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KVPY2016MathematicsBinomial Theorem

The number of all 2 -digit numbers n such that n is equal to the sum of the square of digit in its tens place and the cube of the digit in units place is

Options

  1. A0
  2. B1
  3. C2
  4. D4

Correct answer

C. 2

Step-by-step solution

n = ab ab = a ²+ b ³ 10 a + b = a ²+ b ³ a (10- a )+ b (1- b )(1+ b )=0 a (10- a )=( b -1)( b )( b +1) If b =2 ; a (10- a )=6 no value of ^ a ^ b =3 ; a (10- a )=24 a 4,6 nos. are 43 & 63 b =4 ; a (10- a )=60 no value of a b =5 ; a (10- a )=120 no need to check further nos. are 43 & 63 .

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