$[15$ marks$]$ A frequency modulated signal with carrier frequency $=$

$10$ is given by

$()=10$ cos$[2+10$ sin $2000].$

a$)$ Calculate the power of the modulated signal. $(3$ marks$)$

b$)$ Find the modulation index $.(4$ marks$)$

c$)$ Find the maximum frequency deviation $.(4$ marks$)$

d$)$ Estimate the bandwidth of the FM signal. $(4$ marks$)$