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Recent questions and answers in Engineering Mathematics
0
votes
1
answer
1
GATE201319
The minimum eigenvalue of the following matrix is $\begin{bmatrix} 3& 5& 2\\5 &12 &7 \\2 &7 & 5\end{bmatrix}$ $0$ $1$ $2$ $3$
answered
Nov 26, 2019
in
Linear Algebra
by
Lakshman Patel RJIT
(
230
points)
gate2013ec
linearalgebra
eigenvalues
0
votes
0
answers
2
GATE2016 EC3: 3
The probability of getting a “head” in a single toss of a biased coin is 0.3. The coin is tossed repeatedly till a “head” is obtained. If the tosses are independent, then the probability of getting “head” for the first time in the fifth toss is _________
asked
Nov 21, 2019
in
Probability and Statistics
by
Kushagra गुप्ता
(
260
points)
gate2016ec
probability
0
votes
0
answers
3
GATE2009 EC: 11
A fair coin is tossed 10 times. What is the probability that ONLY the first two tosses will yield heads. (A) $\left(\dfrac{1}{2}\right)^{2}$ (B) $^{10}C_2\left(\dfrac{1}{2}\right)^{2}$ (C) $\left(\dfrac{1}{2}\right)^{10}$ (D) $^{10}C_2\left(\dfrac{1}{2}\right)^{10}$
asked
Nov 21, 2019
in
Probability and Statistics
by
Kushagra गुप्ता
(
260
points)
gate2009ec
probability
+1
vote
0
answers
4
GATE201531
For $A = \begin{bmatrix} 1 &\tan x \\ \tan x &1 \end{bmatrix},$ the determinant of $A^{T}A^{1}$ is $\sec^{2}x$ $\cos 4x$ $1$ $0$
asked
Mar 28, 2018
in
Linear Algebra
by
Milicevic3306
(
15.7k
points)
gate2015ec3
linearalgebra
matrix
0
votes
0
answers
5
GATE201414
A real $(4 \times 4)$ matrix $A$ satisfies the equation $A^{2} = I$, where $I$ is the $(4 \times 4)$ identity matrix. The positive eigen value of $A$ is ______.
asked
Mar 26, 2018
in
Linear Algebra
by
Milicevic3306
(
15.7k
points)
gate2014ec1
linearalgebra
matrix
eigenvalues
numericalanswers
0
votes
0
answers
6
GATE201355
The state diagram of a system is shown below. A system is described by the statevariable equations $\dot{X}= AX+Bu;\:\: y = CX+Du$ The state transition matrix $e^{At}$ of the system shown in the figure above is $\begin{bmatrix} e^{t}& 0\\te^{t} &e^{t} \end{bmatrix}$ ... $\begin{bmatrix} e^{t}&te^{t} \\ 0 &e^{t} \end{bmatrix}$
asked
Mar 26, 2018
in
Linear Algebra
by
Milicevic3306
(
15.7k
points)
gate2013ec
linearalgebra
matrix
0
votes
0
answers
7
GATE201326
Let $U$ and $V$ be two independent zero mean Gaussian random variables of variances $\dfrac{1}{4}$ and $\dfrac{1}{9}$ respectively. The probability $P(3V\geq 2U)$ is $4/9$ $1/2$ $2/3$ $5/9$
asked
Mar 26, 2018
in
Probability and Statistics
by
Milicevic3306
(
15.7k
points)
gate2013ec
probability
randomvariable
0
votes
0
answers
8
GATE201327
Let $A$ be an $m \times n$ matrix and $B$ an $n \times m$ matrix. It is given that determinant $(I_{m} + AB) =$ determinant $(I_{n} + BA),$ where $I_{k}$ is the $k \times k$ ... $2$ $5$ $8$ $16$
asked
Mar 26, 2018
in
Linear Algebra
by
Milicevic3306
(
15.7k
points)
gate2013ec
linearalgebra
matrix
determinant
0
votes
0
answers
9
GATE2017 EC2: 28
If the vector function $\overrightarrow{F}=\widehat{a_x}(3yk_1z)+\widehat{a_y}(k_2x2z)\widehat{a_z}(k_3y+z)$ is irrotational, then the values of the constants $k_1$,$k_2$ and $k_3$, respectively, are $0.3, 2.5, 0.5$ $0.0, 3.0, 2.0$ $0.3, 0.33, 0.5$ $4.0, 3.0, 2.0$
asked
Nov 23, 2017
in
Linear Algebra
by
admin
(
2.8k
points)
gate2017ec2
vectoranalysis
+1
vote
0
answers
10
GATE2017 EC2: 29
Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is $40 \%$ chance of getting reservation in any attempt by a passenger, then the average number of attempts that passengers need to make to get a seat reserved is __________
asked
Nov 23, 2017
in
Probability and Statistics
by
admin
(
2.8k
points)
gate2017ec2
numericalanswers
0
votes
0
answers
11
GATE2017 EC2: 30
The minimum value of the function $f(x)=\frac{1}{3} x(x^23)$ in the interval $100≤x≤100$ occurs at $x =$ ________.
