LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – PHYSICS

FIRST SEMESTER – NOVEMBER 2012

MT 1100 – MATHEMATICS FOR PHYSICS

 

 

Date : 03/11/2012             Dept. No.                                        Max. : 100 Marks

Time : 1:00 – 4:00

 

 

SECTION A

ANSWER ALL THE QUESTIONS:                                                                                         (10×2 =20)

 

• Find the n^th derivative of.
• Write down the formula for subtangent and subnormal.
• Prove that .
• Find the rank of the matrix.
• Show that .
• State the formula for Laplace transformation of a periodic function.
• Write down the expansion for.
• If Show that
• What is the chance that a leap year selected at random will contain 53 Sundays?
• Define Binomial distribution.

 

SECTION B

ANSWER ANY FIVE QUESTONS:                                                                               (5×8 =40)

 

• Find the angle of intersection of cardioidsand.
• Find the minimum and maximum value of the function.
• Find the sum to infinity series.
• Show that the system of equations

 

are consistent and solve them.

• Find the L(f(t)) if
• Find a)   b) .
• Prove that cos8θ = 1- 32sin² θ + 160sin⁴ θ-256sin⁶ θ+128 sin⁸ θ.
• Find the moment generating function for the Poisson distribution and hence find its

mean and variance.

 

SECTION C

ANSWER ANY TWO QUESTIONS:                                                                                  (2×20 = 40)

• a) If then Prove that. b) Find the n^th derivative of. (10+10)
• If then

1. a) Find the characteristic value and characteristic vector of the matrix.
2. b) Verify Cayley Hamilton Theorem and find A^-1. (10+10)

• a) Express cos⁵θ sin³θ in terms of sines of multiples of θ.

1. b) Separate into real and imaginary parts of tan^-1(α+iβ). (10+10)

• a) Solve with using Laplace transform.

1. b) An urn contains 6 white, 4 red and 9 black balls. If 3 balls are drawn at random, find the probability that: (i) two of the ball drawn is white; (ii) one is of each colour,

(iii) none is red.

(14+6)

 

 

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