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  • Can someone help me with this, If the digits at ten’s and hundred’s places in (11)2016 are x and y respectively, then the ordered pair (x , y) is equal to :

If the digits at ten’s and hundred’s places in (11)2016  are x and y respectively, then the ordered pair (x , y) is equal to :

 
 
  • Option 1)

    (1, 8)

  • Option 2)

    (1, 6)

  • Option 3)

    (6, 1)

  • Option 4)

    (8, 1)

 

Answers (1)

best_answer

As we have learned

Expression of Binomial Theorem -

\left ( x+a \right )^{n}= ^{n}\! c_{0}x^{n}a^{0}+^{n}c_{1}x^{n-1}a^{1}+^{n}c_{2}x^{n-2}a^{2}x-----^{n}c_{n}x^{0}a^{n}

 

- wherein

for n  +ve integral .

 

 (11) ^{2016}= (1+10)^{2016}

= 1+^{2016}C_1(10)+^{2016}C_2+.......^{2016}C_{2016}(10)^{2016}

= 1+ (20160)+\left ( \frac{2016\times 2015}{2} \right )(100)+(....)(1000)+.... = 1+(20160)+ (203112000)+(...)\times (1000)+......

\therefore X = 6 \: \: and \: \: Y = 1

 

 

 

 

 


Option 1)

(1, 8)

Option 2)

(1, 6)

Option 3)

(6, 1)

Option 4)

(8, 1)

Posted by

gaurav

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