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ignou PHE 4 BPHE 104 solved assignment 2024

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Last Date of Submission of IGNOU PHE-04 (BSC) 2024 Assignment is for January 2024 Session: 30th September, 2024 (for December 2024 Term End Exam).
Semester Wise
January 2024 Session: 30th March, 2024 (for June 2024 Term End Exam).
July 2024 Session: 30th September, 2024 (for December 2024 Term End Exam).

Title Name	ignou PHE 4 BPHE 104 solved 2024
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	BACHELOR DEGREE PROGRAMMES
Course Code	BSC
Course Name	Bachelor in Science
Subject Code	PHE 4 BPHE 104
Subject Name	Mathematical Methods in Physics-I
Year	2024
Session	-
Language	English Medium
Assignment Code	PHE-04/Assignmentt-1//2024
Product Description	Assignment of BSC (Bachelor in Science) 2024. Latest PHE 04 2024 Solved Assignment Solutions
Last Date of IGNOU Assignment Submission	Last Date of Submission of IGNOU PHE-04 (BSC) 2024 Assignment is for January 2024 Session: 30th September, 2024 (for December 2024 Term End Exam). Semester Wise January 2024 Session: 30th March, 2024 (for June 2024 Term End Exam). July 2024 Session: 30th September, 2024 (for December 2024 Term End Exam).
Assignment Code	PHE 4 BPHE 104/2024

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Questions Included in this Help Book

Ques 1.

a) Calculate the volume of the tetrahedron whose vertices are the points A = (3, 2, 1), B = (1, 2, 4), C = (4, 0, 3) and D = (1, 1, 7).

b) For three vectors $\left ( \vec{u}\times \vec{v} \right )\left [ \left ( \vec{v}\times \vec{w} \right ) \times \left ( \vec{w} \times \vec{u}\right )\right ]=\left [ \vec{u.}\left ( \vec{v}\times \vec{w} \right ) \right ]^{2}.$

Ques 2.

a) Obtain the derivative and the unit tangent vector for a vector function $\bar{a}(t)=t\hat{i}+e^{t^{2}}\hat{j}+sin2t\hat{k}$

b) For a scalar field $\phi(x,y,z)=x^{n}+y^{n}+z^{n},$ where n is a non-zero real constant, show that $(\vec{\bigtriangledown}\phi).\vec{r}=n\phi.$

Ques 3.

a) Determine the value of the constant a for which the vector field

$\vec{F}=(2x^{2}y+z^{2})\hat{i}+(xy^{2}-x^{2}z)\hat{j}+(axyz-2x^{2}y^{2})\hat{k}$ is incompressible.

b) Show that for any vector field \bar $\vec{F}$

$\vec{\bigtriangledown }.(\vec\bigtriangledown\times \vec{F})=0.$

Ques 4.

a) Obtain the divergence of the following vector field:

$\vec{A}=\left ( \rho ^{3}\hat{e}_\rho+\rho z\hat{e}_\phi +\rho z\, sin\, \phi \hat{e_z}\right )$

Ques 5.

b) Determine the metric coefficients for the coordinate system (u,v,z) whose coordinates are related to the Cartesian coordinates by the following equations:

$x=\frac{1}{2}(u^{2}+v^{2});y=2uv;\; z=z$

Is the system orthogonal?

Ques 6.

The position vector of an object of mass m moving along a curve is given by $\vec{r}(t)=at^{2}\hat{i}+sin\, bt\hat{j}+cosbt\, \hat{k},0\leq t\leq 1$ where a and b are constants. Calculate the force acting on the object and the work done by the force.

Ques 7.

Using Stokes’ theorem evaluate $\int_c\vec{F}.d\vec{l}$ where $\vec{F}=y\hat{i}+xz^{3}\, \hat{j}-zy^{3}\hat{k}$ and C is the circle $x^{2}+y^{2}=4;z=-3.$

Ques 8.

show that $\vec{\bigtriangledown }\left ( \frac{r}{1+r^{2}} \right )=\frac{1-r^{2}}{(1+r^{2})^{2}}\hat{e_r}.$

Ques 9.

Using Green’s Theorem evaluate the integral $\oint_{C}^{}(xydx+x^{2}y^{2}dy)$ where C is the triangle with vertices (0,0),(1,0) and (1,2).

Ques 10.

An unbiased coin is tossed three times. If A is the event that a head appears on each of the first two tosses, B is the event that a tail occurs on the third toss and C is the event that exactly two tails appear in the three tosses, show that:

i) Events A and B are independent
ii) Events B and C are dependent.

Ques 11.

A random variable X has the following probability distribution: $f(x)=\left\{\begin{matrix} \frac{4}{\pi (1+x^{2})}\, for &0<x<1 \\0 & elsewhere \end{matrix}\right.$

Calculate E(X)

Ques 12.

Out of 90 applicants for a job, 60 people get selected after the interview. If five applicants are selected at random, calculate the probability that 2 will get selected.

Ques 13.

A metal sheet has, on the average, 5 defects per 10 sq. ft. Assuming a Poisson distribution, calculate the probability that a 15 sq. ft. piece of the metal sheet will have at least 4 defects

Ques 14.

The measurements of the bulk modulus of a material at different temperatures is as follows: