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General
Easy

Question

STATEMENT-I : If [4x] = [x], then the largest set of values of x is. open square brackets negative fraction numerator 1 over denominator 4 end fraction comma fraction numerator 1 over denominator 4 end fraction close parentheses and
STATEMENT-II : If [nx] = [x], n element of I to the power of plus end exponent then the largest set of values of x is open square brackets negative fraction numerator 1 over denominator n end fraction comma fraction numerator 1 over denominator n end fraction close parentheses

  1. Statement-I is True, Statement-II is True; Statement-II is a correct explanation for Statement-I    
  2. Statement-I is True, Statement-II is True; Statement-II is NOT a correct explanation for Statement-I    
  3. Statement-I is True, Statement-II is False    
  4. Statement-I is False, Statement-II is True    

The correct answer is: Statement-I is True, Statement-II is True; Statement-II is a correct explanation for Statement-I


    [nx] = [x]
    Let x = m + f where m element of I and 0 less or equal than f less than 1
    Let fraction numerator r over denominator n end fraction less or equal than f less than fraction numerator r plus 1 over denominator n end fraction where 0 less or equal than r less or equal than n plus 1 then r less or equal than n f less than r plus 1
    the equation becomes [ n( m + 1 ) ] = [ m + f ]
    i.e. nm + r = m
    i.e. m equals fraction numerator negative r over denominator n minus 1 end fraction

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