asked
Nov 23, 2017
in
Linear Algebra
by
admin
(
2.8k
points)
gate2017ec2
numericalanswers
0
votes
0
answers
12
GATE2017 EC2: 26
The values of the integrals $\int_{0}^{1}\left ( \int_{0}^{1}\frac{xy}{(x+y)^3}dy \right )dx$ and $\int_{0}^{1}\left ( \int_{0}^{1}\frac{xy}{(x+y)^3}dx \right )dy$ are same and equal to $0.5$ same and equal to $0.5$ $0.5$ and $0.5$, respectively $0.5$ and $0.5$, respectively
asked
Nov 23, 2017
in
Calculus
by
admin
(
2.8k
points)
gate2017ec2
0
votes
0
answers
13
GATE2017 EC2: 22
Consider the random process $X(t)=U+Vt,$ Where $U$ is a zeromean Gaussian random variable and V is a random variable uniformly distributed between $0$ and $2$. Assume that $U$ and $V$ are statistically independent. The mean value of the random process at $t = 2$ is ________
asked
Nov 23, 2017
in
Probability and Statistics
by
admin
(
2.8k
points)
gate2017ec2
numericalanswers
0
votes
0
answers
14
GATE2017 EC2: 4
The residues of a function $f(z)=\frac1{(z4)(z+1)^3 }$ are $\frac{1}{27}$ and $\frac{1}{125} \\$ $\frac{1}{125}$ and $\frac{1}{125} \\$ $\frac{1}{27}$ and $\frac{1}{5} \\$ $\frac{1}{125}$and $\frac{1}{5}$
asked
Nov 23, 2017
in
Linear Algebra
by
admin
(
2.8k
points)
gate2017ec2
0
votes
0
answers
15
GATE2017 EC2: 3
The smaller angle (in degrees) between the planes $x+y+z=1$ and $2xy+2z=0$ is ________.
asked
Nov 23, 2017
in
Vector Analysis
by
admin
(
2.8k
points)
gate2017ec2
vectorinplanes
numericalanswers
0
votes
0
answers
16
GATE2017 EC2: 2
The general solution of the differential equation $\frac{d^2y}{dx^2}+2\frac{dy}{dx}5y=0$ in terms of arbitrary constants $K_1$ and $K_2$ is $K_1e^{(1+\sqrt{6})x}+K_2e^{(1\sqrt{6})x}$ $K_1e^{(1+\sqrt{8})x}+K_2e^{(1\sqrt{8})x}$ $K_1e^{(2+\sqrt{6})x}+K_2e^{(2\sqrt{6})x}$ $K_1e^{(2+\sqrt{8})x}+K_2e^{(2\sqrt{8})x}$
asked
Nov 23, 2017
in
Differential Equations
by
admin
(
2.8k
points)
gate2017ec2
secondorderdifferentialequation
0
votes
0
answers
17
GATE2017 EC2: 1
The rank of the matrix $\begin{bmatrix} 1 & 1& 0& 0& 0& \\ 0& 0& 1& 1& 0& \\ 0& 1& 1& 0& 0& \\ 1& 0& 0& 0& 1& \\ 0& 0& 0& 1& 1& \end{bmatrix}$ is ________.
