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AP EAMCET202017 Sep 2020Morning ShiftMathematicsFunctionsActual

If ([x] ) denotes the greatest integer function on (x ), then the number of positive integral divisors of ( [(2+ 3 )^5 ] ) is

Options

  1. A6
  2. B4
  3. C2
  4. D8

Correct answer

B. 4

Step-by-step solution

( aligned & (2+ 3 )^5= ^5 C₀ 2^5 ( 3 )^0+ ^5 C₁ 2^4 ( 3 ) & ^5 C₂ 2^3( 3 )^2+ ^5 C₃ 2^2 ( 3 )^3 & + ^5 C₄ 2 ( 3 )^4+ ^5 C₅ 2^0( 3 )^5 & =32+80 3 +240+120 3 +90+9 3 & (2+ 3 )^5=362+209 3 =723.99 & [(2+ 3 )^5 ]=723 723=3^1 241^1 aligned ) Now, positive integral divisors of (723=(1+1)(1+1)=4 )

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