Elitmus
Exam
Logical Reasoning
Number Series
plz correct answer he btana ...
find the last two digits of the following expression
(1122)^(1122!)
Read Solution (Total 14)
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- (1122)^(1122!)=(11)^(1122!)*(102)^(1122!)
1122!= will have a even number and zeroes for example:2536200000000
(11)^(1122!)----will have last two digits as 01
because it repeats itself every power of 10 like 11^10,11^20
and so on......last two digits for all these are 01
(102)^(1122!)---will have last two digits as 76
bez it repeats every power of 20 like 102^20,102^40
and so on ...has last two digits for all these are 76
so 01*76=76
so Last two digits of the expression is 76 - 10 years agoHelpfull: Yes(16) No(0)
- exlain to krdo
- 10 years agoHelpfull: Yes(6) No(1)
- 1122!=*****00
So last digit is 2^4=*6(As remainder of the value divided by 4 is 0)
And Last 2nd Digit is 2*0(As last digit is 0)
last 2 digit is 06
- 10 years agoHelpfull: Yes(4) No(4)
- answer is 76
- 10 years agoHelpfull: Yes(2) No(0)
- 1122! is 10*even no from
so (2^10) ^even always give last digit as 76 - 10 years agoHelpfull: Yes(2) No(2)
- Ans. iz 56
- 9 years agoHelpfull: Yes(2) No(1)
- when result of 28 sep kolkata test ll be declared, any idea guys??????
- 10 years agoHelpfull: Yes(1) No(3)
- answer is 76
- 10 years agoHelpfull: Yes(0) No(1)
- 1122!= will have a even number and zeroes for example:2536200000000...explain it @Ram or anyone else
- 8 years agoHelpfull: Yes(0) No(0)
- (1122)^(1122!)
we can split 1122! in term of 4x+c
there for
1122!=4x+2
1122^2= 125884
so the last 2 digit of the number =84 - 8 years agoHelpfull: Yes(0) No(0)
- correct ans is 84 . go for it :D
- 8 years agoHelpfull: Yes(0) No(0)
- 1122/100 = 22 ^1122/100
Now R1= 2^1122! /100
R2= 11^1122! / 100
1122! have many zeros in last … as w.k.t after 5! There may have one single zero
So( 2^10)^even no / 100 = 76
e.g 2^10=1024
(1024)^2 mod 100 = 76
(1024)^4 mod 100 = (24)^4 mod 100= 76
(1024)^6 mod 100 =(24)^6 mod 100 =76
so (2^10)^even always gives 76
now 11^1122! /100
see 11^2 = 121
11^3 = __ 31 ( last two digit)
11^4 = … 41
Similarly 11^10 = 01 (last two digit )
Now (11^10) ^even num / 100
= 01 as last two digit
So last two digit = R1*R2 = 76*1 = 76 - 7 years agoHelpfull: Yes(0) No(0)
- We know the last two digits can only result in a number lower than 100,
we know multiplication between two large numbers is basically an accumulation of simple multiplications.
In this case we have (1000+100+20+2)*(1000+100+20+2),
since we can only allow numbers smaller than 100 we can drop 1000 and 100.
We get (20+2)*(20+2) which results in 400+40+40+4,
400 is greater than 100,
so 40+40+4=84.
84 are the last two digits. - 7 years agoHelpfull: Yes(0) No(0)
- 1122*1121*1120!=last digit is 0
and when it is expanded to 1100!,ssecond last digit is also 0.
so answer is 00. - 7 years agoHelpfull: Yes(0) No(1)
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