Maths-
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Easy

Question

The total number of function ‘ƒ’ from the set {1, 2, 3} into the set {1, 2, 3, 4, 5} such that ƒ(i) less or equal than ƒ(j), straight for all i < j, is equal to-

  1. 35    
  2. 30    
  3. 50    
  4. 60    

The correct answer is: 35


    Let ‘l’ is associated with ‘r’ ,
    element of {1, 2, 3, 4, 5} then ‘2’ can be associated with r, r + 1, ….., 5.
    Let ‘2’ is associated with ‘j’ then 3 can be associated with j, j + 1, …., 5. Thus required number of functions
    = not stretchy sum subscript r equals 1 end subscript superscript 5 end superscript open parentheses not stretchy sum subscript j equals r end subscript superscript 5 end superscript left parenthesis 6 minus j right parenthesis close parentheses= not stretchy sum subscript r equals 1 end subscript superscript 5 end superscript fraction numerator left parenthesis 6 minus r right parenthesis left parenthesis 7 minus r right parenthesis over denominator 2 end fraction
    = fraction numerator 1 over denominator 2 end fraction open parentheses not stretchy sum subscript r equals 1 end subscript superscript 5 end superscript left parenthesis 42 minus 13 r plus r to the power of 2 end exponent right parenthesis close parentheses
    = fraction numerator 1 over denominator 2 end fraction open parentheses 42.5 minus 13. fraction numerator 6.5 over denominator 2 end fraction plus fraction numerator 5.6.11 over denominator 6 end fraction close parentheses= 35
    Hence (a) is correct answer.

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