JEE Main 2022 · 29 Jun · Shift 1 · Mathematics Q1

MathematicsSingle correct+4 / -1Question 1 of 90

The probability that a randomly chosen $2\times2$ matrix with all the entries from the set of first 10 primes, is singular, is equal to :

\dfrac{133}{10^4}

\dfrac{18}{10^3}

\dfrac{19}{10^3}

\dfrac{271}{10^4}

Answer and worked solution

Official answer: C

Singular means $ad=bc$ ; with primes this needs $\{a,d\}=\{b,c\}$ .

Count. $a\ne d$ : 90 ordered pairs, each with 2 choices of $(b,c)$ : 180. $a=d$ : 10, with $b=c=a$ . Total 190 out of $10^4$ .

Probability $\frac{19}{10^3}$ .

(C)

Topics:Classical probability Determinants and properties

JEE Main 2022 · 29 Jun · Shift 1, Mathematics question 1