IGNOU PHE 14 SOLVED ASSIGNMENT HINDI

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IGNOU PHE 14 SOLVED ASSIGNMENT HINDI

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IGNOU PHE 14 SOLVED ASSIGNMENT HINDI

~~Rs. 80~~
Rs. 41

Last Date of Submission of IGNOU PHE-014 (BSC) 2026 Assignment is for January 2026 Session: 30th September, 2026 (for December 2026 Term End Exam).
Semester Wise
January 2026 Session: 30th March, 2026 (for June 2026 Term End Exam).
July 2026 Session: 30th September, 2026 (for December 2026 Term End Exam).

Title Name	IGNOU PHE 14 SOLVED ASSIGNMENT HINDI
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	BACHELOR DEGREE PROGRAMMES
Course Code	BSC
Course Name	Bachelor in Science
Subject Code	PHE 14
Subject Name	Mathematical Methods in Physics-III
Year	2026
Session
Language	English Medium
Assignment Code	PHE-014/Assignmentt-1//2026
Product Description	Assignment of BSC (Bachelor in Science) 2026. Latest PHE 014 2026 Solved Assignment Solutions
Last Date of IGNOU Assignment Submission	Last Date of Submission of IGNOU PHE-014 (BSC) 2026 Assignment is for January 2026 Session: 30th September, 2026 (for December 2026 Term End Exam). Semester Wise January 2026 Session: 30th March, 2026 (for June 2026 Term End Exam). July 2026 Session: 30th September, 2026 (for December 2026 Term End Exam).

~~Rs. 80~~
Rs. 41

Questions Included in this Help Book

Ques 1.

विषम-हर्मिटी आव्यूह, लांबिक आव्यूह और ऐकिक आव्यूह को उदाहरण सहित परिभाषित कीजिए।

Ques 2.

निम्नलिखित आव्यूह A के आइगेन मान और आइगेन सदिश प्राप्त कीजिए :

$$A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & 1 \\ 3 & 2 & 3 \end{bmatrix}$

Ques 3.

सिद्ध कीजिए कि ऐकिक आव्यूह का प्रत्येक आइगेनमान एकक मापांक वाला होता है।

Ques 4.

उस शंकु परिच्छेद को पहचानिए जिसका समीकरण $5x^2 - 4xy + 5y^2 = 4$ है।

Ques 5.

कोटि दो वाले सहपरिवर्ती और प्रतिपरिवर्ती टेन्सरों को परिभाषित कीजिए। सिद्ध करें कि वेग और त्वरण प्रतिपरिवर्ती सदिश हैं।

Ques 6.

सिद्ध कीजिए कि समीकरण $z^4 - 1 = 0$ के मूल, कोटि 4 का चक्रीय समूह बनाते हैं।

Ques 7.

सिद्ध कीजिए कि फलन $\omega = \sin z$ कौशी-रीमान और लाप्लास समीकरणों को संतुष्ट करता है।

Ques 8.

निम्नलिखित समाकल को परिकलित कीजिए :

$$\oint_{C} \frac{5z^2 - 3z + 2}{(z - 1)^3} dz$

Ques 9.

निम्नलिखित समाकल को परिकलित कीजिए :

$$\oint_{C} \frac{5z^2 - 3z + 2}{(z - 1)^3} dz$

जहां $C, z = 1$ को परिबद्ध करने वाला एक साधारण बंद वक्र है।

Ques 10.

विचित्रता $z = 2$ के प्रति फलन $\frac{e^z}{(z - 2)^2}$ का लौराँ श्रेणी प्रसार प्राप्त कीजिए।

Ques 11.

अवशिष्ट विधि का उपयोग कर, सिद्ध करें कि :

$$\int_{0}^{\infty} \frac{dx}{x^2 + 1} = \frac{\pi}{2}$

Ques 12.

निम्नलिखित फलन का फूरिये रूपांतर निर्धारित करें :

$<div style=$ $f(t)=\begin{cases}\sin&space;3t,&-\pi\le&space;t\le\pi,\\0,&\text{otherwise}.\end{cases}$ ">

Ques 13.

फलन $f(t) = t^2 e^{2t}$ का लाप्लास रूपांतर निर्धारित करें।

Ques 14.

