In some old texts it is mentioned that `4pi` lines of force
. orginate form each unit positive charge. Comement on
. the statement in view of the fact that `4pi` is not an
. interger.

Each question has four choices, a,b,c and d,out of which only one is correct. Each question contains STATEMENT 1 and STATEMENT 2. if both the statements are true and statement 2 is the correct explanation of statement 1. If both the statements are true but statement 2 is not the correct explanation of statement 1. If statement is True and statement2 is false. If statement1 is false and statement2 is true. Statement 1: If x in [1,sqrt(3)], then the range of f(x)=tan^(-1)x is [pi/4,pi/3] Statement 2 : If x in [a , b], then the range of f(x)i s[f(a),f(b)]dot

The point (4, 1) undergoes the following three transformations successively: (a) Reflection about the line y = x (b) Translation through a distance 2 units along the positive direction of the x-axis. (c) Rotation through an angle pi/4 about the origin in the anti clockwise direction. The final position of the point is given by the co-ordinates.

Each question has four choices a,b,c and d out of which only one is correct. Each question contains Statement 1 and Statement 2. Make your answer as: If both the statements are true and Statement 2 is the correct explanation of statement 1. If both the statements are True but Statement 2 is not the correct explanation of Statement 1. If Statement 1 is True and Statement 2 is False. If Statement 1 is False and Statement 2 is True. If A+B+C=pi, then Statement 1: cos^2A+cos^2B+cos^2C has its minimum value 3/4dot Statement 2: Maximum value of cosAcosBcosC is 1/8

Two large conducting spheres carrying charges Q_1, and Q_2, are brought close to each other. Is the magnitude of electrostatic force between theme exactly given by (Q_1Q_2)/(4pi epsi_(0) r^(2)) , where r is the distance between their centres? b. If Coulomb's law involved 1/r^(3) dependence ("instead of "1/r^2), would Gauss law be still true? c. A small test charge is released at rest at a point in an electrostatic field configuration. Will it travel along the field line passing through that point? d. What is the work done by the field of a nucleus in a complete circular orbit of the electron? What if the orbit is elliptical? e. We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there? f. What meaning would you give to the capacitance of a single conductor? g. Guess a possible reason why water has a much greater dielectric constant (=80) than say, mica (= 6).

If a line makes an angle of pi/4 with the positive direction of each of x-axis and y-axis, then the angel that the line makes with the positive direction of the z-axis is a. pi/3 b. pi/4 c. pi/2 d. pi/6

Each side of a square has length 4 units and its center is at (3,4). If one of the diagonals is parallel to the line y=x , then anser the following questions. The radius of the circle inscribed in the triangle formed by any three vertices is

Consider a curve C : y=cos^(-1)(2x-1) and a straight line L :2p x-4y+2pi-p=0. Statement 1: The set of values of p for which the line L intersects the curve at three distinct points is [-2pi,-4]dot Statement 2: The line L is always passing through point of inflection of the curve Cdot

Each side of a square has length 4 units and its center is at (3,4). If one of the diagonals is parallel to the line y=x , then anser the following questions. ,brgt The radius of the circle inscribed in the triangle formed by any two vertices of the square and the center is

The lines 2x + 3y + 1 = 0 and 3x - y - 4 = 0 lie along the diameters of a circle of circumference 10 pi unit then the equation of the circle is

Consider two straight lines, each of which is tangent to both the circle x^2+y^2=1/2 and the parabola y^2=4x . Let these lines intersect at the point Q . Consider the ellipse whose center is at the origin O(0,\ 0) and whose semi-major axis is O Q . If the length of the minor axis of this ellipse is sqrt(2) , then which of the following statement(s) is (are) TRUE? For the ellipse, the eccentricity is 1/(sqrt(2)) and the length of the latus rectum is 1 (b) For the ellipse, the eccentricity is 1/2 and the length of the latus rectum is 1/2 (c) The area of the region bounded by the ellipse between the lines x=1/(sqrt(2)) and x=1 is 1/(4sqrt(2))(pi-2) (d) The area of the region bounded by the ellipse between the lines x=1/(sqrt(2)) and x=1 is 1/(16)(pi-2)