- Complete the series given below:
149, 162536, 496481, 100121144,?
a)16819225
b)169196200
c)144289324
d)169169225
e)169196225
Explanation
SOLUTION[ E ]
Question-2
How many 3-digit positive integers, with digits a, b and c exist such that a < band c<b?
Assume that a is in hundred’s place, b is in ten’s place, c is in unit’s place and that a is a non-zero digit.
a)240
b)256
c)648
d)302
e)364
Explanation
SOLUTION[ A ]-240
b = 2 a = 1 c = 0 or 1; Total possible numbers = 1 ^ * 2 b = 2 a = 1 or 2; c = 0 1 or 2; Total possible numbers = 2 ^ * 3
b = 8 a = 1 ,2….., 7; c = 0 ,1…………,7 Total possible numbers = 7 ^ * 8 b = 9 a = 1 ,2……,8; 8; c = 0 ,1………….,8; Total possible numbers = 8 ^ * 9
Total possible numbers= ( 1 ^ * 2)+(2^ * 3)+……+(7^ * 8)+(8^ * 9)
Sigma*n(n + 1) = Sigma(n ^ 2 + n) = (n(n + 1)(2n + 1))/6 + (n(n + 1))/2
Put n = 8 we get ( 1 ^ * 2)+(2^ * 3)+……+(7^ * 8)+(8^ * 9)=240
Question-3
Determine the total whole numbers that lie between 100 and 800 which contain the digit 2:
a)232
b)240
c)224
d)230
e)214
Explanation
SOLUTION[E]-214
had a very strange doubt in this question while I was solving it. Now in order to solve first I calculated the three digit numbers which won’t have 2 at all in them and the number of such three digit numbers between 100 and 800 will be 6×9×9= 486.
Now as per the question we do no have to include 100 and 800 while counting so the total number of numbers between 100 and 800 will be 699 and hence the number of whole numbers which will have 2 in it should be 699486 = 213.
But let’s say you have included 100 and 800 too then this will give the total number of numbers between 100 and 800 (both inclusive) will be 701 and hence the number of whole numbers which will have 2 in it should be 701-486= 215.
And when you include only 100 or 800 any one of them then the total number of numbers between 100 and 800 (any one of them is inclusive) will be 700 and hence the number of whole numbers which will have 2 in it should be 700-486 = 214
Question-4
What will be the last two digits of the number 745?
a)45
b)35
c)07
d)49
e)21
Explanation
SOLUTION-[C] -07
Question-5
Find how many times in the given series, a number is preceded by an even number but not followed by 0 or a multiple of 3? 759461803967389201393043912
a)5
b)7
c)4
d)3
e)6
Explanation
SOLUTION[C] – 4
