Bsc Nautical Model
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BNA011
B.Sc. (NAUTICAL SCIENCE ) Model Examination November, 2009
BNA-011
:
APPLIED MATHEMATICS
Time :2 hours Marks : 70 Note:
Maximum
Attempt any five questions . Use of calculator is permitted.
1. a. Find the constant λ such that the vectors a=2i-j+k, b=i+2j-3k and
c=3i+ λ j+5k are coplanar. Also find the angle between a and b b. Find the work done by a force F = 4i+2j+3k acting on a particle such
that the particle is displaced from (1,2,0) to (2,-1,3) . Also find a unit vector perpendicular to the plane of action of the force and the displacement . 2x7 = 14 2. a.
i) Find dydx if y=cos-1 1+x2 ii) If y=emcos-1x , Prove that 1-x2d2ydx2-xdydx-m2y=0
b.
i) Evaluate 15+4sinx dx ii) Find the area included between the curves y2=4ax and x2=4ay 4x3½ =14
3. a. In a spherical triangle PQR, p=73o05’ , q=90o00’ and r=79o12’.
Calculate P and Q . b. Ina spherical triangle ABC, A=60o , b=c=66o12’ . Calculate B and C .
2x7 = 14
Euto Tech Maritime Academy , Cochin
P.T.O
BNA011
4.
a. A pack of 50 tickets numbered 1 to 50 is well shuffled and then two
tickets are drawn. Find the probability that a) both the tickets drawn have prime numbers b) none of the tickets drawn has prime numbers. b. The following marks have been obtained by a class of students in statistics (out of 100) Paper I
45 55 56 58 60 65 68 70 75 80 85
Paper II
56 50 48 60 62 64 65 70 74 82 90
Find the regression line of paper II on paper I = 14
2x7
5. a. A solid of revolution is formed by rotating about x axis the area enclosed by the ordinates x=0 and x=1 and a curve through the points given by (0,1.0) , (0.25 , 0.9896 ) , (0.50 , 0.9589) , (0.75 , 0.9089) , (1.0 , 0.8415) . Calculate the volume of the solid formed using Simpson’s 1/3 rule. b. Find the vertex, focus and directrix of the parabola y2-8x-2y+17=0
2x7 = 14 6. a. Find the equation of the circle described on the line joining (2,3) and (4,5) as diameter. Also find the equations of the tangent which are perpendicular to the diameter. b. Find the volume and total surface area of the toy which is in the form
of a right circular cone surmounted on right circular cylinder of 8 cm and height 7 cm . The total height of the toy is 13 cm . 2x7 = 14
Euto Tech Maritime Academy , Cochin
BNA-
B.Sc. (NAUTICAL SCIENCE ) Model Examination November, 2009
BNA-011
:
APPLIED MATHEMATICS
Time :2 hours Marks : 70 Note:
Maximum
Attempt any five questions . Use of calculator is permitted.
1. a. Find the constant λ such that the vectors a=2i-j+k, b=i+2j-3k and
c=3i+ λ j+5k are coplanar. Also find the angle between a and b b. Find the work done by a force F = 4i+2j+3k acting on a particle such
that the particle is displaced from (1,2,0) to (2,-1,3) . Also find a unit vector perpendicular to the plane of action of the force and the displacement . 2x7 = 14 2. a.
i) Find dydx if y=cos-1 1+x2 ii) If y=emcos-1x , Prove that 1-x2d2ydx2-xdydx-m2y=0
b.
i) Evaluate 15+4sinx dx ii) Find the area included between the curves y2=4ax and x2=4ay 4x3½ =14
3. a. In a spherical triangle PQR, p=73o05’ , q=90o00’ and r=79o12’.
Calculate P and Q . b. Ina spherical triangle ABC, A=60o , b=c=66o12’ . Calculate B and C .
2x7 = 14
Euto Tech Maritime Academy , Cochin
P.T.O
BNA011
4.
a. A pack of 50 tickets numbered 1 to 50 is well shuffled and then two
tickets are drawn. Find the probability that a) both the tickets drawn have prime numbers b) none of the tickets drawn has prime numbers. b. The following marks have been obtained by a class of students in statistics (out of 100) Paper I
45 55 56 58 60 65 68 70 75 80 85
Paper II
56 50 48 60 62 64 65 70 74 82 90
Find the regression line of paper II on paper I = 14
2x7
5. a. A solid of revolution is formed by rotating about x axis the area enclosed by the ordinates x=0 and x=1 and a curve through the points given by (0,1.0) , (0.25 , 0.9896 ) , (0.50 , 0.9589) , (0.75 , 0.9089) , (1.0 , 0.8415) . Calculate the volume of the solid formed using Simpson’s 1/3 rule. b. Find the vertex, focus and directrix of the parabola y2-8x-2y+17=0
2x7 = 14 6. a. Find the equation of the circle described on the line joining (2,3) and (4,5) as diameter. Also find the equations of the tangent which are perpendicular to the diameter. b. Find the volume and total surface area of the toy which is in the form
of a right circular cone surmounted on right circular cylinder of 8 cm and height 7 cm . The total height of the toy is 13 cm . 2x7 = 14
Euto Tech Maritime Academy , Cochin
BNA-
