Torque024
m not getting 1st
@dream_IIMA said:1) A three digit number is eleven times the two digit number formed by using the hundreds and the units digit of three digit number respectively. in the tens and units place of the two digit number. if the difference between the digit in tens place and the digit in hundred place is 1 then what is the digit in the unit place???A 2 B 3 C 4D 12) in addition to the above data if the difference between the digit in tens place and that in the units place of three digit no. is also 1 then what is the number??A 121B 321C 212D 231
d A ?
@dream_IIMA said:@Torque02410(a-b)+10c=0 kese??
100a+10b+c=11(10a+c)
100a+10b+c=110a+11c
0=110a-100a-10b+11c-c
10a-10b+10c=0
10a-10b+10c=0
10(a-b)+10c=0
100a+10b+c=110a+11c
0=110a-100a-10b+11c-c
10a-10b+10c=0
10a-10b+10c=0
10(a-b)+10c=0
@dream_IIMA said:1) A three digit number is eleven times the two digit number formed by using the hundreds and the units digit of three digit number respectively. in the tens and units place of the two digit number. if the difference between the digit in tens place and the digit in hundred place is 1 then what is the digit in the unit place???A 2 B 3 C 4D 12) in addition to the above data if the difference between the digit in tens place and that in the units place of three digit no. is also 1 then what is the number??A 121B 321C 212D 231
[1] let the number be 100a+10b+c
from first condition, a+c=b
from second condition, b-a=1.
put thus value in first equation, c=1
[2] b-c=1 => b=2, a=1 ==> number =121
@19rsb said:Let S be the set of real numbers that can be represented as repeating decimals of the form 0.(abc) where a,b,c are distinct digits. Find the sum of the elements of S. Here () indicates recurring.
If abc/999 is one such repeating decimal, then (999 - abc)/999 will also be one such repeating decimal
So, now the problem reduces to finding the number of such repeating decimals
No of such repeating decimals = 10*9*8 = 720
So, sum = (720/2)(abc/999 + (999 - abc)/999) = 360
Farmer Matru is grazing his cows at the origin. There is a river that runs east to west 50 feet north of the origin. The barn is 100 feet to the south and 80 feet to the east of the origin. Farmer Matru leads his cows to the river to take a swim, then the cows leave the river from the same place they entered and Farmer Matru leads them to the barn. He does this using the shortest path possible, and the total distance he travels is d feet. Find the value of d.
50+ sqrt(80^2+150^2)???
=50+170
=220ft is the answer??
A cube of side 1 has another cube of side 1/2 stuck to the top of it, on top of that cube we have another cube of side 1/4 stuck on... On top of that is another cube of side 1/8 and so on to infinity with each cube having a side length 1/2 the one it is on top of. What is the total surface area of the resulting solid?
@chillfactor said:If abc/999 is one such repeating decimal, then (999 - abc)/999 will also be one such repeating decimalSo, now the problem reduces to finding the number of such repeating decimalsNo of such repeating decimals = 10*9*8 = 720So, sum = (720/2)(abc/999 + (999 - abc)/999) = 360
Are you sure there will be 720 such numbers?
a=> can take 1-9 = 9
b=> can take 0-9=10
c=> can take 0-9 = 10
ie. 9*10*10=900
subtact 1 to remove the 999 case
ie 899 numbers.
am i going wrong somewhere?
a=> can take 1-9 = 9
b=> can take 0-9=10
c=> can take 0-9 = 10
ie. 9*10*10=900
subtact 1 to remove the 999 case
ie 899 numbers.
am i going wrong somewhere?
Surface area of the biggest cube = 6*1*1=6
but something is stuck on it
so new surface area will be 6-.5*.5=6-.25=5.75
surface area of the next biggest cube=6*.5*.5=6*.25=1.5
but something is stuck on it, and also it is stuck on something
so for this cube, surface area will be 6*.5*.5-.5*.5-.5*.5/4
=5*.5*.5-.5*.5/4
=19*(.5*.5)/4
Continiung in this way, after 1 or 2 more cubes, we can see a pattern emerging...
though i dont know what it is
:D
@joyjitpal said:A cube of side 1 has another cube of side 1/2 stuck to the top of it, on top of that cube we have another cube of side 1/4 stuck on... On top of that is another cube of side 1/8 and so on to infinity with each cube having a side length 1/2 the one it is on top of. What is the total surface area of the resulting solid?
total surface area = 6*1^2-1/2^2+5*(1/2)^2-(1/4)^2+5*(1/4)^2-(1/8)^2...
=6+ 5*(1/2^2+1/2^4+1/2^6.....)- (1/2^2+1/2^4+1/2^6+1/2^8......)
