} <2$ What is the value of $\underset{x \to 0}{\lim} \dfrac{x \sin x}{1 – \cos x}$? $0$ $1/2$ $1$ $2$
The following inequality is true for all $x$ close to $0$.$$2-\dfrac{x^2}{3} < \dfrac{x \sin x}{1- \cos x} <2$$What is the value of $\underset{x \to 0}{\lim} \dfrac{x \si...
Arjun
13.0k
points
Arjun
asked
Feb 12, 2019
Calculus
gate2019-ce-2
calculus
limits
+
–
0
votes
0
answers
56
GATE2019 CE-2: 1
Euclidean norm (length) of the vector $\begin{bmatrix} 4 & -2 & -6 \end{bmatrix}^T$ is $\sqrt{12}$ $\sqrt{24}$ $\sqrt{48}$ $\sqrt{56}$
Euclidean norm (length) of the vector $\begin{bmatrix} 4 & -2 & -6 \end{bmatrix}^T$ is$\sqrt{12}$$\sqrt{24}$$\sqrt{48}$$\sqrt{56}$
Arjun
13.0k
points
Arjun
asked
Feb 12, 2019
Linear Algebra
gate2019-ce-2
linear-algebra
matrices
unit-vector
+
–
0
votes
0
answers
57
GATE2019 CE-1: 26
Which one of the following is NOT a correct statement? The function $\sqrt[x]{x}, \: (x>0)$, has the global maxima at $x=e$ The function $\sqrt[x]{x}, \: (x>0)$, has the global minima at $x=e$ The function $x^3$ has neither global minima nor global maxima The function $\mid x \mid$ has the global minima at $x=0$
Which one of the following is NOT a correct statement?The function $\sqrt[x]{x}, \: (x>0)$, has the global maxima at $x=e$The function $\sqrt[x]{x}, \: (x>0)$, has the gl...
Arjun
13.0k
points
Arjun
asked
Feb 14, 2019
Calculus
gate2019-ce-1
calculus
maxima-minima
+
–
0
votes
0
answers
58
GATE2019 CE-1: 44
Consider the ordinary differential equation $x^2 \dfrac{d^2y}{dx^2} – 2x \dfrac{dy}{dx} +2y=0$. Given the values of $y(1)=0$ and $y(2)=2$, the value of $y(3)$ (round off to $1$ decimal place), is _________
Consider the ordinary differential equation $x^2 \dfrac{d^2y}{dx^2} – 2x \dfrac{dy}{dx} +2y=0$. Given the values of $y(1)=0$ and $y(2)=2$, the value of $y(3)$ (round of...
Arjun
13.0k
points
Arjun
asked
Feb 14, 2019
Ordinary Differential Equation (ODE)
gate2019-ce-1
ordinary-differential-equation
numerical-answers
+
–
0
votes
0
answers
59
GATE2019 CE-2: 18
The value of the function $f(x)$ is given at $n$ distinct values of $x$ and its value is to be interpolated at the point $x^*$, using all the $n$ points. The estimate is obtained first by the Lagrange polynomial, denoted by $I_L$, and then by the ... than $I_N$ $I_L$ and $I_N$ are always equal $I_L$ is always less than $I_N$ Not definite relation exists between $I_L$ and $I_N$
The value of the function $f(x)$ is given at $n$ distinct values of $x$ and its value is to be interpolated at the point $x^*$, using all the $n$ points. The estimate is ...
Arjun
13.0k
points
Arjun
asked
Feb 12, 2019
Numerical Methods
gate2019-ce-2
numerical-methods
newtons-polynomial
+
–
0
votes
0
answers
60
GATE2019 CE-2: 26
The probability density function of a continuous random variable distributed uniformly between $x$ and $y$ (for $y>x$) is $\dfrac{1}{x-y}$ $\dfrac{1}{y-x}$ $x-y$ $y-x$
The probability density function of a continuous random variable distributed uniformly between $x$ and $y$ (for $y>x$) is$\dfrac{1}{x-y}$$\dfrac{1}{y-x}$$x-y$$y-x$
Arjun
13.0k
points
Arjun
asked
Feb 12, 2019
Probability and Statistics
gate2019-ce-2
probability-and-statistics
probability
probability-density-function
random-variable
uniform-distribution
+
–
0
votes
0
answers
61
GATE2019 CE-2: 4
What is curl of the vector field $2x^2y \textbf{i} + 5z^2 \textbf{j} – 4yz \textbf{k}$? $6z \textbf{i} + 4x \textbf{j} – 2x^2 \textbf{k}$ $6z \textbf{i} - 8xy \textbf{j} + 2x^2 y\textbf{k}$ $- 14 z \textbf{i} + 6y \textbf{j} + 2x^2 \textbf{k}$ $-14z \textbf{i} – 2x^2 \textbf{k}$
What is curl of the vector field $2x^2y \textbf{i} + 5z^2 \textbf{j} – 4yz \textbf{k}$?$6z \textbf{i} + 4x \textbf{j} – 2x^2 \textbf{k}$$6z \textbf{i} - 8xy \textbf{j...