लाप्लास रूपांतरण विधि का प्रयोग करके निम्नलिखित आदि मान समस्या का हल प्राप्त करें :

$$y'' - 3y' + 2y = 6e^{-t}; \quad y(0) = 3, \quad y'(0) = 3$

Ques 15.

सिद्ध करें कि P_l(x), अंतराल (-1, 1) में P_k(x) के लांबिक है।

Ques 16.

सिद्ध करें कि :

$$J_0(x) - J_2(x) = 2 \frac{d}{dx} [J_1(x)]$

Ques 17.

फलन $f(x) = x^4 - 1$ का प्रसार $\sum_{k=0}^{\infty} A_k P_k(x)$ के रूप की श्रेणी में करें।

Ques 18.

रोड्रिगेज़ सूत्र का प्रयोग करके हर्मिट बहुपद H₄(x) का व्यंजक प्राप्त करें और सिद्ध करें कि $H_3'(x) = 6 H_2(x)$ ।

Ques 19.

Define skew-hermitian matrix, orthogonal matrix and unitary matrix with an example of each.

Ques 20.

Determine the eigenvalues and eigenvectors of the following matrix A:

$$A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & 1 \\ 3 & 2 & 3 \end{bmatrix}$

Ques 21.

Show that every eigenvalue of a unitary matrix is of unit modulus.

Ques 22.

Identify the conic section whose equation is

$$5x^2 - 4xy + 5y^2 = 4$

Ques 23.

Define covariant and contravariant tensors of rank two. Show that the velocity and acceleration are contravariant vectors.

Ques 24.

Show that the roots of the equation $z^4 - 1 = 0$ form a cyclic group of order 4.

Ques 25.

Show that the function $\omega = \sin z$ satisfies the Cauchy-Riemann and Laplace equations.

Ques 26.

Evaluate the integral

$$\oint_C \frac{5z^2 - 3z + 2}{(z - 1)^3} dz$
where C is any simple closed curve enclosing $z = 1$ .

Ques 27.

Obtain the Laurent series expansion of the function $\frac{e^z}{(z-2)^2}$ about the singularity $z = 2$ .

Ques 28.

Using the method of residues, show that:

$$\int_{0}^{\infty} \frac{dx}{x^2 + 1} = \frac{\pi}{2}$

Ques 29.

Determine the Fourier transform of the function :

$$f(t) = \begin{cases} \sin 3t & -\pi \le t \le \pi \\ 0 & \text{otherwise} \end{cases}$

Ques 30.

Determine the Laplace transform of $f(t) = t^2 e^{2t}$ .

Ques 31.

Using the method of Laplace transforms, solve the following initial value problem:

$$y'' - 3y' + 2y = 6e^{-t}; \quad y(0) = 3, \quad y'(0) = 3$

Ques 32.

Show that P₁(x) is orthogonal to [P_n(x)]² on the interval (-1, 1).

Ques 33.

Show that:-

$$J_0(x) - J_2(x) = 2 \frac{d}{dx} [J_1(x)]$

Ques 34.

Expand the function $f(x) = x^4 - 1$ in a series of the form $\sum_{k=0}^{\infty} A_k P_k(x)$ .

Ques 35.

Using Rodrigue’s formula, obtain expression for the Hermite polynomial H₃(x) and show that $H_3'(x) = 6H_2(x)$ .

Ques 36.

Ques 37.

निम्नलिखित आव्यूह A के आइगेन मान और आइगेन सदिश प्राप्त कीजिए :

$$A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & 1 \\ 3 & 2 & 3 \end{bmatrix}$

Ques 38.

सिद्ध कीजिए कि ऐकिक आव्यूह का प्रत्येक आइगेनमान एकक मापांक वाला होता है।

Ques 39.

उस शंकु परिच्छेद को पहचानिए जिसका समीकरण $5x^2 - 4xy + 5y^2 = 4$ है।

Ques 40.

Ques 41.

सिद्ध कीजिए कि समीकरण $z^4 - 1 = 0$ के मूल, कोटि 4 का चक्रीय समूह बनाते हैं।

Ques 42.

Ques 43.

निम्नलिखित समाकल को परिकलित कीजिए :

$$\oint_{C} \frac{5z^2 - 3z + 2}{(z - 1)^3} dz$

Ques 44.

