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.

If hat a , hat b ,a n d hat c are three unit vectors inclined to each other at angle theta, then the maximum value of theta is pi/3 b. pi/4 c. (2pi)/3 d. (5pi)/6

The plane denoted by pi_(1) : 4x+7y+4z+81=0 is rotated through a right angle about its line of intersection with the plane pi_(2) : 5x+3y+ 10 z = 25 . If the plane in its new position is denoted by pi , and the distance of this plane from the origin is sqrtk , where k in N , then k=

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

Two fixed, equal, positive charges, each of magnitude 5xx10^-5 coul are located at points A and B separated by a distance of 6m. An equal and opposite charge moves towards them along the line COD, the perpendicular bisector of the line AB. The moving charge, when it reaches the point C at a distance of 4m from O, has a kinetic energy of 4 joules. Calculate the distance of the farthest point D which the negative charge will reach before returning towards C.

A conducting sphere A of radius a , with charge Q , is placed concentrically inside a conducting shell B of radius b . B is earthed. C is the common center of A and B . Study the following statements. (i) The potential at a distance r from C , where a le r le b, is (1)/(4 pi epsilon_0)(q/( r)) (ii) The potential difference between A and B is (1)/(4 pi epsilon_0) Q ((1)/( r) - (1)/B) (iii) The potential at a distance r from C , where a le r le b, is (1)/(4 pi epsilon_0) Q ((1)/r - (1)/B) Which of the following statements are correct ? .

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.

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.

At time t second, a particle of mass 3 kg has position vector r metre, where r = 3that(i) - 4 cos t hat(j) . Find the impulse of the force during the time interval 0 le t le(pi)/(2)

At time t second, a particle of mass 3 kg has position vector r metre, where r = 3that(i) - 4 cos t hat(j) . Find the impulse of the force during the time interval 0 le t le(pi)/(2)

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. Statement 1: sin(pi/18) is a root of 8x^3-6x+1=0 Statement 2: For any theta in R ,sin3theta=3sintheta-4sin^3theta