Five equi-spaced points labeled 1, 2, 3, 4, 5 are marked in the same order in clockwise direction on the circumference of a circle. An ant is moving on the circumference of this circle in the clockwise direction. If the ant is at an odd numbered point it shifts one point ahead and if it is at an even numbered point it shifts two points ahead. If the ant starts from point 5, then where would it be after 2010 such movements?(a) 1 (b) 3 (c) 5 (d) None of these
Five equi-spaced points labeled 1, 2, 3, 4, 5 are marked in the same order in clockwise direction on the circumference of a circle. An ant is moving on the circumference of this circle in the clockwise direction. If the ant is at an odd numbered point it shifts one point ahead and if it is at an even numbered point it shifts two points ahead. If the ant starts from point 5, then where would it be after 2010 such movements?(a) 1 (b) 3 (c) 5 (d) None of these
There are five cities in a state and each of them is to be connected to exactly two other cities using telephone lines. In how many ways can this be done? (a) 12 (b) 24 (c) 36 (d) 9
There are five cities in a state and each of them is to be connected to exactly two other cities using telephone lines. In how many ways can this be done?(a) 12 (b) 24 (c) 36 (d) 9
is this correct ?12 is a factor of (5^36-1)so, (5^36-1)=12^k5^36=12^k+1last digit of 5^36=5so last digit of 12^k has to be 4 which is possible with k=2 (from options)
5^36-1625^9-1(625^3-1)(625^6+625^3+1)(625-1)(625^2+625+1)(625^6+625^3+1)624(625^2+625+1)(625^6+625^3+1)624 is divisible by 12 and leave a quo is 52now if we again devide 52 by 12 rem will be 4 rem for (625^2+625+1) by 12 is 3(625^6+625^3+1) by 12 is 3 alsoso now 4*3*3again divisible by 12 so max power 12^2