Arjun
13.0k
points
Arjun
asked
Feb 12, 2019
Calculus
gate2019-ce-2
calculus
vector-calculus
vector-identities
field-vectors
curl
+
–
0
votes
0
answers
62
GATE2019 CE-2: 28
An ordinary differential equation is given below; $\left ( \dfrac{dy}{dx} \right ) (x \text{ ln } x)=y$ The solution for the above equation is (Note: $K$ denotes a constant in the options) $y=K x \text{ ln } x$ $y=K x e^x$ $y=K x e^{-x}$ $y=K \text{ ln } x$
An ordinary differential equation is given below;$\left ( \dfrac{dy}{dx} \right ) (x \text{ ln } x)=y$The solution for the above equation is(Note: $K$ denotes a constant ...
Arjun
13.0k
points
Arjun
asked
Feb 12, 2019
Ordinary Differential Equation (ODE)
gate2019-ce-2
ordinary-differential-equation
+
–
0
votes
0
answers
63
GATE2019 CE-2: 2
The Laplace transform of $\sin h (\text{at})$ is $\dfrac{a}{s^2-a^2} \\$ $\dfrac{a}{s^2 + a^2} \\$ $\dfrac{s}{s^2-a^2} \\$ $\dfrac{s}{s^2+a^2}$
The Laplace transform of $\sin h (\text{at})$ is $\dfrac{a}{s^2-a^2} \\$$\dfrac{a}{s^2 + a^2} \\$$\dfrac{s}{s^2-a^2} \\$$\dfrac{s}{s^2+a^2}$
Arjun
13.0k
points
Arjun
asked
Feb 12, 2019
Ordinary Differential Equation (ODE)
gate2019-ce-2
ordinary-differential-equation
laplace-transform
+
–
0
votes
0
answers
64
GATE2016-2-4
$X$ and $Y$ are two random independent events. It is known that $P(X)=0.40$ and $P(X \cup Y^C)=0.7$. Which one of the following is the value of $P(X \cup Y)$? $0.7$ $0.5$ $0.4$ $0.3$
$X$ and $Y$ are two random independent events. It is known that $P(X)=0.40$ and $P(X \cup Y^C)=0.7$. Which one of the following is the value of $P(X \cup Y)$?$0.7$$0.5$$0...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ce-2
probability-and-statistics
probability
independent-events
+
–
1
votes
0
answers
65
GATE2016-2-27
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
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{oth...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ce-2
probability-and-statistics
probability
probability-density-function
variance
+
–
0
votes
0
answers
66
GATE2017 CE-1: 1
The matrix $P$ is the inverse of a matrix $Q$. If $I$ denotes the identity matrix, which one of the following options is correct? $PQ=I$ but $QP \neq I$ $QP=I$ but $PQ \neq I$ $PQ=I$ and $QP= I$ $PQ-QP= I$
The matrix $P$ is the inverse of a matrix $Q$. If $I$ denotes the identity matrix, which one of the following options is correct?$PQ=I$ but $QP \neq I$$QP=I$ but $PQ \neq...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 26, 2018
Linear Algebra
gate2017-ce-1
linear-algebra
matrices
inverse-of-matrix
+
–
0
votes
0
answers
67
GATE2016-2-5
What is the value of $\underset{x \rightarrow 0 \\ y \rightarrow 0}{\lim} \dfrac{xy}{x^2+y^2}$? $1$ $-1$ $0$ Limit does not exist
What is the value of $\underset{x \rightarrow 0 \\ y \rightarrow 0}{\lim} \dfrac{xy}{x^2+y^2}$?$1$$-1$$0$Limit does not exist
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 27, 2018
Calculus
gate2016-ce-2
calculus
limits
+
–
0
votes
0
answers
68
GATE2016-2-3
The Fourier series of the function, $\begin{array}{rll} f(x) & =0, & -\pi < x \leq 0 \\ {} & =\pi - x, & 0 < x < \pi \end{array}$ in the interval $[- \pi, \pi ]$ ... $\Sigma_{n-1}^{\infty} \dfrac{(-1)^{n+1}}{2n-1} = \dfrac{\pi}{4}$
The Fourier series of the function,$\begin{array}{rll} f(x) & =0, & -\pi < x \leq 0 \\ {} & =\pi – x, & 0 < x < \pi \end{array}$in the interval $[- \pi, \pi ]$ is$f(x) ...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 27, 2018
Partial Differential Equation (PDE)
