Posted Date: 07 Aug 2008      Posted By:: tamil    Member Level: Gold  Points: 5 (Rs. 1)

2006 Bangalore University B.Sc Mathematics MATHEMATICS Question paper

 Course: B.Sc Mathematics University/board: Bangalore University

I Sem B.SC Examination, Mar/Apr 2006
(Y2K7 scheme)(2007-08 and onwards)
MATHEMATICS
Time:3 hrs
Max marks:80
SECTION-A
1)Define symmetric and skew symmetric matrix and give an example for each
2) Find the chararcteristic roots of the matrix
1 4
3 2
3)State the necessary and sufficient condition for a non empty subset of group G
To be a subgroup of G
4)Find the cross product of vector a=2i+3j-2k and vector b=12i-4j+8k are
Orthogonal
5)Find the cross product of vector a=2i+3j+4k and vector b=i-k
6)The centroid of a triangle is(4,-1,1).If two of the vctorices are(4,-2,7) and
(5,-4,1) find the third vertex.
7)Find the direction cosine of a line equally inclined with the co-ordinate axes
8)Find the centre and the radius of the sphere 4x2+4y2+4z2-16x-24y+16=0
9)Find the second derivative of log(sin x) w.r.t. x
10)Find the nth derivative of y=sin3x
11 if z=xy find delta z/delt x,delta z/delta y
12)Evaluate
Integration cos tita/root of 4-sin2 tita dtita
With lower limit 0 and higher limit pie/2
13)Evaluate
Integration of 1/2x2+x-3 dx
12)Solve dy/dx=ex+y
15)Solve dy/dx +(cot x)y=1

SECTION-B

1)solve the following system of equation by matrix method:
2x+3y=8,2y-z=1,2x+3z=11
2)Verify Cayley Hemilton theorem for the
Matrix a= [3 2 an hence find A-1
-1 4]
3)Find a matrix P such that P-1AP is a diagonal matrix where A=[3 4
-2 -3]
III Answe any two questions(2*5=10)
1)Write the multiplication modulo 6 table for the set G={1,2,3,4,5} is(G,X6) a
Group?Give reason
2)Show that the set of all fourth root of unity form a group under usual
Multiplication
3)Find the area of the parallelogram whose diagonals are 3i-2j-k and -4i+2j+k
4)Prove that[vectora*b;vectorb*c;vectorc*a]=[vectora,vectorb,vectorc]2
1)Find the angle between the diagonals of a cube
2)Find the equation of the plane passing through the point (-2,4,0)(-3,2,-9)
And parallel to the line whose direction ratio are 3,-2,3
3)Derive the equation of a sphere wi9th a centre (x1,y1,z1) and radius R
4)Find the equation of the right circular cone whose vertex is(2,3,4) axis
Makes equal angles with the coordinatues axes and semivertical angle is 300

1)Find the nth drivative of cos4x
2) If y=sin-1x ,show that
(1-x2)yn+2-(2n+1)xyn+1-n2yn=0
3) If u=log(x4+y4/x-y), show that x *delta u/delta x +y*delta u/delta y=3
4)Evaluate the integration of(x-1)/(x-2)(x-3)dx
5) Evaluate the integration of 1/(3-cos x) dx
6)Evaluate the integration of x *sin3x*cos x dx
7) Evaluate the integration sec4tita d tita with upper limits pie/4 and lower limits 0

VI Answe any two (2*5=10
1)Solve y dy/dx=ex+y
2)Solve dy/dx=x2+y2/xy
3)Verify the exactness and solve the equation
(5x4+3x2y2-2xy3)dx+(2x3y-3x2y2-5y4)dy=0
4)Solve cos2x dy/dx +y=tan x

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