Question

A fair dice is thrown three times. If $a, b, c$ are the numbers obtained on the dice then the probability that $f(x)=\sin \pi x|(x-a)(2 x-b)(3 x-c)|$ is non-derivable is

• A. $\frac{1}{6}$
• B. $\frac{5}{6}$
• C. $\frac{1}{2}$
• D. $\frac{2}{3}$

Answer 1

Answer: (B)

For the function to be derivable $a =1,2,3,4,5,6 ; b =2,4,6 ; c =3,6$
$\therefore$ Probability that $f ( x )$ is derivable $=\frac{6 \times 3 \times 2}{6 \times 6 \times 6}=\frac{1}{6}$
$\therefore$ Probability that $f ( x )$ is non-derivable $=1-\frac{1}{6}=\frac{5}{6}$