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Recent questions and answers in Engineering Mathematics
0
votes
0
answers
1
Gate2006-EE
...
asked
Sep 29
in
Linear Algebra
by
Kushagra गुप्ता
(
120
points)
gate2006-ee
linear-algebra
0
votes
1
answer
2
GATE2014-2-GA-6
The old city of Koenigsberg, which had a German majority population before World War $2$, is now called Kaliningrad. After the events of the war, Kaliningrad is now a Russian territory and has a predominantly Russian population. It is bordered by the ... Kaliningrad, as that was its original Russian name Poland and Lithuania are on the route from Kaliningrad to the rest of Russia
answered
Sep 13
in
Probability & Statistics
by
srestha
(
870
points)
gate2014-ee-2
stats
infer
0
votes
1
answer
3
GATE2014-2-1
Which one of the following statements is true for all real symmetric matrices? All the eigenvalues are real. All the eigenvalues are positive. All the eigenvalues are distinct. Sum of all the eigenvalues is zero.
answered
Oct 26, 2018
in
Linear Algebra
by
Abhisek Tiwari 4
(
140
points)
gate2014-ee-2
eigen-values
eigen-matrix
+1
vote
1
answer
4
GATE2014-2-2
Consider a dice with the property that the probability of a face with $n$ dots showing up is proportional to $n$. The probability of the face with three dots showing up is ________.
answered
Nov 4, 2017
in
Probability & Statistics
by
Avik10
(
140
points)
gate2014-ee-2
event
random-variable
numerical-answers
0
votes
0
answers
5
GATE2013-46
A function $y=5x^2+10x$ is defined over an open interval $x$ = $(1, 2)$ . At least at one point in this interval, $\dfrac{\mathrm{dy} }{\mathrm{d} x}$ is exactly $20$ $25$ $30$ $35$
asked
Feb 12, 2017
in
Calculus
by
piyag476
(
1.5k
points)
gate2013-ee
calculus
directional-derivatives
gausss-theorem
+1
vote
0
answers
6
GATE2013-50
The state variable formulation of a system is given as ... The system is controllable but not observable not controllable but observable both controllable and observable both not controllable and not observable
asked
Feb 12, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2013-ee
linear-algebra
state-equations
system-of-linear-equations
0
votes
0
answers
7
GATE2013-51
The state variable formulation of a system is given as $\begin{bmatrix} x^\cdot_1 \\ x^\cdot_2 \end{bmatrix}=\begin{bmatrix} -2 & 0\\ 0 & -1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 1\\ 1 \end{bmatrix}u$ , $x_1(0)=0$ , $x_2(0)=0$ ... $1-\frac{1}{2}e^{-2t}-\frac{1}{2}e^{-t}$ $e^{-2t}-e^{-t}$ $1-e^{-t}$
asked
Feb 12, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2013-ee
linear-algebra
state-equations
system-of-linear-equations
0
votes
0
answers
8
GATE2013-36
$\displaystyle{}\oint \frac{z^2-4}{z^2+4}\: dz$ evaluated anticlockwise around the circle $\mid z-i \mid=2$ , where $i=\sqrt{-1}$, is $-4\pi$ $0$ $2+\pi$ $2+2i$
asked
Feb 12, 2017
in
Differential Equations
by
piyag476
(
1.5k
points)
gate2013-ee
integral
equations
0
votes
0
answers
9
GATE2013-25
The equation$\begin{bmatrix} 2&-2 \\ 1& -1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}=\begin{bmatrix} 0\\0 \end{bmatrix}$ has no solution only one solution $\begin{bmatrix} x1\\x2 \end{bmatrix}=\begin{bmatrix} 0\\0 \end{bmatrix}$ non-zero unique solution multiple solutions
asked
Feb 12, 2017
in
Linear Algebra
by
piyag476
(
1.5k
points)
gate2013-ee
linear-algebra
matrix
system-of-linear-equations
0
votes
0
answers
10
GATE2013-23
Square roots of $-i$,where $i=\sqrt{-1}$, are $i,-i$ $\cos(-\frac{\pi }{4} )+i\sin(-\frac{\pi }{4})+\cos(\frac{3\pi }{4})+i\sin(\frac{3\pi }{4})$ $\cos(\frac{\pi }{4} )+i\sin(\frac{3\pi }{4})+\cos(\frac{3\pi }{4})+i\sin(\frac{\pi }{4})$ $\cos(\frac{3\pi }{4} )+i\sin(-\frac{3\pi }{4})+\cos(-\frac{3\pi }{4})+i\sin(\frac{3\pi }{4})$
asked
Feb 12, 2017
