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Recent questions and answers in Engineering Mathematics
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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
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Nov 23, 2017
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Calculus
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gate2017ec2
0
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GATE2017 EC2: 28
If the vector function $\vec{F}=\widehat{a_x}(3yk_1z)+\widehat{a_y}(k_2x2z)\widehat{a_z}(k_3y+z)$ 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
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Nov 23, 2017
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Linear Algebra
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gate2017ec2
vectoranalysis
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0
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3
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 = ________.
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Nov 23, 2017
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Linear Algebra
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2.7k
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gate2017ec2
0
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4
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 __________
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Nov 23, 2017
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Probability and Statistics
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gate2017ec2
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5
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 ________
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Nov 23, 2017
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Probability and Statistics
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gate2017ec2
0
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0
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6
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 $\frac{1}{5}$
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Nov 23, 2017
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Linear Algebra
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gate2017ec2
0
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7
GATE2017 EC2: 3
The smaller angle (in degrees) between the planes $x+y+z=1$ and $2xy+2z=0$ is ________.
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Nov 23, 2017
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Vector Analysis
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gate2017ec2
vectorinplanes
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8
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 $K_1e^{(1+\sqrt{6})x}+K_2e^{(1\sqrt{6})x}$ $K_1e^{(1+\sqrt{8})x}+K_2e^{(1\sqrt{8})x}$ $K_1e^{(2+\sqrt{6})x}+K_2e^{(2\sqrt{6})x}$ $K_1e^{(2+\sqrt{8})x}+K_2e^{(2\sqrt{8})x}$
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Nov 23, 2017
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Differential Equations
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gate2017ec2
secondorderdifferentialequation
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9
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 ________.
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Nov 23, 2017
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Linear Algebra
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gate2017ec2
matrixalgebra
rank
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10
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
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Nov 17, 2017
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Linear Algebra
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gate2017ec1
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11
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 ____________.
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Nov 17, 2017
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Vector Analysis
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gate2017ec1
0
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12
GATE2017 EC1: 27
A three dimensional region $R$ of finite volume is described by $x^{2}+y^{2}\leq z^{3};0\leq z\leq 1$ where, $x,y,z$ are real.The volume of $R$ (up to two decimal places) is ________.
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Nov 17, 2017
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Calculus
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gate2017ec1
volumeintegrals
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13
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} $
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Nov 17, 2017
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Calculus
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gate2017ec1
taylorseries
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14
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
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Nov 17, 2017
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Differential Equations
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gate2017ec1
firstorderdifferentialequation
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15
GATE2017 EC1: 24
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__________.
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Nov 17, 2017
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Differential Equations
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gate2017ec1
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16
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)________.
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Nov 17, 2017
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Probability and Statistics
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gate2017ec1
probability
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17
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
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Nov 17, 2017
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Linear Algebra
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gate2017ec1
linearequations
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18
GATE2017 EC1: 2
The rank of the matrix M $\begin{bmatrix} 5&10&10 \\ 1 &0 &2 \\ 3&6&6 \end{bmatrix}$is 0 1 2 3
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Nov 17, 2017
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Linear Algebra
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gate2017ec1
matrixalgebra
rank
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19
GATE2017 EC1: 1
Consider the 5X 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
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Nov 17, 2017
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Linear Algebra
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gate2017ec1
matrixalgebra
eigenvalues
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