Nalanda Open University 2009 B.Sc Mathematics Bachelor of Science Hons., Part-II Final , (Subsidiary), -II (Integral Calculus, Differential Equations, Co-ordinate Geometry, Linear Programming) 2nd P
Bachelor of Science Hons., Part-II Final Examination, 2009 Mathematics (Subsidiary), Paper-II (Integral Calculus, Differential Equations, Co-ordinate Geometry, Linear Programming) second Part
10 .(a) Prove that a hyperplane is a convex set..
(b) Solve graphically the following LPP Max'Z-SSxj+lSx
..je,
subject to constraints
f.l. l Solve the question 10(b) by the Simplex method.
Group-C
1-2 Xa) A bullet of mass m moving with velocity us trikes ablockofmass M which is free to move
M-
in the direction of motionof the bullet and is embedded into it. Showthat a portion-
r - m + M;
;oFK.E' is'fost.
(b)'Ob tain the resultant of2SHM's of the same period andinth same straight line.
13 .(a) Show that the energy of a stretched elastic string is equal to half the product of the tension and the extension.
!
(b) A particle with mass m is acted by a force L towards the origin where ft and a
are constants and x is the distance of the particle from the origin. Findthe time taken by the particle to arrive at the origin.
14. (a) Ob tain e xp re ss io ns for radial and transverse ac clerat io ns o f a part ic le moving on a p lane cuive.
(ft). The velocities of a particle along and perpendicular to a radius vector from a fixed origin sr.fc.-vflr.and /-.-Find the equation of thepath.j l,(a3 Obtain the equation of the line of act ion of the resultant of a system of coplanar forces ac ting o n a rigid b ody.
.(b) Forces P, Q and R act along the sides of the traingle formed by the lines x=0, y=0 and xCos#+ySin#=p respectively. Find the magnitude oft he resultant and its line of actiorL 16 .(a) State and prove the converse of the principle of virtual work.'
(b) Two equal uniform rods AB and AC each of length 2b are freely jointed at A and rests on a smooth verticle circle of radius a. If 2 $ be the angle between them then prove that
. bSin'd = aCosd '
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| Earning: Approval pending. |
