State the condition under which `V(X+ Y) = V(X) + V(Y)`?

Mention the condition under which the lines ( x - x _(1))/( l _(1)) = ( y - y _(1))/( m _(1)) = ( z - z _(1))/( n _(1)) and ( x - x _(2))/( l _(2)) = ( y-y _(2))/( m _(2)) = ( z - z _(2))/( n _(2)) will be perpendicular to each other.

What are the conditions under which a body can stay in a state of rest.

State the condition under which a microwave oven heats up food item containing water molecules most efficiently.

Answer as directed: if X and Y are two random variables, under what condition E(XY) = E(X).E(Y) ?

Under what condition the points (3, - 4) and (-5, 2) are equidistant from the point (x, y).

Write down the condition that the vectors u_(1) hati +u_(2) hatj +u_(3) hatk, v_(1) hati +v_(2) hatj + v_(3) hatk and w_(1) hati + w_(2) hatj + w_(3) hatk are coplanar .

Write negation of the following statements consisting of quantifiers: (v) There exists a capital for every state in India.

Which of the two is paramagnetic V(IV) and V(V) and why?

Find the second dirivative of : (v) e^x sin x