@ChirpiBird said:1^1=12^2=43^3=74^4=65^5=56^6=67^7=38^8=69^9=9(6,4),(4,6)(8,6)(6,8)(4,8)(8,4) (4,4)(6,6)(8,8)??? 9 such pairs??correct me if i am wrong.
it is given not necessarily distinct so cant it be (1,1)(2,2)....(9,9)
@jain4444 said:If, 4^y=5.3^(2x)=4.5^z=8.Find value 9^(yxz) *3^2=...?
2xylog3=log5=3log2/z
so xyz*log9=log8
9^xyz=8
8*9=72
@iLoveTorres said:it is given not necessarily distinct so cant it be (1,1)(2,2)....(9,9)
so that makes .. 15 pairs.. ?
9+6
9+6
@amresh_maverick said:How many ordered pairs (P, Q) are there such that the unit âŽâĒs digits of P^P and Q^Q are the same? P and Q are natural numbers less than 10 and are not necessarily distinct.
@ChirpiBird said:1^1=12^2=43^3=74^4=65^5=56^6=67^7=38^8=69^9=9(6,4),(4,6)(8,6)(6,8)(4,8)(8,4) (4,4)(6,6)(8,8)??? 9 such pairs??correct me if i am wrong.
@iLoveTorres said:22?
OA : 15
when P=Q ----9
when not equal -------6-- (4,6) (6,8) (4,8)
when P=Q ----9
when not equal -------6-- (4,6) (6,8) (4,8)
The value of (222)X in base 'X' when converted to base 10 is 'P'. The value of (222)Y in base 'Y' when converted to base 10 is Q. If (P â Q)10 = 28, then what is the value of (Q â X)10?
@iLoveTorres said:it is given not necessarily distinct so cant it be (1,1)(2,2)....(9,9)
so that makes .. 15 pairs.. ?
9+6
9+6
@MANJULNEOGI said:Two clubs play against each other in badminton tournament. Each club is represented by 12 students. Every game is a doubles game, & every possible pair from the first club must play one game against every possible pair from the second club. How many games will each student play ?
12c2*11=726
Pipes A and B can completely fill a water tank independently in 4 hrs and 5 hrs respectively. A pipe C can empty the tank filled completely with water in 3 hrs. Initially the tank is empty and all the pipes are closed. Pipe A is opened first at time t = 0 hrs and pipe C is opened at the instant when the tank is exactly half filled with water. Pipe B is opened after pipe C and at the instant when the tank is exactly one-fourth filled with water. Find the total time taken to fill the tank completely counting from t = 0 hrs.
@amresh_maverick said:The value of (222)X in base 'X' when converted to base 10 is 'P'. The value of (222)Y in base 'Y' when converted to base 10 is Q. If (P â Q)10 = 28, then what is the value of (Q â X)10?
2(x^2+x+1)=P
2(y^2+y+1)=Q
P-Q=2(x^2-y^2)+2(x-y)=2(x-y)(x+y+1)
2(x-y)(x+y+1)=28
(x-y)(x+y+1)=14
x+y+1=7
x+y=6
x-y=2
x=4
y=2
P=42
Q=14
Q-X=10??
@amresh_maverick said:Pipes A and B can completely fill a water tank independently in 4 hrs and 5 hrs respectively. A pipe C can empty the tank filled completely with water in 3 hrs. Initially the tank is empty and all the pipes are closed. Pipe A is opened first at time t = 0 hrs and pipe C is opened at the instant when the tank is exactly half filled with water. Pipe B is opened after pipe C and at the instant when the tank is exactly one-fourth filled with water. Find the total time taken to fill the tank completely counting from t = 0 hrs.
14hrs 24 mins?
