How to bell the CAT..: January 2009

Wednesday, January 28, 2009

if R(n) = 1111111.....111 (n times), then R(n) is known as repunit no. For how many 256 < n < 343, R(n) will be perfect square???

a.) 135^251

b.) 145^260

c.)165^266

how many natural nos. between 1 and 100 have exactly 4 factors??

***remainder when 141414141........1414 (404 digits) is divided by 909??
(a) 9
(b)303
(c)101
(d)505
(e) none of these

what are the last two digits of 9 raise to power 9 raise to power 9?

*** last two places of 399^43???

*** What are d last 2 digits of 36! - 24! ???

****N=21600, how many pairs (a,b) exist such that a & b are factors of N and hcf (a,b) = 45???