User: Aditya Mekha

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Aditya Mekha10
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Posts by Aditya Mekha

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Answer: A: Using Rayleigh- ritz method solve the boundry value problem $J=\int_0^1 (xy +\fr
... Solution: $I=\int_0^1 (xy +\frac {1}{2}y'^2)dx$ where $F=xy+ \frac {1}{2}y'^2$-----(2) Assume the trial solution , $\bar y(x)=c_0+c_1x+c_2 x^2$ ----(3) put $x=0$ in eqn(3) $\bar y(0)=c_0+c_1(0)+c_2 (0)$ But $\bar y(0)=0$ $0=c_0+(0)+(0)$ $0=c_0$ Put $x=1$ in eqn(3) $y_(1) = c_0+c_1(1)+c_ ...
written 28 days ago by Aditya Mekha10 • updated 21 days ago by Ankit Pandey ♦♦ 10
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Answer: A: Using cauchy residue theorem evaluate the following integral $\oint_c \frac{e^{z
... Solution: $\oint_c \frac{e^{z}dz}{(z^{2}+\pi^2)^2} dz $ The poles are , $(z^2+\pi ^2)=0$ $(z^2-\pi ^2i^2)=0$ $(z-\pi i )(z+\pi i ) = 0$ $z=\pi i $ and $ z = -\pi i$ Hence both poles are the poles of order two, Since unit circle is at |z|=4, Hence both the poles lies inside the circle ...
written 28 days ago by Aditya Mekha10 • updated 21 days ago by Ankit Pandey ♦♦ 10
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Using cauchy residue theorem evaluate the following integral $\oint_c \frac{e^{z}dz}{(z^{2}+\pi^2)^2} dz $ Where C is the circle $|z|=4$
... **Subject :** Applied maths 4 **Difficulty :** Medium **Marks:** 10M ...
m4e(34) written 28 days ago by Aditya Mekha10 • updated 21 days ago by Ankit Pandey ♦♦ 10
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Answer: A: $A=\begin{bmatrix} 1 & 0 & 0 \\ 1 & 0 & 1 \\ 0& 1 & 0 \end{bmatrix} find A^{50}$
... Solution: $A=\begin{bmatrix} 1 & 0 & 0 \\ 1 & 0 & 1 \\ 0& 1 & 0 \end{bmatrix}$ characteristic equation is given by $|A-\lambda I|=0$ $\left |\begin{matrix} 1-\lambda & 0 & 0 \\ 1 & 0-\lambda & 1 \\ 0& 1 & 0-\lambda \end{matrix} \right |$=0 $\lam ...
written 4 weeks ago by Aditya Mekha10 • updated 21 days ago by Ankit Pandey ♦♦ 10
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$A=\begin{bmatrix} 1 & 0 & 0 \\ 1 & 0 & 1 \\ 0& 1 & 0 \end{bmatrix} find A^{50}$
... **Subject :** Applied maths 4 **Difficulty :** Medium **Marks:** 10M ...
m4e(34) written 4 weeks ago by Aditya Mekha10
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Answer: A: In an examination marks obtained by students in maths ,physics and cehmistry are
... Solution: Let $x_1 ,x_2 ,x_3 $ denotes the marks obtained in three subjects. The $x_1 ,x_2 ,x_3 $ are normal distribution with mean $51 ,53,46$ and variance $15^2 ,12^2,16^2$ Assuming the variates to be independent $y=x_1+x_2+x_3$ is distribbuted normally with mean $m= 51+53+46 =150$ and $\sig ...
written 4 weeks ago by Aditya Mekha10 • updated 21 days ago by Ankit Pandey ♦♦ 10
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In an examination marks obtained by students in maths ,physics and cehmistry are normally distributed with mean 51,53,46 and with standard deviation 15,12,16 respctively find the probability of
... of securing total marks i) 180 or above ii)90 or below. **Subject :** Applied maths 4 **Difficulty :** Medium **Marks:** 10M ...
m4e(34) written 4 weeks ago by Aditya Mekha10
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Answer: A: Using cauchy residue theorem evaluate the following integral $\int_0^{2\pi} \fra
... Solution: Given, $\int_0^{2\pi} \frac{cos2\theta}{5+4cos\theta} d\theta$ Put $z=e^{i\theta}$ $dz=ie^{i\theta} d\theta $ $dz=iz d\theta $ $d\theta=\frac{dz} {iz}$ $cos\theta =\frac{e^{i\theta}+e^{-i\theta}}{2}$ $cos\theta =\frac{z+z^{-1}}{2}$ $cos\theta =\frac{z+\frac{1}{z}}{2}$ $\int_0^{ ...
written 4 weeks ago by Aditya Mekha10 • updated 21 days ago by Ankit Pandey ♦♦ 10
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Using cauchy residue theorem evaluate the following integral $\int_0^{2\pi} \frac{cos2\theta}{5+4cos\theta} d\theta$
... **Subject :** Applied maths 4 **Difficulty :** Medium **Marks:** 10M ...
m4e(34) written 4 weeks ago by Aditya Mekha10

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