@pavimai said:find the number of positive integer solutions of the equation 2/x +15/y=5...share the approach Thanks in advance
It's a hyperbola.
Only one solution (1, 5)
@pavimai said:find the number of positive integer solutions of the equation 2/x +15/y=5...share the approach Thanks in advance
2y + 15x = 5xy
(5x - 2)(y - 3) = 6
only solution , x = 1 and y = 5
(5x - 2)(y - 3) = 6
only solution , x = 1 and y = 5
@pavimai said:find the number of positive integer solutions of the equation 2/x +15/y=5...share the approach Thanks in advance
x= 1, y = 5...
@pavimai said:find the number of positive integer solutions of the equation 2/x +15/y=5...share the approach Thanks in advance
x=1,y=5
@pratyush9811 said:The top speed of a rail engine is 80 km/hr. When pulling a train of wagons, its top speed is reduced by a quantity proportional to the square-root of the number of wagons. When the number of wagons attached to the engine is 25, its top speed is 55 km/hr. If the top speed must be more than 20 km/hr, what is the maximum number of wagons that can be attached to the engine?
144 hein??
144 pe perfect 20km/hr aata hein ok I understand -_-
N=7777.......7777,where the digit 7 repeats itself 429 times.what is the remainder left when N is divided by 1144 ??
@pavimai said:N=7777.......7777,where the digit 7 repeats itself 429 times.what is the remainder left when N is divided by 1144 ??
777
@pavimai said:N=7777.......7777,where the digit 7 repeats itself 429 times.what is the remainder left when N is divided by 1144 ??
D = 1144 = 4*(286) = 8*(13)*(11)
N mod 8 = 777 mod 8 = 1 -> N = 8k + 1
N mod 13 = 777 mod 13 = 10 -> N = 13m + 10
N mod 11 = 777 mod 11 = 7 -> N = 11p + 7
8k + 1 = 13m + 10 = 11p + 7
N = 13(8a + 3) + 10 = 104a + 49
Also, N = 104(11r + 7) + 49 => N = 1144r + 104*7 + 49 = 1144r + 728 + 49 = 1144r + 777
-> Remainder = 777 ?
@pavimai said:N=7777.......7777,where the digit 7 repeats itself 429 times.what is the remainder left when N is divided by 1144 ??
1144=2^3*11*13
77777...mod8=1
77777...mod11=7
77777...mod13=10
=>11x+7=13y+10
=>11x=11y+2y+3
y=4
13*4+10=62
62+143k=8x+1
=>8k=136k+7k+61
=>k=5
62+143*5=777
77777...mod8=1
77777...mod11=7
77777...mod13=10
=>11x+7=13y+10
=>11x=11y+2y+3
y=4
13*4+10=62
62+143k=8x+1
=>8k=136k+7k+61
=>k=5
62+143*5=777
@pavimai said:N=7777.......7777,where the digit 7 repeats itself 429 times.what is the remainder left when N is divided by 1144 ??
very popular question. ans is 777
@pavimai said:@vijay_chandola can u explain
7777..... 429 times
=7*11111.... 429 times
=7*(1+10+100+1000+.....)
=7*(10^429-1)/9
=7*11111.... 429 times
=7*(1+10+100+1000+.....)
=7*(10^429-1)/9
Now, 7*(10^429-1)/9 mod 1144
=7*(10^9-1)/9 mod 1144 (Using Eular, 429 mod 60 =9)
=777777777 mod 1144
=(777777000+777) mod 1144
=777
Four of the five numbers given below are all alike in a certain way so as to form a group. Which one does not belong to the group?
A 110
B 29
C 47
D 48
E 740
A 110
B 29
C 47
D 48
E 740
post reason for ur ans also
A regular pentagon is drawn on a piece of paper.In how many ways can five identical re.1 coins be placed on the five vertices of the pentagon if exactly one coin is to be placed oneach vertex???
@pavimai said:A regular pentagon is drawn on a piece of paper.In how many ways can five identical re.1 coins be placed on the five vertices of the pentagon if exactly one coin is to be placed oneach vertex???
8?
@maddy2807 said:Four of the five numbers given below are all alike in a certain way so as to form a group. Which one does not belong to the group?A 110 B 29 C 47 D 48 E 740 post reason for ur ans also
i am guessing it to be 48 