31. If x,y,z are non negative integers and x=6. Find the number of solutions of 1/x +1/y = 1/z?

1/x+1/y=1/z
1/6+1/y=1/z
z=6y/(6+y)
z is a non-negative integer
therefore 6y=(6+y)*k where 'k' is a non-negative integer
y=6k/(6-k)
0<(6-k)<6 data-blogger-escaped-br="">
k={1,2,3,4,5}
y={3,6,12,30}
z={2,3,4,5}
(x,y,z)={(6,3,2),(6,6,3),(6,12,4),(6,30,5)}
number of solutions=4

32. How many 8 digit numbers divisible by 25 can be formed with 0,1,2,3,4,5,6,7 ,if repetition of digits is not allowed?

last 2 digit number can be 25,50,75
25 - rest 6 digits will b considered bt 0 can not be at first place so 5* 5!
75 - Same as 25 so 5*5!
50 - 0 is already used so we have all left 6 digit no. to be used so 6!
5*5!+5*5!+6! = 1920

33. How many numbers are there between 0 and 1000 which on division by 2, 4, 6, 8 leave remainders
1, 3, 5, 7 respectively?

To find the smallest number satisfying the given condition, find the LCM of 2, 4, 6, 8, which is 24
Now, the given factors and remainders differ by 1, so subtract 24 by 1
Hence, 23 is the number.
To find the next number add 24 to 23 and so on..
Hence the series would be 23, 47, 71 ... 983, which is in AP.
Using l=a+(n-1)*d, we get n=21.
Hence the answer is 21

34. How many six digit numbers are possible using 1,2,3,4,5,6 such that the number formed is divisible by the digit at its units place?

If digt place has 1 then possible numbers = 120(5!)
if 2 then possible numbers = 120
if 3 then possible numbers =120
if 4 then possible numbers = 48 (4!*2)
if 5 then possible numbers = 120
if 6 then possible numbers = 20
so totl no=648

35. Amit can complete a piece of work in 2.25 days. Badri takes double the time taken by amit.chetan takes double dat of badro,and das takes double dat of chetan to complete the same task. They are split into two groups(of one or more persons)such that the differnce b/w the times taken by the two groups to complete the same work is minimum.what could be the compostion of the faster group?

a)amit and das

b)badri nd chetan

c)badri,chetan nd das

d)amit alone

A = 2.25 days => 1 day = 1/2.25 = 0.44 work/day
B = 4.5 days => 0.22 work / day
C = 9 days => 0.11 work per day
D = 18 days => 0.055 work / day

now add all 1 day work of b,c,d then we ll get 0.345 which is less than 1 days amit work...
so if we all add in amit's work the it will definetly increase the differnce
so group form like, amit in a single group and another group consist of b,c,d

In question 32, Its not mentined that the no. need to be of 8 digits, So in this case, 2 digits no. 3 digits no. 4 digits no. 5 digits no. 6 digits no. 7 digits no. 8 digits no.

Well, actually the question submitted to us by one of our visitors was in a raw form, we tried to put that into something polished..But the number to be formed is 8 digit. Thanks for notifying that :)

In question 32,

ReplyDeleteIts not mentined that the no. need to be of 8 digits,

So in this case,

2 digits no.

3 digits no.

4 digits no.

5 digits no.

6 digits no.

7 digits no.

8 digits no.

need to be considered separately.

Well, actually the question submitted to us by one of our visitors was in a raw form, we tried to put that into something polished..But the number to be formed is 8 digit.

DeleteThanks for notifying that :)

U are putting ur hard efforts to collect and post, thats really nice.

DeleteNd its my pleasure to contribute in this blog by any means.

in question 33.

ReplyDelete987=23+(n-1)*24

n=41

but urs answer is 21. how??

Well, my bad it is 21. Thanks for letting us know about that mistake!

Delete