10^21 here we have two option

1. 1+1 = 2

2. 2+0 =2

Now for the first option ,

10^21 can be written as = 1,000,000,000,000,000,000,000 i.e 21 zero's

Here we have to fill two places with 1 out of 21 places i.e 11,1001,100001 ....(since the number has to be less than 10^21)

so we can use the combination formula as 21C2 as we are choosing two places from the 21 places of zero's
=210 ways.

Now for the option 2, choosing 2
we have 21 ways i.e 02,020,200,2000 ....(i.e we can fill up the 21 zero's places with 2,as the number has to be less than 10^21)

Therefore total no of ways =210+21=231 ways.