Elitmus
Exam
Numerical Ability
Number System
How many three digits no. can be formed also including the condition that the no. can have at least two same digits ?
Read Solution (Total 16)
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- total 3 digit no. is-9*10*10=900
and total no. of non repeated digits are=9*9*8=648
So the total no. of repeated digits(2 & 3 repeated)=900-648=252 - 9 years agoHelpfull: Yes(51) No(8)
- 110,111,112,113,114,115,116,117,118,119 = 10 numbers
220,221,222,223,224,225,226,227,228,229= 10 numbers
.......................................................................=......9 times i.e upto 999
so we have now 90 numbers.
Also 100,101,121,122,131,133,141,144,151,155,161,166,171,177,181,188,191,199 = 18 Numbers
200,202,211,212,232,233,242,244,252,255,262,266,272,277,282,288,292,299= 18 Numbers
...............................................................................................................................= upto 9 times
so 18*9=162 Number
Now 162+90=252 Numbers - 9 years agoHelpfull: Yes(16) No(2)
- question is find the three digit no so that at least two digit is repeated
soln
total 3digit number is 900
total 3 digit number which is not repeated digit without zero 7*8*9=504
and with zero 9*8+9*8=144
900-504-144=252 - 9 years agoHelpfull: Yes(13) No(4)
- The Possible combinations are
----------------------------------------------------------------------------------------------------------
_11=8 ways 1_1=9 ways 11_=9 ways 111
_22=8 ways 2_2=9 ways 22_=9 ways 222
_33=8 ways 3_3=9 ways 33_=9 ways 333
_44=8 ways 4_4=9 ways 44_=9 ways 444
_55=8 ways 5_5=9 ways 55_=9 ways 555
_66=8 ways 6_6=9 ways 66_=9 ways 666
_77=8 ways 7_7=9 ways 77_=9 ways 777
_88=8 ways 8_8=9 ways 88_=9 ways 888
_99=8 ways 9_9=9 ways 99_=9 ways 999
_00=9 ways
TOTAL=81 + TOTAL= 81 + TOTAL= 81 + 9 = 252 ans. - 9 years agoHelpfull: Yes(11) No(3)
- Take
11__ total- 1*1*9=9
1__1 total- 1*9*1=9
__ 11 total- 8*1*1=8 (it will not be a 3-digit no if 0 is in the first position.)
so total 9+9+8=26 cases for repetition of '1' only.
Likewise there can be cases from 1 to 9.
Therefore, 26*9=234
But there can be cases with 0 also.
So 0 __ 0 , 00__ is not acceptable as they will not be a 3digit no. But __ 00 can be.So,9 more combination is occurring and so
234+9=243 - 9 years agoHelpfull: Yes(3) No(1)
- 81 for (1_ _)+81 for (1 _ 1)+81 (_ _ 1)+9 for(_ 00)=252 :)
- 9 years agoHelpfull: Yes(3) No(3)
- 810 two digit numbers can be formed.
- 9 years agoHelpfull: Yes(1) No(6)
- it says atleast 2 same digits so all 3 digits may be also same...253+9
- 9 years agoHelpfull: Yes(1) No(0)
- Guys Question was ATLEAST 2 DIGIT must be same...
=> total numbers= no. having 2 digits are same + no. having 3 digits are same
=> (9*1*1+1*1*10+1*10*1)*9
=> 29*9
=>261 - 9 years agoHelpfull: Yes(1) No(0)
- sorry the answer is 1810.
- 9 years agoHelpfull: Yes(0) No(6)
- 253 ,,,81+81+90+1
- 9 years agoHelpfull: Yes(0) No(1)
- i think the answer will be 234.
- 9 years agoHelpfull: Yes(0) No(0)
- Ans is 252.
Solution:
for 1: 110,111,112,113,114,115,116,117,118,119; 101,121,131,141,151,161,171,181,191; 211,311,411,511,611,711,811,911
total for 1: 10+9+8=27
total for 1 to 9: 27*9=243
for 0: 100,200,300,400,500,600,700,800,900(note:001,011.....009,099 not a 3 digit number)
total for 0: 9
so, total all 0 to 9:=243+9=252 - 9 years agoHelpfull: Yes(0) No(0)
- ans=891
total no of 3 digits are 900
and condition is givn that d no can hve 2 sam digit.
for getting answer we have to minus all 3 digit sam no with 900
total no of 3 sam digit no are 9
so 900-9=891 - 9 years agoHelpfull: Yes(0) No(0)
- Explanation:
Total number of 3 digit numbers = 9×10×10 = 900
Total number of numbers in which no digit repeats = 9×9×8 = 648
So the total number of numbers in which at least one digit repeats = 900 - 648 = 252
- 9 years agoHelpfull: Yes(0) No(0)
- take 2 mins time to calc. manually
100, 101,110=3
(111..... 119)=9
(121...1_1..191)=8
122...1_ _ ..199)=8
At least 2 digits repeated in between 100-199 = 3+9+8+8= 28
similarly 200 - 299 ...... 900-999 = 28x9 =252 - 9 years agoHelpfull: Yes(0) No(0)
Elitmus Other Question
If a, b and c are forming increasing terms of G.P. , r is the common ratio then find the minimum value of (c-b), given that (log a+log b+log c)/log 6 =6.Note that r can be any real no.
Oligodendrocytes are a group of highly specialised glial cells in the
central nervous system. They are responsible for the formation of
the fatrich
myelin sheath that surrounds the nerve fibres as an
insulating layer. The comparison with the coating on electricity
cables is an obvious one; however, myelin can do much more than
act as the insulating layer on electricity cables: it increases the
transmission speed of the axons and also reduces ongoing energy
consumption. The extreme importance of myelin for a functioning
nervous system is shown by the diseases that arise from a defective
insulating layer, such as multiple sclerosis
Interestingly, the function of the oligodendrocytes goes far beyond
the mere provision of myelin. KlausArmin
Nave and his team at the
Max Planck Institute in Göttingen already succeeded in
demonstrating years ago that healthy glial cells are also essential for
the longterm
function and survival of the axons themselves,
irrespective of myelination. “The way in which the oligodendrocytes
functionally support their associated axons was not clear to us up to
now,” says Nave. In a new study, the researchers were able to show
that the glial cells are involved in, among other things, the
replenishment of energy in the nerve fibres. “They could be
described as the petrol stations on the data highway of the axons,”
says Nave, explaining the results.
But how does the energy refuelling work? Is there a metabolic
connection between the oligodendrocytes and axons? To find out,
Ursula Fünfschilling generated genetically modified mice: the
function of the mitochondria was deliberately disrupted in the
oligodendrocytes through the inactivation of the Cox10 gene. This
affects the final stages of sugar breakdown taking place in the
mitochondria where energy is harnessed – a process known as the
respiratory chain. If a link in this chain is missing, in this instance
cytochrome oxidase, which is only functional when cells have the
enzyme Cox10, the glial cells gradually lose the capacity for cell
respiration in their mitochondria. “Without independent breathing,
the manipulated glial cells of the nervous systems should have died,”
explains the scientist. That is, unless the low level of energy
harnessed from the splitting of the glucose to form pyruvate or milk
acid, a process known as glycolysis, is sufficient for them