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JEE Main202427 Jan 2024Evening ShiftMathematicsStraight LinesActual

Let A and B be two finite sets with m and n elements respectively. The total number of subsets of the set A is 56 more than the total number of subsets of B . Then the distance of the point P ( m , n ) from the point Q ( - 2 , - 3 ) is

Options

  1. A10
  2. B6
  3. C4
  4. D8

Correct answer

A. 10

Step-by-step solution

We know that, the total number of subsets of a set having n elements is 2 n . ⇒ 2 m - 2 n = 56 ⇒ 2 n 2 m - n - 1 = 2 3 × 7 ⇒ 2 n = 2 3 and 2 m - n - 1 = 7 ⇒ n = 3 and 2 m - n = 8 ⇒ n = 3 and m - n = 3 ⇒ n = 3 and m = 6 Distance between P 6 , 3 and Q - 2 , - 3 is given by, PQ = 6 + 2 2 + 3 + 3 2 ⇒ PQ = 8 2 + 6 2 ⇒ PQ = 100 ⇒ PQ = 10 units

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