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General
Easy

Question

The number of positive integers satisfying the inequality blank to the power of n plus 1 end exponent C subscript n minus 2 end subscript minus to the power of n plus 1 end exponent C subscript n minus 1 end subscript less or equal than 50 is

  1. 9    
  2. 8    
  3. 7    
  4. 6    

The correct answer is: 7


    Given, n+1Cn-2-n+1C n-1less or equal than 50
    rightwards double arrow blank fraction numerator open parentheses n minus 1 close parentheses factorial over denominator 3 factorial open parentheses n minus 2 close parentheses factorial end fraction minus fraction numerator open parentheses n plus 1 close parentheses factorial over denominator 2 factorial open parentheses n minus 1 close parentheses factorial end fraction less or equal than 50
    rightwards double arrow blank fraction numerator open parentheses n plus 1 close parentheses factorial over denominator 3 factorial end fraction open square brackets fraction numerator 1 over denominator open parentheses n minus 2 close parentheses factorial end fraction minus fraction numerator 3 over denominator open parentheses n minus 1 close parentheses factorial end fraction close square brackets less or equal than 50
    rightwards double arrow open parentheses n plus 1 close parentheses factorial open parentheses fraction numerator n minus 1 minus 3 over denominator open parentheses n minus 1 close parentheses factorial end fraction close parentheses less or equal than 300
    rightwards double arrow open parentheses n plus 1 close parentheses n left parenthesis n minus 4 right parenthesis less or equal than 300
    For n equals 8, it satisfy to the above inequality
    But n equals 1 it does not satisfy the above inequality

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