Given:
- A rectangular conductor PQRS, where PQ is free to move
- The conductor is kept in a magnetic field B, which is perpendicular to PQRS and lies in a single plane
- The conductor PQ has a length l and moves with a speed v

To find:
- Induced EMF in the conductor PQ

Solution:
When a conductor moves in a magnetic field, it experiences a force called the Lorentz force. This force is given by the vector cross product of the velocity of the conductor and the magnetic field. Mathematically, it can be expressed as:

F = q(v x B)

where q is the charge on the conductor, v is the velocity of the conductor, and B is the magnetic field.

In the case of a conductor carrying a current, the charge q is given by the product of the current and the time taken for the charge to move through the conductor. This product is known as the charge carrier density, and is denoted by n.

q = nAe

where A is the cross-sectional area of the conductor and e is the charge on an electron.

In this case, however, the conductor PQ is not carrying a current, but is moving through a magnetic field. The induced EMF in the conductor is therefore given by Faraday's Law, which states that the EMF induced in a conductor is proportional to the rate of change of magnetic flux through the conductor.

EMF = -d(phi)/dt

where phi is the magnetic flux through the conductor.

The magnetic flux through the conductor is given by:

phi = B.A

where A is the area of the conductor perpendicular to the magnetic field.

Since the conductor PQ is a rectangle, its area is given by:

A = l.w

where l is the length of PQ and w is the width of the conductor.

Therefore, the magnetic flux through the conductor is:

phi = B.l.w

Differentiating this expression with respect to time, we get:

d(phi)/dt = B.l(dw/dt)

Since the width of the conductor is assumed to be constant, dw/dt is zero, and we get:

d(phi)/dt = 0

Hence, the induced EMF in the conductor is:

EMF = -d(phi)/dt = 0

This implies that there is no induced EMF in the conductor PQ.

However, if we assume that the conductor PQ is not moving at a constant velocity, but is accelerating, then there will be an induced EMF in the conductor. The induced EMF can be calculated using the equation:

EMF = Blv

where B is the magnetic field, l is the length of the conductor, and v is the velocity of the conductor.

Therefore, the correct answer is option A, Blv.