in
Complex Variables
by
piyag476
(
1.5k
points)
gate2013-ee
complex-number
trigonometry
0
votes
0
answers
11
GATE2013-11
A continuous random variable $X$ has a probability density function $f(x)=e^{-x}, 0< x< \infty$. then $P\{X> 1\}$ $0.368$ $0.5$ $0.632$ $1.0$
asked
Feb 12, 2017
in
Probability & Statistics
by
piyag476
(
1.5k
points)
gate2013-ee
random-variable
probability-density-function
0
votes
0
answers
12
GATE2014-3-26
Integration of the complex function $f(z)=\frac{z^2}{z^2-1}$ , in the counterclockwise direction, around $\mid z-1 \mid$ = $1$, is $-\pi i$ $0$ $\pi i$ $2 \pi i$
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-3
complex-functions
integration
0
votes
0
answers
13
GATE2014-3-1
Two matrices $A$ and $B$ are given below: $A=\begin{vmatrix} p & q\\ r & s \end{vmatrix}$ ; $B=\begin{vmatrix} p^2+q^2 & pr+qs\\ pr+qs &r^2+s^2 \end{vmatrix}$ If the rank of matrix $A$ is $N$, then the rank of matrix $B$ is $N/2$ $N$-$1$ $N$ $2N$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-3
matrix
rank
0
votes
0
answers
14
GATE2014-3-4
Lifetime of an electric bulb is a random variable with density $f(x)=kx^2$ , where $x$ is measured in years. If the minimum and maximum lifetimes of bulb are $1$ and $2$ years respectively, then the value of k is ________.
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-3
random-variable
probability-density-function
numerical-answers
0
votes
0
answers
15
GATE2014-3-GA-5
The table below has question-wise data on the performance of students in an examination. The marks for each question are also listed. There is no negative or partial marking in the examination. ... $1.34$ $1.74$ $3.02$ $3.91$
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-3
mean
stats
0
votes
0
answers
16
GATE2014-3-GA-8
The Gross Domestic Product $(GDP)$ in Rupees grew at $7$% during $2012$-$2013$.For international comparison, the $GDP$ is compared in $US$ Dollars $(USD)$ after conversion based on the market exchange rate. During the period $2012$-$2013$ ... $USD$ during the period $2012$-$2013$ increased by $5 $% decreased by $13$% decreased by $20$% decreased by $11$%
asked
Feb 12, 2017
in
Engineering Mathematics
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-3
gross-domestic-product
market-exchange-rate
0
votes
0
answers
17
GATE2014-3-GA-9
The ratio of male to female students in a college for five years is plotted in the following line graph If the number of female students in $2011$ and $2012$ is equal, what is the ratio of male students in $2012$ to male students in $2011$? $1:1$ $2:1$ $1.5:1$ $2.5:1$
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-3
graph
stats
0
votes
0
answers
18
GATE2014-2-18
The state transition matrix for the system $\begin{bmatrix} \dot{x_1}\\ \dot{x_2} \end{bmatrix}=\begin{bmatrix} 1 & 0\\ 1 & 1 \end{bmatrix}\begin{bmatrix} x_1\\ x_2 \end{bmatrix}+\begin{bmatrix} 1\\ 1 \end{bmatrix}u$ ... $\begin{bmatrix} e^t &te^t \\ 0&e^t \end{bmatrix}$
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-2
state
transition
matrix
0
votes
0
answers
19
GATE2014-2-26
To evaluate the double integral $\int_{0}^{8}(\int_{(y/2)}^{y/2+1}(\frac{2x-y}{2})dx)dy$ , we make the substitution $u=(\frac{2x-y}{2})$ and $v=\frac{y}{2}$ The integral will reduce $\int_{0}^{4}(\int_{0}^{2}2udu) dv$ $\int_{0}^{4}(\int_{0}^{1}2udu) dv$ $\int_{0}^{4}(\int_{0}^{1}udu) dv$ $\int_{0}^{4}(\int_{0}^{2}udu) dv$
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-2
integral
upper-limit
lower-limit
0
votes
0
answers
20
GATE2014-2-27
Let $X$ be a random variable with probability density function $f(x)=\begin{cases} 0.2,& \text{for } \mid x \mid \leq 1\\ 0.1,& \text{for }1< \mid x \mid \leq 4\\ 0 & \text{otherwise } \end{cases} \\$ The probability $P(0.5 < X < 5)$ is ______.
