Annamalai University 2010-1st Year B.Sc Physics , ( APPLIED CHEMISTRY / ELECTRONIC SCIENCE / ) ( ) ( PART - III - B - ANCILLARY ) ( - I ) 550MATHEMATICS - I ( Including Lateral Entry ) - Question

B.Sc. DEGREE EXAMINATION, 2010
( APPLIED CHEMISTRY / ELECTRONIC SCIENCE /
PHYSICS )
( 1st YEAR )
( PART - III - B - ANCILLARY )
( PAPER - I )
550. MATHEMATICS - I
( Including Lateral Entry )

(b) Prove that

4

1 + tan hx

- = cos hx + sin h 2x.

1 - tan hx

8.    (a) Prove that

u = log I + Jl] iff cos hu = sec 9 ^e I 4 2)

(b) If

i^{x + iy} = A + iB, show that

A² + B² = e^{-(4n+ 1)7ly}.

9.    (a) Find the equation of the plane containing

the point (-1, 7, 2) and the line

x + 3 _y ⁺ 2 _z-2

2 ~ 3 -2 '

(b) Find the equation of the sphere passing through the points (0, 0, 0), (1, 0, 0), (0, 1, 0) and (0, 0, 1)

10.    Find the shortest distance between the lines

x-1 _y^-2 _z-3

2    3    4

x-2 _ Y - 3 z-4

3    4    5

Name of the Candidate :

12 16 B.Sc. DEGREE EXAMINATION, 2010

(APPLIED CHEMISTRY/ELECTRONIC SCIENCE/ PHYSICS)

(FIRST YEAR)

(PART - III - B - ANCILLARY)

(PAPER -1)

550. MATHEMATICS - I

(Including Lateral Entry )

May ]    [ Time : 3 Hours

Maximum : 75 Marks

Answer any FIVE questions.

All questions carry equal marks.

(5x15 = 75)

1. (a) Sum the series to infinity

1-2 2-3 3-4

- + - + - +

3 ! 4 ! 5 !

CO

2 (ⁿ~ !) _xⁿ _n = I (n + 2) n !

2.    (a) Prove that a subgroup of a cyclic group

is cyclic.

(b)    Let H be a subgroup of index 2 in a group G. Show that H is a normal subgroup of G.

2

(c)    Let G be a group such that a = e for all a g G. Then prove that G is abelian.

3.    (a) If

_{y = g}a sin^-1 (x)

prove that

(l-x²)y_{n + 2} (2n+ l)xy_n+1

- (n² + a²) y_n=0.

(b) Find the radius of curvature of the curve r² = a² sin 29.

4.    (a) Find the rank of the matrix

1111

4 10 2

0 3 4 2

(b) Show that the non - singular matrix

-C !

satisfies the equation

A² - 2A - 51 = 0.

5.    Find the eigen values and the eigen vectors of the matrix

8

3

24

6.    Show that the equations

x + y + z = 6 x + 2y + 3z = 14

x + 4y + 7z = 30 are consistent and solve them.

7.    (a) Expand sin⁷0 in a series of sines of

multiples of 9.

Turn over

Attachment: annamalai-university-2010-b-sc-physics-16724-1.pdf

Earning:   Approval pending.