1.. a telegraph has a number of arms and each arm is capable of  taking 4 different positions, including the position of rest. if 1023 different signalscan be sent in all. find the no. of arms?.. (i didn't even understood the question)

2...in how many ways 6 boys and 4 girls sit in a row so that no boy is between 2 girls??

3....inhow many ways can the letter of the word ALGEBRA be arranged without changing the relative order of vowels and consonents?

(please please post a detailed solution)

friend can u please first of all clear that what does the first question means . i didn' t understand the question itself 

1) Different postition of the arms result in different signals, thats understood .So total no. of signals are 4^N, where N is the total no. of arms. But in these selections, there is a combination which has all the arms at rest, thats not a signal. So 4^N -1 = 1023 => N =5

2)Working on this!.

@ little genius: The arrangement can be like this also:

BBGBBGBBGG, in this no boy is between two girls.

3) There are 3 vowels : A,E,A. Not changing the relative ordering means that the first place must be occupied by a vowel, the second and third place by consonants, the fourth place by a vowel, the next two places by consonants and the last place by a vowel.

That gives 4! * (3! /2) , 4 places for consonants and 3 for vowels in which A is repeated once.