Physics, Chemistry, Mathematics Forums

1.Is the induced electric field conservative or non conservative?
2.Are the lines of force of induced electric field open or closed?
I am really confused about this.Please help me out.

A variable line is drawn through the point (2,1). Perpendiculars are drawn to it from the points (a₁,4), (a₂,5),(a₃,-3) and (2,b₁),(3,b₂),(7,b₃) such that their sum is zero. If all the a_i and b_i are non-negative real numbers determine their values.


Please reply with explanation..

the number of functions f from the set A = (0,1,2) in to the set B = (0,1,2,3,4,5,6,7) such that f(i)is less than or equal to f(j) and i,j~~A is.........

Three infinitely long linear charges of charge density: lamda, lamda, and -2lamda; are placed in space. A point in space is specified by its perpendicular distance r1,r2,r3 respectively from the linear charges. prove that for the points which are equipotential.
r1*r2/r3^2 = constant

Solve the following differential equation:

(1-x^2)dy/dx - xy=x^2
This is a standard linear differential equation.Please solve it without directly using the formula ,instead solve it by the basic approach that is multiplying the 'Integrating factor' on both the sides. I am unable to do it this way.

The algebraic sum of the perpendicular distances from A(a₁,b₁), B(a₂,b₂) and C(a₃,b₃) to a variable line is zero, then the line passes through
(a) the orthocentre of ΔABC
(b) the centroid of ΔABC
(c) the circumcentre of ΔABC
(d) none of these

Let P(x1,y1) Q(x2,y2), y1,0 and y2,0 be the end points of the latusrectum of the ellipse x^2 + y^2=4 ;Then find. the equation of the parabola with latusrectum PQ

 If theta 1 and theta 2 be the angles which the lines (x^2+y^2)(cos^2 theta sin^alpha+ sin^2 theta)= (x tan theta - y sin theta)^2 make  with the x axis and theta = pi/6 , then what is the value of (tan theta1+ tan theta2) ?

The answer I have is (-8/3 cosec 2 alpha)

The number of irrational terms in the expansion of [5^(1/6) + 2^(1/8)]^100 is

A) 96          B)97         C)98            D)99

The answer I have is 97

1) An ideal gas is taken through a process such that when the volume is halved the temperaure gets doubled .Prove that change in entropy is given by Cp *ln2.

2) When an egg is boiled the yolk and the albumin get solidified; so shouldn't the entropy decrease? But it increases. How?

3) Work done in a reversible process is slightly more than work done in an irriversible process. Why?