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KVPY2012MathematicsPermutation and Combination

How many ordered pairs of ( m , n ) integers satisfy m 12 = 12 n ?

Options

  1. A30
  2. B15
  3. C12
  4. D10

Correct answer

A. 30

Step-by-step solution

array l m 12 = 12 n mn =144 n = 144 3 array We want to find here total number of divisors of 144 144=2⁴ 3² Total divisors are (4+1)(2+1)=15 But negative pairs are also possible hence =30

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