how many perfect cubes are there in the sequence 1^1,2^2,3^3,4^4........100^100 2)the value of n for which 2^200-2^192*31+2^2n 3)if the product of three digit numbers 2a5 and 13b is divisible by 36 where a and b are integers between 0and9 inclusive,then maximum possible value of (a+b) is ? 4)the number of positive divisor which divides 10^999 but not 10^998 are?

Asked by  | 29th May, 2012, 03:12: PM

Expert Answer:

(1) 13, 23, 33, 34, ... , 3100.
Powers are: 1, 2, 3, 4, ... , 100.
 
Multiple of 3 are: 3, 6, 9, ..., 99
 
Here, a = 3 and d = 3
 
Now, a + (n-1)d = 99
Or, 3 + (n-1)3 = 99
Or, 3(n-1) = 96
Or, n-1 = 32
Or, n = 33
Thus there are 33 perfect cube numbers.


Answered by  | 29th May, 2012, 05:06: PM

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