JEE Mains · Maths · STD 12 - 13. probability
The probability that a randomly chosen \(2 \times 2\) matrix with all the entries from the set of first \(10\) primes, is singular, is equal to
- A \(\frac{133}{10^{4}}\)
- B \(\frac{18}{10^{3}}\)
- C \(\frac{19}{10^{3}}\)
- D \(\frac{271}{10^{4}}\)
Answer & Solution
Correct Answer
(C) \(\frac{19}{10^{3}}\)
Step-by-step Solution
Detailed explanation
Let matrix \(A\) is singular then \(| A |=0\) Number of singular matrix \(=\) All entries are same \(+\) only two prime number are used in matrix \(=10+10 \times 9 \times 2\) \(=190\) Required probability \(=\frac{190}{10^{4}}=\frac{19}{10^{3}}\)
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