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-2
random-variable
probability-density-function
numerical-answers
0
votes
0
answers
21
GATE2014-2-28
The minimum value of the function $f(x)=x^3-3x^2-24x+100$ in the interval $[-3,3]$ is $20$ $28$ $16$ $32$
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-2
linear-functions
0
votes
0
answers
22
GATE2014-2-5
Consider the differential equation $x^2\frac{d^2y}{dx^2}+x\frac{dy}{dx}-y=0$ . Which of the following is a solution to this differential equation for$x>0$? $e^x$ $x^2$ $1/x$ $lnx$
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-2
derivatives
equations
0
votes
0
answers
23
GATE2014-2-3
Minimum of the real valued function $f(x)=(x-1)^{2/3}$ occurs at x equal to $-\infty$ 0 1 $\infty$
asked
Feb 12, 2017
in
Numerical Methods
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-2
complex-functions
minima
maxima
0
votes
0
answers
24
GATE2014-2-4
All the values of the multi-valued complex function $1^i$,where $i=\sqrt{-1}$ are purely imaginary. real and non-negative on the unit circle. equal in real and imaginary parts.
asked
Feb 12, 2017
in
Complex Variables
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-2
imaginary
complex-functions
0
votes
0
answers
25
GATE2014-2-GA-9
The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students doubled in $2009$, by what percent did the number of male students increase in $2009?$
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-2
line-graph
stats
numerical-answers
0
votes
0
answers
26
GATE2014-2-GA-8
If x is real and $|x^2 − 2x + 3|$ = $11$, then possible values of $| -x^3 + x^2 − x|$ include $2,4$ $2,14$ $4,52$ $14,52$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-2
algebra
matrix
0
votes
0
answers
27
GATE2014-1-46
A system matrix is given as follows. $A=\begin{bmatrix} 0 & 1 & -1\\ -6 & -11 &6 \\ -6& -11& 5 \end{bmatrix}$ The absolute value of the ratio of the maximum eigenvalue to the minimum eigenvalue is _______
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-1
linear-algebra
eigen-values
eigen-matrix
numerical-answers
0
votes
0
answers
28
GATE2014-1-28
The line integral of function $F = yzi$, in the counterclockwise direction, along the circle $x^2+y^2 = 1$ at $z = 1$ is $-2\pi$ $-\pi$ $\pi$ $2\pi$
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-1
line-integral
circle-equation
quadratic-function
0
votes
0
answers
29
GATE2014-1-27
A fair coin is tossed $n$ times. The probability that the difference between the number of heads and tails is $(n-3)$ is $2^{-n}$ $0$ $^{n}C_{n-3}2^{-n}$ $2^{-n+3}$
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-1
probability
coins
0
votes
0
answers
30
GATE2014-1-17
In the formation of Routh-Hurwitz array for a polynomial, all the elements of a row have zero values. This premature termination of the array indicates the presence of only one root at the origin Imaginary roots only positive real roots only negative real roots
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-1
routh-hurwitz
array
polynomial
0
votes
0
answers
31
GATE2014-1-2
Let $f(x)=xe^{-x}$ . The maximum value of the function in the interval $(0,\infty)$ is $e^{-1}$ $e$ $1-e^{-1}$ $1+e^{-1}$
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-1
interval
functions
0
votes
0
answers
32
GATE2014-1-3
The solution for the differential equation $\dfrac{d^2x}{dt^2}=-9x,$ with initial conditions $x(0)=1$ and $\dfrac{dx}{dt}\mid_{t=0}=1$ , is $t^2+t+1$ $\sin3t+\frac{1}{3}\cos3t+\frac{2}{3}$ $\frac{1}{3}\sin3t+\cos3t$ $\cos3t+t$