gate2016-ce-2
partial-differential-equation
fourier-series
+
–
0
votes
0
answers
69
GATE2015-2-29
For step-size, $\Delta x =0.4$, the value of following integral using Simpson’s $1/3$ rule is _______. $\int_0^{0.8} (0.2 + 25 x – 200 x^2 + 675 x^3 – 900 x^4 +400 x^5) dx$
For step-size, $\Delta x =0.4$, the value of following integral using Simpson’s $1/3$ rule is _______.$$\int_0^{0.8} (0.2 + 25 x – 200 x^2 + 675 x^3 – 900 x^4 +400 ...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 26, 2018
Numerical Methods
gate2015-ce-2
numerical-answers
numerical-methods
integration-by-trapezoidal-and-simpsons-rule
+
–
0
votes
0
answers
70
GATE2017 CE-1: 26
For the function $f(x)=a+bx,0\leq x\leq1,$ to be a valid probability density function,which one of the following statements is correct? $a=1,b=4$ $b=0.5,b=1$ $a=0,b=1$ $a=1,b=-1$
For the function $f(x)=a+bx,0\leq x\leq1,$ to be a valid probability density function,which one of the following statements is correct?$a=1,b=4$$b=0.5,b=1$$a=0,b=1$$a=1,b...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 26, 2018
Probability and Statistics
gate2017-ce-1
probability-and-statistics
probability
probability-density-function
+
–
0
votes
0
answers
71
GATE2016-1-29
The magnitudes of vectors $\textbf{P, Q}$ and $\textbf{R}$ are $100$ kN, $250$ kN and $150$ kN, respectively as shown in the figure. The respective values of the magnitude (in kN) and the direction (with respect to the x-axis) of the resultant vector are $290.9$ and $96.0^{\circ}$ $368.1$ and $94.7^{\circ}$ $330.4$ and $118.9^{\circ}$ $400.1$ and $113.5^{\circ}$
The magnitudes of vectors $\textbf{P, Q}$ and $\textbf{R}$ are $100$ kN, $250$ kN and $150$ kN, respectively as shown in the figure.The respective values of the magnitude...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 27, 2018
Calculus
gate2016-ce-1
calculus
vector-identities
+
–
0
votes
0
answers
72
GATE2016-1-26
Probability density function of a random variable $X$ is given below $f(x) = \begin{cases} 0.25 & \text{ if } 1 \leq x \leq 5 \\ 0 & \text{ otherwise} \end{cases}$ $P(X \leq 4)$ is $\dfrac{3}{4} \\$ $\dfrac{1}{2} \\$ $\dfrac{1}{4} \\$ $\dfrac{1}{8}$
Probability density function of a random variable $X$ is given below$$f(x) = \begin{cases} 0.25 & \text{ if } 1 \leq x \leq 5 \\ 0 & \text{ otherwise} \end{cases}$$$P(X \...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ce-1
probability-and-statistics
probability
probability-density-function
random-variable
+
–
0
votes
0
answers
73
GATE2016-2-28
The angle of intersection of the curves $x^{2}=4y$ and $y^{2} = 4x$ at point $(0,0)$ is $0^{\circ}$ $30^{\circ}$ $45^{\circ}$ $90^{\circ}$
The angle of intersection of the curves $x^{2}=4y$ and $y^{2} = 4x$ at point $(0,0)$ is$0^{\circ}$$30^{\circ}$$45^{\circ}$$90^{\circ}$
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 27, 2018
Calculus
gate2016-ce-2
calculus
curves
+
–
0
votes
0
answers
74
GATE2014-2-5
If $\{x\}$ is a continuous, real valued random variable defined over the interval $(- \infty, + \infty)$ and its occurrence is defined by the density function given as: $f(x) = \dfrac{1}{\sqrt{2 \pi} *b} e^{-\frac{1}{2} (\frac{x-a}{b})^2}$ where $'a'$ and $b'$ are the statistical ... $1$ $0.5$ $\pi$ $\dfrac{\pi}{2}$
If $\{x\}$ is a continuous, real valued random variable defined over the interval $(- \infty, + \infty)$ and its occurrence is defined by the density function given as: $...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Probability and Statistics
