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JEE Main202528 Jan 2025Morning ShiftMathematicsProbabilityActual

Two number k ₁ and k ₂ are randomly chosen from the set of natural numbers. Then, the probability that the value of i ^ k ₁ + i ^ k ₂ ,( i = -1 ) is non-zero, equals

Options

  1. A1 2
  2. B3 4
  3. C1 4
  4. D2 3

Correct answer

B. 3 4

Step-by-step solution

Let k₁=4 ₁+r₁, r₁ 0,1,2,3 k₂=4 ₂+r₂ aligned & (i)^ k₁ +(i)^ k₂ =(i)^ r₁ +(i)^ r₂ & (i)^ r₁ 1, i,-1,-i aligned Zero 1,(-1) pair array cc 1, & -1 i, & -i -i,+i -1, & 1 array i,(-i) pair aligned & Zero probability = 4 ^4 C₁ ^4 C₁ = 1 4 & Probability (non-zero) =1- 1 4 = 3 4 aligned

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