If ln 2 then the value of the definite integral equals

Let the unit vectors  and  be perpendicular and the unit vector  be inclined at an angle θ to both  and  If  then

We should know how to take dot product of two vectors.

A random variable X has the probability distribution

For the events is prime number} and , the probability of is

Three long, straight and parallel wires carrying currents are arranged as shown in the figure. The wire C which carries a current of 5.0 amp is so placed that it experiences no force. The distance of wire C from wire D is then

A 100 turns coil shown in figure carries a current of 2 amp in a magnetic field . The torque acting on the coil is

Three long, straight and parallel wires carrying currents are arranged as shown in figure. The force experienced by 10 cm length of wire Q is

Four wires each of length 2.0 metres are bent into four loops P, Q, R and S and then suspended into uniform magnetic field. Same current is passed in each loop. Which statement is correct

A rectangular loop carrying a current i is situated near a long straight wire such that the wire is parallel to the one of the sides of the loop and is in the plane of the loop. If a steady current I is established in wire as shown in figure, the loop will

A very long straight wire carries a current . At the instant when a charge at point has velocity , as shown, the force on the charge is

In the given figure, the electron enters into the magnetic field. It deflects in .. direction

An electron (mass = 9× 10^–31kg. Charge = 1.6 × 10^–19C) whose kinetic energy is 7.2 × 10^–18 joule is moving in a circular orbit in a magnetic field of 9 × 10^–5 weber/m². The radius of the orbit is

Two particles A and B of masses and respectively and having the same charge are moving in a plane. A uniform magnetic field exists perpendicular to this plane. The speeds of the particles are  and respectively, and the trajectories are as shown in the figure. Then

In the figure, what is the magnetic field at the point O

A coil having N turns carry a current I as shown in the figure. The magnetic field intensity at point P is

A current of 10A is passing through a long wire which has semicircular loop of the radius 20cm as shown in the figure. Magnetic field produced at the centre of the loop is

A part of a long wire carrying a current i is bent into a circle of radius r as shown in figure. The net magnetic field at the centre O of the circular loop is