## User: Aditya Mekha

Aditya Mekha •

**10**- Reputation:
**10**- Status:
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- Location:
- Last seen:
- 4 weeks ago
- Joined:
- 2 months ago
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#### Posts by Aditya Mekha

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... 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 Mekha •

**10**• updated 21 days ago by Ankit Pandey ♦♦**10**0

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... **Subject :** Applied maths 4
**Difficulty :** Medium
**Marks:** 10M ...

written 28 days ago by
Aditya Mekha •

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... 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 Mekha •

**10**• updated 21 days ago by Ankit Pandey ♦♦**10**0

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... **Subject :** Applied maths 4
**Difficulty :** Medium
**Marks:** 10M ...

written 28 days ago by
Aditya Mekha •

**10**• updated 21 days ago by Ankit Pandey ♦♦**10**0

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... 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 Mekha •

**10**• updated 21 days ago by Ankit Pandey ♦♦**10**0

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... **Subject :** Applied maths 4
**Difficulty :** Medium
**Marks:** 10M ...

written 4 weeks ago by
Aditya Mekha •

**10**0

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... 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 Mekha •

**10**• updated 21 days ago by Ankit Pandey ♦♦**10**0

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... of securing total marks i) 180 or above ii)90 or below.
**Subject :** Applied maths 4
**Difficulty :** Medium
**Marks:** 10M ...

written 4 weeks ago by
Aditya Mekha •

**10**0

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... 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 Mekha •

**10**• updated 21 days ago by Ankit Pandey ♦♦**10**0

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53

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... **Subject :** Applied maths 4
**Difficulty :** Medium
**Marks:** 10M ...

written 4 weeks ago by
Aditya Mekha •

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