Answer
a) No.
b) $ 1.3967\times 10^{-22}\;\rm kg.m/s$
c) The proton's direction.
Work Step by Step
a) To see whether the momentum in the decaying of the neutron is conserved or not, we need to find the final momentum of the two daughter subatomic particles.
We know that the momentum of the neutron just before the decay is zero since it was at rest.
$$p_{ix}=0$$
And we know that the final momentum is given by
$$p_{fx}=m_pv_{xp}+m_ev_{xe}$$
Noting that the electron and the proton are fired in opposite directions.
Thus, the velocity of one of them had to have a negative sign. Let's assume that the proton is fired in the positive direction and the electron is in the negative direction.
Plugging the known;
$$p_{fx}=(1.67\times 10^{-27}\times 1\times 10^5)+(9.11\times 10^{-31}\times- 3\times 10^7)$$
$$p_{fx}=\bf 1.3967\times 10^{-22}\;\rm kg.m/s$$
It is obvious now that the momentum is not conserved.
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c) if there is a neutrino ejected with the proton and the electron from the neutron decay, as the experiments approved, then its momentum will be equal to the final momentum we found above.
$$p_{\nu}=\bf \color{red}{\bf 1.3967\times 10^{-22}}\;\rm kg.m/s$$
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b) And since the amount of momentum carried by the momentum is positive, as we see above, it must be in the positive direction which is the same direction as the proton.
