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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) $y_(1) = c_0+c_1(1)+c_ ... written 28 days ago by Aditya Mekha10 • updated 21 days ago by Ankit Pandey ♦♦ 10 1 answer 34 views 1 answer ... **Subject :** Applied maths 4 **Difficulty :** Medium **Marks:** 10M ... written 28 days ago by Aditya Mekha10 1 answer 31 views 1 answers ... Solution:$\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 ) = 0z=\pi i $and$ z = -\pi i$Hence both poles are the poles of order two, Since unit circle is at |z|=4, Hence both the poles lies inside the circle ... written 28 days ago by Aditya Mekha10 • updated 21 days ago by Ankit Pandey ♦♦ 10 1 answer 31 views 1 answer ... **Subject :** Applied maths 4 **Difficulty :** Medium **Marks:** 10M ... written 28 days ago by Aditya Mekha10 • updated 21 days ago by Ankit Pandey ♦♦ 10 1 answer 48 views 1 answers ... Solution:$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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... **Subject :** Applied maths 4 **Difficulty :** Medium **Marks:** 10M ...
written 4 weeks ago by Aditya Mekha10
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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 $\sig ... written 4 weeks ago by Aditya Mekha10 • updated 21 days ago by Ankit Pandey ♦♦ 10 1 answer 47 views 1 answer ... of securing total marks i) 180 or above ii)90 or below. **Subject :** Applied maths 4 **Difficulty :** Medium **Marks:** 10M ... written 4 weeks ago by Aditya Mekha10 1 answer 53 views 1 answers ... Solution: Given,$\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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