@amresh_maverick said:Pipes A and B can completely fill a water tank independently in 4 hrs and 5 hrs respectively. A pipe C can empty the tank filled completely with water in 3 hrs. Initially the tank is empty and all the pipes are closed. Pipe A is opened first at time t = 0 hrs and pipe C is opened at the instant when the tank is exactly half filled with water. Pipe B is opened after pipe C and at the instant when the tank is exactly one-fourth filled with water. Find the total time taken to fill the tank completely counting from t = 0 hrs.
pipe A alone works for 2 hours
den 1/4th water is taken out
(1/3-1/4)n=1/4
(1/12)n=1/4
n=3 hours
after C is opened we need 3/4th to be filled
(1/4+1/5-1/3)n=3/4
(15+12-20/60)n=3/4
(7/60)n=3/4
n=45/7 hours
2+3+45/7=5+6.28=11.28 hours?
@amresh_maverick said:The value of (222)X in base 'X' when converted to base 10 is 'P'. The value of (222)Y in base 'Y' when converted to base 10 is Q. If (P â Q)10 = 28, then what is the value of (Q â X)10?
2(x-y)(x+y+1)=28
(x-y)(x+y+1)=14
x+y+1=7
x-y=2
x=4, y=2
2y^2+2y+2-x= 10
@ChirpiBird said:hahaha.. koi nhi yar, happy to help
ladkiya yaar yaar bolke seene pe war kar deti hai :P
Sorry for spamming
Sorry for spamming
@amresh_maverick said:The value of (222)X in base 'X' when converted to base 10 is 'P'. The value of (222)Y in base 'Y' when converted to base 10 is Q. If (P â Q)10 = 28, then what is the value of (Q â X)10?
OA = 79 for X=7 and Y=6
@amresh_maverick said:The value of (222)X in base 'X' when converted to base 10 is 'P'. The value of (222)Y in base 'Y' when converted to base 10 is Q. If (P â Q)10 = 28, then what is the value of (Q â X)10?
(222)x = p---> p = 2x^2 + 2x + 2
(222)y = q ---> q = 2y^2 + 2y + 2
(p - q) = 28
2x^2 + 2x + 2 - 2y^2 + 2y + 2 = 28
(x - y)(x + y + 1) = 14
x - y = 2
x + y + 1 = 7
x = 4
y = 2
q - x = 2(2)^2 + 2*2 + 2 - 4 = 10?
@Subhashdec2 said:pipe A alone works for 2 hoursden 1/4th water is taken out(1/3-1/4)n=1/4(1/12)n=1/4n=3 hoursafter C is opened we need 3/4th to be filled(1/4+1/5-1/3)n=3/4(15+12-20/60)n=3/4(7/60)n=3/4n=45/7 hours2+3+45/7=5+6.28=11.28 hours?
I took the time to empty it to 1/4 as 6 hours. my bad. 
@mailtoankit said:(222)x = p---> p = 2x^2 + 2x + 2(222)y = q ---> q = 2y^2 + 2y + 2(p - q) = 282x^2 + 2x + 2 - 2y^2 + 2y + 2 = 28(x - y)(x + y + 1) = 14x - y = 2x + y + 1 = 7x = 4y = 2q - x = 2(2)^2 + 2*2 + 2 - 4 = 10?
Y cannot be 2 as base is 2
also (x - y)(x + y + 1) = 14 - 1*14 or 2*7
also (x - y)(x + y + 1) = 14 - 1*14 or 2*7
@amresh_maverick said:Pipes A and B can completely fill a water tank independently in 4 hrs and 5 hrs respectively. A pipe C can empty the tank filled completely with water in 3 hrs. Initially the tank is empty and all the pipes are closed. Pipe A is opened first at time t = 0 hrs and pipe C is opened at the instant when the tank is exactly half filled with water. Pipe B is opened after pipe C and at the instant when the tank is exactly one-fourth filled with water. Find the total time taken to fill the tank completely counting from t = 0 hrs.
OA : 11(3/7) hrs
LCM (A,B,C) = 60
A=15, B=12,C=-20
A will fill half in 2 hrs
A and C will make it 1/4th in 3 hrs , total until now = 5hrs
A,B and C will add another 3/4th to make it full in = 45/7 hrs
LCM (A,B,C) = 60
A=15, B=12,C=-20
A will fill half in 2 hrs
A and C will make it 1/4th in 3 hrs , total until now = 5hrs
A,B and C will add another 3/4th to make it full in = 45/7 hrs