Problem $8.$ As Time$-$To$-$Maturity comes to $0,$ Gamma of European options will:

a$.$ be infinity for at the money options

b$.$ go to infinity for at the money puts, but will be close to $0$ for at the money calls

c$.$ go to infinity for $10\%$ out of the money options

d$.$ be infinity for in the money puts

Please explain your answer.

Problem $9.$ When close to maturity, the Vega:

a$.$ will tend to be close to zero

b$.$ will increase tremendously

c$.$ will increase extremely for out of the money options

Please explain your answer.