A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of the magnetic field is -

Magnetic field inside a long solenoid: $B = \mu_0 n i$, where n is the number of turns per unit length.
New values: $n' = \dfrac{n}{2}$, $i' = 2i$
$B' = \mu_0 n' i' = \mu_0 \cdot \dfrac{n}{2} \cdot 2i = \mu_0 n i = B$
So the magnetic field remains B.