gate2014-ce-2
probability-and-statistics
probability
probability-density-function
random-variable
+
–
0
votes
0
answers
75
GATE2016-2-25
A circular curve of radius R connects two straights with a deflection angle of $60^{\circ}$. The tangent length is $0.577 \: R$ $1.155 \: R$ $1.732 \:R$ $3.464 \: R$
A circular curve of radius R connects two straights with a deflection angle of $60^{\circ}$. The tangent length is$0.577 \: R$$1.155 \: R$$1.732 \:R$$3.464 \: R$
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 27, 2018
Calculus
gate2016-ce-2
calculus
circular-curve
+
–
0
votes
0
answers
76
GATE2016-2-26
Consider the following linear system. $x+2y-3z=a$ $2x+3y+3z=b$ $5x +9y-6z=c$ This system is consistent if $a, b$ and $c$ satisfy the equation $7a-b-c=0$ $3a+b-c=0$ $3a-b+c=0$ $7a-b+c=0$
Consider the following linear system.$x+2y-3z=a$$2x+3y+3z=b$$5x +9y-6z=c$This system is consistent if $a, b$ and $c$ satisfy the equation$7a-b-c=0$$3a+b-c=0$$3a-b+c=0$$7a...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 27, 2018
Linear Algebra
gate2016-ce-2
linear-algebra
system-of-equations
+
–
0
votes
0
answers
77
GATE2016-2-2
The optimum value of the function $f(x)=x^2-4x+2$ is $2$ (maximum) $2$ (minimum) $ – 2$ (maximum) $ – 2$ (minimum)
The optimum value of the function $f(x)=x^2-4x+2$ is$2$ (maximum)$2$ (minimum)$ – 2$ (maximum)$ – 2$ (minimum)
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 27, 2018
Calculus
gate2016-ce-2
calculus
maxima-minima
+
–
0
votes
0
answers
78
GATE Civil 2013 | Question: 1
There is no value of $x$ that can simultaneously satisfy both the given equations. Therefore, find the ‘least squares error’ solution to the two equations, i.e., find the value of $x$ that minimizes the sum of squares of the errors in the two equations. _____ $2x=3$ $4x=1$
There is no value of $x$ that can simultaneously satisfy both the given equations. Therefore, find the ‘least squares error’ solution to the two equations, i.e., find...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Numerical Methods
gate2013-ce
numerical-answers
numerical-methods
+
–
0
votes
0
answers
79
GATE2016-2-1
The spot speeds (expressed in km/hr) observed at a road section are $66, 62, 45, 79, 32, 51, 56, 60, 53,$ and $49$. The median speed (expressed in km / hr) is ______ (Note: answer with one decimal accuracy)
The spot speeds (expressed in km/hr) observed at a road section are $66, 62, 45, 79, 32, 51, 56, 60, 53,$ and $49$. The median speed (expressed in km / hr) is ______(Note...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 27, 2018
Probability and Statistics
gate2016-ce-2
numerical-answers
probability-and-statistics
statistics
mean-median-mode
+
–
0
votes
0
answers
80
GATE Civil 2013 | Question: 51
For a portion of national highway where a descending gradient of $1$ in $25$ meets with an ascending gradient of $1$ in $20$, a valley curve needs to be designed for a vehicle travelling at $90$ kmph based on the following conditions. headlight sight ... ; and beam angle $1^{\circ}$. What is the length of valley curve (in m) based on the comfort condition? __________
For a portion of national highway where a descending gradient of $1$ in $25$ meets with an ascending gradient of $1$ in $20$, a valley curve needs to be designed for a ve...
Milicevic3306
11.9k
points
Milicevic3306
asked
Mar 25, 2018
Calculus
gate2013-ce
numerical-answers
calculus
gradient
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