In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49, and the sum of the first and third terms is 35, then the first term of this geometric progression is

Statements-1: = (2n + (a) cost (0 t)
Statements-2:
and if f(a + x) = f(x)

If x enotes the rounded off value of x  and the area bounded by the two curves defined by y =  and . In the interval 0 x 1 is equal to 2 square units, The value of the constant is

Statement-1: then
Statement-2 : is the reflection of

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