asked
Nov 23, 2017
in
Linear Algebra
by
admin
(
2.8k
points)
gate2017ec2
matrixalgebra
rank
numericalanswers
0
votes
0
answers
18
GATE2017 EC1: 48
Which one of the following options correctly describes the locations of the roots of the equation $s^{4}+s^{2}+1=0$ on the complex plane? Four left half plane(LHP) roots One right half plane(RHP) root,one LHP root and two roots on the imaginary axis Two RHP roots and two LHP roots All four roots are on the imaginary axis
asked
Nov 17, 2017
in
Linear Algebra
by
admin
(
2.8k
points)
gate2017ec1
0
votes
0
answers
19
GATE2017 EC1: 26
Let $f(x)=e^{x+x^{2}}$ for real $x$ . From among the following, choose the Taylor series approximation of $f(x)$ around $x=0$, which includes all powers of $x$ less than or equal to $3$. $1 + x + x^{2} + x^{3} $ $1 + x +\frac{3}{2} x^{2} + x^{3} $ $1 + x +\frac{3}{2} x^{2} + \frac{7}{6}x^{3} $ $1 + x +3 x^{2} + 7x^{3} $
asked
Nov 17, 2017
in
Calculus
by
admin
(
2.8k
points)
gate2017ec1
taylorseries
0
votes
0
answers
20
GATE2017 EC1: 9
A bar of Gallium Arsenide (GaAs) is doped with silicon such that the silicon atoms occupy Gallium and Arsenic sites in the GaAs crystal. Which one of the following statements is true? Silicon atoms act as $p$type dopants in Arsenic sites and $n$type ... in Arsenic sites as well as Gallium sites Silicon atoms act as $n$type dopants in Arsenic sites as well as Gallium sites
asked
Nov 17, 2017
in
Calculus
by
admin
(
2.8k
points)
gate2017ec1
volumeintegrals
0
votes
0
answers
21
GATE2017 EC1: 28
Let $I=\int_{c}\left ( 2zdx+2ydy+2xdx \right )$ where $x,y,z$ are real, and let $C$ be the straight line segment from point $A:(0,2,1)$ to point $B:(4,1,1)$.The value of $I$ is ____________.
asked
Nov 17, 2017
in
Vector Analysis
by
admin
(
2.8k
points)
gate2017ec1
numericalanswers
0
votes
0
answers
22
GATE2017 EC1: 29
Which one of the following is the general solution of the first order differential equation $\frac{dy}{dx}=(x+y1)^{2},$ where $x,y$ are real? $y=1+x+\tan^{1}(x+c)$, where $c$ is a constant $y=1+x+\tan(x+c)$, where $c$ is a constant $y=1x+\tan^{1}(x+c)$, where $c$ is a constant $y=1x+\tan(x+c)$, where $c$ is a constant
asked
Nov 17, 2017
in
Differential Equations
by
admin
(
2.8k
points)
gate2017ec1
firstorderdifferentialequation
0
votes
0
answers
23
GATE2017 EC1: 30
Starting with $x=1$, the solution of the equation $x^{3}+x=1$, after two iterations of NewtonRaphson’s method(up to two decimal places) is__________.
asked
Nov 17, 2017
in
Differential Equations
by
admin
(
2.8k
points)
gate2017ec1
numericalanswers
0
votes
0
answers
24
GATE2017 EC1: 4
Three fair cubical dice are thrown simultaneously . The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place)________.
asked
Nov 17, 2017
in
Probability and Statistics
by
admin
(
2.8k
points)
gate2017ec1
probability
numericalanswers
0
votes
0
answers
25
GATE2017 EC1: 1
Consider the 5 $\times$ 5 matrix $\begin{bmatrix} 1&2&3&4&5\\ 5&1 &2& 3 &4\\ 4&5&1&2&3\\ 3&4&5&1&2\\ 2&3&4&5&1 \end{bmatrix}$ It is given that A has only one real eigenvalue. Then the real eigenvalue of A is $2.5$ $0$ $15$ $25$
asked
Nov 17, 2017
in
Linear Algebra
by
admin
(
2.8k
points)
gate2017ec1
matrixalgebra
eigenvalues
0
votes
0
answers
26
GATE2017 EC1: 2
The rank of the matrix $\textbf{M} = \begin{bmatrix} 5&10&10 \\ 1 &0 &2 \\ 3&6&6 \end{bmatrix}$ is $0$ $1$ $2$ $3$
asked
Nov 17, 2017
in
Linear Algebra
by
admin
(
2.8k
points)
gate2017ec1
matrixalgebra
rank
0
votes
0
answers
27
GATE2017 EC1: 3
Consider the following statements about the linear dependence of the real valued function $y_{1}=1,y_{2}=x$ and $y_{3}=x^{2}$ over the field of real numbers. $y_{1},y_{2}$ and $y_{3} $ are linearly independent on $1\leq x\leq 0$ ... Which one among the following is correct? Both I and II are true Both I and III are true Both II and IV are true Both III and IV are true
asked
Nov 17, 2017
in
Linear Algebra
by
admin
(
2.8k
points)
gate2017ec1
linearequations
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