निम्नलिखित समाकल को परिकलित कीजिए :

$$\oint_{C} \frac{5z^2 - 3z + 2}{(z - 1)^3} dz$

जहां $C, z = 1$ को परिबद्ध करने वाला एक साधारण बंद वक्र है।

Ques 45.

विचित्रता $z = 2$ के प्रति फलन $\frac{e^z}{(z - 2)^2}$ का लौराँ श्रेणी प्रसार प्राप्त कीजिए।

Ques 46.

अवशिष्ट विधि का उपयोग कर, सिद्ध करें कि :

$$\int_{0}^{\infty} \frac{dx}{x^2 + 1} = \frac{\pi}{2}$

Ques 47.

निम्नलिखित फलन का फूरिये रूपांतर निर्धारित करें :

$<div style=$ $f(t)=\begin{cases}\sin&space;3t,&-\pi\le&space;t\le\pi,\\0,&\text{otherwise}.\end{cases}$ ">

Ques 48.

फलन $f(t) = t^2 e^{2t}$ का लाप्लास रूपांतर निर्धारित करें।

Ques 49.

$$y'' - 3y' + 2y = 6e^{-t}; \quad y(0) = 3, \quad y'(0) = 3$

Ques 50.

सिद्ध करें कि P_l(x), अंतराल (-1, 1) में P_k(x) के लांबिक है।

Ques 51.

सिद्ध करें कि :

$$J_0(x) - J_2(x) = 2 \frac{d}{dx} [J_1(x)]$

Ques 52.

फलन $f(x) = x^4 - 1$ का प्रसार $\sum_{k=0}^{\infty} A_k P_k(x)$ के रूप की श्रेणी में करें।

Ques 53.

Ques 54.

Define skew-hermitian matrix, orthogonal matrix and unitary matrix with an example of each.

Ques 55.

Determine the eigenvalues and eigenvectors of the following matrix A:

$$A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & 1 \\ 3 & 2 & 3 \end{bmatrix}$

Ques 56.

Show that every eigenvalue of a unitary matrix is of unit modulus.

Ques 57.

Identify the conic section whose equation is

$$5x^2 - 4xy + 5y^2 = 4$

Ques 58.

Define covariant and contravariant tensors of rank two. Show that the velocity and acceleration are contravariant vectors.

Ques 59.

Show that the roots of the equation $z^4 - 1 = 0$ form a cyclic group of order 4.

Ques 60.

Show that the function $\omega = \sin z$ satisfies the Cauchy-Riemann and Laplace equations.

Ques 61.

Evaluate the integral

$$\oint_C \frac{5z^2 - 3z + 2}{(z - 1)^3} dz$
where C is any simple closed curve enclosing $z = 1$ .

Ques 62.

Obtain the Laurent series expansion of the function $\frac{e^z}{(z-2)^2}$ about the singularity $z = 2$ .

Ques 63.

Using the method of residues, show that:

$$\int_{0}^{\infty} \frac{dx}{x^2 + 1} = \frac{\pi}{2}$

Ques 64.

Determine the Fourier transform of the function :

$$f(t) = \begin{cases} \sin 3t & -\pi \le t \le \pi \\ 0 & \text{otherwise} \end{cases}$

Ques 65.

Determine the Laplace transform of $f(t) = t^2 e^{2t}$ .

Ques 66.

Using the method of Laplace transforms, solve the following initial value problem:

$$y'' - 3y' + 2y = 6e^{-t}; \quad y(0) = 3, \quad y'(0) = 3$

Ques 67.

Show that P₁(x) is orthogonal to [P_n(x)]² on the interval (-1, 1).

Ques 68.

Show that:-

$$J_0(x) - J_2(x) = 2 \frac{d}{dx} [J_1(x)]$

Ques 69.

Expand the function $f(x) = x^4 - 1$ in a series of the form $\sum_{k=0}^{\infty} A_k P_k(x)$ .

Ques 70.

Using Rodrigue’s formula, obtain expression for the Hermite polynomial H₃(x) and show that $H_3'(x) = 6H_2(x)$ .

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Course Name	Bachelor in Science
Course Code	BSC
Programm	BACHELOR DEGREE PROGRAMMES Courses
Language	English

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IGNOU PHE 14 SOLVED ASSIGNMENT HINDI

IGNOU PHE 14 SOLVED ASSIGNMENT HINDI

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