=6+ 5*1/2^2 {1/(1-1/2^2)}- 1/2^2 {1/(1-1/2^2)}
=22/3
@Maxray2 said:Are you sure there will be 720 such numbers?a=> can take 1-9 = 9b=> can take 0-9=10c=> can take 0-9 = 10ie. 9*10*10=900subtact 1 to remove the 999 caseie 899 numbers.am i going wrong somewhere?
Yeah, there will be 720 such numbers.
First of all a, b, c are distinct (and a can be 0 also), 0.(abc) can be 0.(012), it is no where written that abc is three digit number
@joyjitpal said:A cube of side 1 has another cube of side 1/2 stuck to the top of it, on top of that cube we have another cube of side 1/4 stuck on... On top of that is another cube of side 1/8 and so on to infinity with each cube having a side length 1/2 the one it is on top of. What is the total surface area of the resulting solid?
1+4(1)^2+(1^2-(1/2)^2)+4(1/2)^2+((1/2)^2-(1/4)^2)+4(1/4)^2+((1/4)^2-(1/8)^2)......
1+4(1^2+1/2^2+1/4^2.......)+(1^2+(1/2)^2+(1/4)^2...)-((1/2)^2+(1/4)^2+(1/8)^2....)
1+4(1^2+1/2^2+1/4^2.......)+1
1+4(1+1/4+1/16+1/64)+1=4/(1-1/4) + 1 =1+16/3+1=2+16/3=22/3?
1+4(1^2+1/2^2+1/4^2.......)+(1^2+(1/2)^2+(1/4)^2...)-((1/2)^2+(1/4)^2+(1/8)^2....)
1+4(1^2+1/2^2+1/4^2.......)+1
1+4(1+1/4+1/16+1/64)+1=4/(1-1/4) + 1 =1+16/3+1=2+16/3=22/3?
@joyjitpal said:A cube of side 1 has another cube of side 1/2 stuck to the top of it, on top of that cube we have another cube of side 1/4 stuck on... On top of that is another cube of side 1/8 and so on to infinity with each cube having a side length 1/2 the one it is on top of. What is the total surface area of the resulting solid?
4 sides of each cube will be added to the sum
4*(1^2+1/2^2+1/4^2+...)
= 4*1/(1-3/4)
= 4*4/3=16/3..............(i)
base of the cube with side 1 will be added to the area....
1.........................(ii)
now of the remaining structure.....we have
sum of (top of the cube - base of the cube above it...)
i.e.
(1-1/2^2)+(1/2^2-1/4^2)+..... = 1...............................(iii)
here all term will cancel out and we will be left with 1
adding (i), (ii), (iii), we get
16/3+1+1 = (16+3+3)/3 = 22/3
@dream_IIMA said:1) A three digit number is eleven times the two digit number formed by using the hundreds and the units digit of three digit number respectively. in the tens and units place of the two digit number. if the difference between the digit in tens place and the digit in hundred place is 1 then what is the digit in the unit place???A 2 B 3 C 4D 12) in addition to the above data if the difference between the digit in tens place and that in the units place of three digit no. is also 1 then what is the number??A 121B 321C 212D 231
1. d
2 a?
@19rsb said:Farmer Matru is grazing his cows at the origin. There is a river that runs east to west 50 feet north of the origin. The barn is 100 feet to the south and 80 feet to the east of the origin. Farmer Matru leads his cows to the river to take a swim, then the cows leave the river from the same place they entered and Farmer Matru leads them to the barn. He does this using the shortest path possible, and the total distance he travels is d feet. Find the value of d.
approx 215.4 feet??
@Aman.Malhotra said:If x and y are real numbers, then the minimum value of x^2 + 4xy + 6y^2 - 4y + 4 is
MIN value is 2....at x=-2 and y=1???
differntiate the equation wrt x...u will get minima at x=-2y
substitute the value in the equation....you will get an equation in terms of y...
differentiate again...wrt y....and value is minimum at y=1
put the values of x and y in the original equation...
so 2??
@joyjitpal said:A cube of side 1 has another cube of side 1/2 stuck to the top of it, on top of that cube we have another cube of side 1/4 stuck on... On top of that is another cube of side 1/8 and so on to infinity with each cube having a side length 1/2 the one it is on top of. What is the total surface area of the resulting solid?
22/3??
@dream_IIMA said:1) A three digit number is eleven times the two digit number formed by using the hundreds and the units digit of three digit number respectively. in the tens and units place of the two digit number. if the difference between the digit in tens place and the digit in hundred place is 1 then what is the digit in the unit place???A 2 B 3 C 4D 12) in addition to the above data if the difference between the digit in tens place and that in the units place of three digit no. is also 1 then what is the number??A 121B 321C 212D 231
100a+10b+c = 110a+c
=>b=a+c
now c= b-a........for first question...
and a=b-c.........for second part...