Write a note on ‘Socio Economic Factors’.

Write a note on the Consumer Manifesto

Write a note on ‘Social Environmen

. Define ‘who is a Consumer

Discuss the ‘use of Advertising and Unfair Trade Practices for promotion of Consumerism’

Write a note on ‘Public Policy and Social Accountability’.

. Write a note on “Consumer Education in India’.

Discuss the ‘Key definitions of concepts in the Consumer Protection Act, 1986’

Discuss the role of ‘Consumer Movement in Europe’.

Discuss the role of ‘Consumer in Market Economy’

Discuss in detail the role and functions of “Mass Media”

Discuss in detail the Meaning, Scope and Importance of the six Rights in the Consumer Protection Act.

. Discuss in detail the ‘Consumer Movement’ in the Modern Period.

Discuss in detail the ‘nature and reasons for attitudinal changes among people’

The joint probability mass function of X and Y , p ( x , y ) , is given by

p(1,1) = 1/4 , p(2,1) = 1/4 , p(3,1) = 1/16 ,

p(1,2) = 1/16 ,p(2,2) = 0 , p(3,2) = 1/16 ,

p(1,3) = 0 , p(2,3)=1/16, p(3,3)=1/4

i) Compute for for i =1,2,3

ii) Find P[x/y=1]

iii) Marginal distributions of X and Y.

a) Suppose the events of a Poisson-process { N (t )} are classified as belonging to categ with probabilities independently of N(t).be the number of events of category  during ( 0 , t ] . Show that

i) { N (t )} i is a Poisson process with rate  p , (i 1, 2 ,......, k ).

ii) are mutuallyin dependent.

(Hint: For given

b) A machine component is found to have life-time distribution with probability density function

Show that the renewal function is given by

if the process starts with a new component.

(a) Suppose the joint density function of X and Y is given by

(b) Let X^, =[ X₁,X₂]be a random vector with mean vector and variance-covariance matrix = [,] and variance-covariance matrix

or

in terms of and .

a) Find the equation of the right circular cone whose vertex is (1,−1,2), the axis is

and the semi-vertical angle is 45^{◦ .}

b) Prove that the path traced by the foot of the perpendicular from the focus of a parabola on any tangent to the parabola is the tangent at its vertex.

c) Let S ≡ 4x² −9y² −36 = 0 and S^, ≡ y 2 −4x = 0 be two conics. Under what conditions on k, will the conic S+kS^,= 0 represent:

i) an ellipse?

ii) a hyperbola?

d) Find the section of the conicoid  by the plane x−2y+z = 1. What conic does this section represent? Justify your answer.

a) Show that the angle between the two lines in which the plane x−y+2z = 0 intersects the cone x² +y² −4z² +6yz = 0 is .

b) Show that if ux+vy+wz = p is a tangent plane to the paraboloid ax² +by² = 2z, then

c) Prove that the planes 7x+4y−4z+30 = 0,36x−51y+12z+17 = 0,14x+8y−8z−12 = 0 and 12x−17y+4z−3 = 0 form the four faces of a cuboid.

a) Find the equation of the normal of the paraboloid 3x² +4z² +4y = 0 at the point (2,−4,1). Also find the point where this line again intersects the paraboloid.

b) Let R be the point which divides the line segment joining P(2,1,0) and Q(−1,3,4) into the ratio 1 : 2 such that PR < PQ. Find the equation of the line passing through R and parallel to the line

c) Find the equation of the line which passes through the point () and makes an angle of 30^◦ with the line

d) Find the vertices, eccentricity, foci and asymptotes of the hyperbola  Also trace it. Under what conditions on  the line x+y = 2 will be tangent to this hyperbola? Explain geometrically.