A wire whose cross-sectional area is increasing linearly from its one end to the other, is connected across a battery of V volts.
Which of the following quantities remain constant in the wire?
(a) drift speed
(b) current density
(c) electric current
(d) electric field

The electric current will remain constant in a wire whose cross-sectional area is increased linearly from its one end to the other, is connected across a battery of V volts.

Because current is the only quantity that does not depend on the area of cross- sections of the wire.
I=dq/dt, that is the rate of flow of charge, where as drift speed, current density and electric field depending on the increasing area of the cross-section of the following relations:

Drift speed: ν_d=I/An_e
Current density = I/A
Electric field = J/σ