Name of the University : North Maharashtra University
Degree : B.Sc
Department : Physics
Year : II
Name Of The Subject : Phy211 Mathematical Methods For Physics
Document type : Question Bank
Website : nmu.ac.in
Download Model/Sample Question Papers :https://www.pdfquestion.in/uploads/nmu.ac.in/5292.-S.Y.%20B.Sc.(%20Physics%20)%20Question%20Bank.pdf
NMU Mathematical Methods For Physics Model Paper
NORTH MAHARASHTRA UNIVERSITY, JALGAON
QUESTION BANK FOR S. Y. B. Sc. Physics
Phy 211 : Mathematical Methods For Physics
CHAPTER 1 :
Complex Algebra
TWO marks Questions
1) Define a complex number.
2) State De Moivre’s theorem.
Related : North Maharashtra University Numerical Analysis B.Sc Question Bank : www.pdfquestion.in/5286.html
3) Enlist the fundamental operations on complex numbers.
4) What is an Argand diagram-
5) Define modulus and argument of a complex number.
6) Explain subtraction of two complex numbers.
7) State the polar form of a rectangular complex number.
8) Using Argand diagram explain addition of two complex numbers.
9) Using the Argand diagram explain substraction of two complex numbers.
10) If (3+i)x + (1-i)y = 1+7i, find x & y.
11) Why complex number, in general, multiple valued-
12) What do you meant by complex conjugate number-
13) If x + iy = a-ib, show that x = a2-b2 & y = -2ab.
14) Find the multiplication of 7 + 5i & -2 + i.
15) Find the value of i + i2 + i3 + i4.
16) Transform z = 2v3 +2i into the polar form.
17) Find x and y if, 3x + 2y + i(x+3y) = 6 + 8i
18) Transform z = 2v3 +2i into exponential form.
19) State Euler’s formula.
20) Represent 4 + 5i & 8 – 9i on Argand diagram.
THREE marks Questions
1) Find the value of (1 + i) 8.
2) Find p & q if, 2p + q + i(p + 2q) = 7 + 8i
3) Using exponential form of sin- and cos- prove that, sin(p/2 – ) = cos-
4) Prove that cos2- + sin2- = 1.
5) Evaluate, [cosp/8 + isinp/8]4
6) Express 2e5pi/6 in rectangular form x+iy.
7) Evaluate [cosp/5 + isinp/5] [cos2p/5 + isin2p/5]2
8) Find the square root of 8 + 6i.
9) Show that, eip/2 = 1.
10)If p + i q =ii5 33 2
11) Show that, eip +1 =0
FOUR marks Questions
1) Find all roots of (-1)1/4
2) Using Argand diagram explain the division of two complex numbers.
3) Find cube roots of unity.
4) Explain polar form of complex number.
5) Express in the rectangular form, (1 + i)2 + (1 + i)4 .
6)Show that,62321
7)If a+ib =x + iy1 show that, (a2 + b2) (x2 + y2) = 1
8) State and obtain Euler’s formula.
9) Explain the fundamental mathematical operations on complex number.
10) Using Euler’s formula, obtain the trigonometric functions, sin- , cos- , cosec- , sec- .
11) Find the different values of sixth root of z = 1 + v3 i.
12) Find all possible roots of i1/3.
13) Using exponential form of sin- & cos- , prove that a) sin3- = 3sin- – 4 sin3-
14) Find the value of (1 + i)8 + (1 – i)8
15) Find the modulus & argument ofii3 23 2-16)Express (1 i)2
17) Using exponential form of sin- & cos- , prove that cos3- = 4 cos3- – 3cos .
SIX marks Questions :
1) Obtain the values of sin and cos using Euler’s formula , hence prove that, cos (1 + 2) = cos1 cos2 – sin1 sin2.
2) Obtain the values of sin and cos using Euler’s formula , hence prove that, sin (1 + 2) = sin1 cos2 + cos1 sin2.
3) State Euler’s formula. Use it to obtain the trigonometric functions cos, sin, tan and cot.
4) State De Moivre’s theorem.Explain the exponential form for powers and roots of a complex number.
5) What is an Argand Diagram? Explain multiplication and division of two complex numbers using an Argand Diagram.
6) Find the different values of the fifth root of 1 + i 3 .
CHAPTER 2 :
Partial Differentiation
TWO marks Questions
1) Define Partial Differentiation
2) Define total differential when a Physical quantity is function of only one variable.
3) What is the formula for total differential dF, if F=F(x, y)?.
4) If F(x,y) = esinx. tan xy ; Find Fx for x = p/4 & y = 1.
5) State the equation of represent the chain rule for obtaining differentiation of function
6) What is an implicit function?
7) State the relations between Cartesian and Polar co-ordinates.
Pattern of Question Paper
Note: Attempt ALL Questions.
Q. 1 Objective type (Answer four out of six) 8
Q. 2 Short answer type (Answer two out of three) 8
Q. 3 a) Short answer type (Answer two out of three) 6
b) Compulsory (two marks question) 2
Q. 4 Short answer type (Answer two out of three) 8
Q. 5 a) Long answer type 6
OR
a) Long answer type 6
b) Compulsory (two marks question) 2
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