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Mathematics · JEE I SETS

हिन्दी

Let \( S \) be the set of all integers \( x \) such that \( -3 \le x < 7 \). If \( T = \{ x \in S : x \text{ is prime} \} \), then the number of subsets of \( T \) containing the smallest prime number is:

  1. A
    8
  2. B
    16
  3. C
    2
  4. D
    4
View Answer & Solution

Correct answer · Option D

4

Explanation

Primes in \( S = \{-3, -2, -1, 0, 1, 2, 3, 4, 5, 6\} \) are \( \{2, 3, 5\} \) (since primes are natural numbers \( > 1 \)). Smallest prime is 2. Subsets containing 2 is \( 2^{3-1} = 2^2 = 4 \).
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