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-1
boundary-limits
differential
equation
0
votes
0
answers
33
GATE2014-1-5
Let $S$ be the set of points in the complex plane corresponding to the unit circle. $(\text{That is}, S = \{z :\:\: \mid z \mid =1\}).$ Consider the function $f(z)=zz^{\ast}$ where $z^{\ast}$ denotes the complex conjugate of $z$. The ... of the following in the complex plane unit circle horizontal axis line segment from origin to $(1, 0)$ the point $(1, 0)$ the entire horizontal axis
asked
Feb 12, 2017
in
Complex Variables
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-1
complex-conjugate
complex-variables
0
votes
0
answers
34
GATE2014-1-1
Given a system of equations: $x+2y+2z=b_1$ $5x+y+3z=b_2$ Which of the following is true regarding its solutions The system has a unique solution for any given $b_1$ and $b_2$ The system will have infinitely many solutions for any given $b_1$ and $b_2$ Whether ... a solution exists depends on the given $b_1$ and $b_2$ The system would have no solution for any values of $b_1$ and $b_2$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-1
linear-equation
matrix
system-of-linear-equations
0
votes
0
answers
35
GATE2014-1-GA-4
If $(z+1/z)^2 = 98,$ compute $(z^2+1/z^2).$
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.2k
points)
gate2014-ee-1
complex-number
numerical-answers
0
votes
0
answers
36
GATE2015-2-27
Two coins $R$ and $S$ are tossed. The $4$ joint events $H_{R}H_{S}, T_{R}T_{S}, H_{R}T_{S}, T_{R}H_{S}$ have probabilities $0.28, 0.18, 0.30, 0.24$, respectively, where $H$ represents head and $T$ represents tail. Which one of the following is TRUE? The coin tosses are independent. R is fair, S is not. S is fair, R is not. The coin tosses are dependent.
asked
Feb 12, 2017
in
Probability & Statistics
by
makhdoom ghaya
(
9.2k
points)
gate2015-ee-2
events
sample-space
0
votes
0
answers
37
GATE2015-2-28
A differential equation $\frac{di}{dt}-0.2i=0$ is applicable over $−10 < t < 10$. If $i(4) = 10$, then $i(−5)$ is _________.
asked
Feb 12, 2017
in
Differential Equations
by
makhdoom ghaya
(
9.2k
points)
gate2015-ee-2
non-linear-equation
eulers-equation
numerical-answers
0
votes
0
answers
38
GATE2015-2-26
The volume enclosed by the surface $f(x, y) = e^{x}$ over the triangle bounded by the lines $x = y; x = 0; y = 1$ in the $xy$ plane is ________.
asked
Feb 12, 2017
in
Calculus
by
makhdoom ghaya
(
9.2k
points)
gate2015-ee-2
line-equations
3d-system
numerical-answers
0
votes
0
answers
39
GATE2015-2-3
Match the following. P. Stokes’s Theorem 1. $∯ D.ds = Q$ Q. Gauss’s Theorem 2. $\oint f(z) dz =0$ R. Divergence Theorem 3. $\int \int \int (\triangledown. A) dv = ∯ A. ds$ S. Cauchy’s Integral Theorem 4. $\int \int (\triangledown \times A).ds = \oint A. dl$ (A) P-2 Q-1 R-4 S-3 (B) P-4 Q-1 R-3 S-2 (C) P-4 Q-3 R-1 S-2 (D) P-3 Q-4 R-2 S-1
asked
Feb 12, 2017
in
Linear Algebra
by
makhdoom ghaya
(
9.2k
points)
gate2015-ee-2
gauss-elimination
integral-theorem
0
votes
0
answers
40
GATE2015-2-1
Given $f(z) = g(z) + h(z)$, where $f, g, h$ are complex valued functions of a complex variable $z$. Which one of the following statements is TRUE? If $f(z)$ is differentiable at $z_{0}$, then $g(z)$ and $h(z)$ are also differentiable at $z_{0}$ ... at $z_{0}$, then it is differentiable at $z_{0}$. If $f(z)$ is differentiable at $z_{0}$, then so are its real and imaginary parts
asked
Feb 12, 2017
in
Complex Variables
by
makhdoom ghaya
(
9.2k
points)
gate2015-ee-2
complex-valued-functions
complex-variable
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