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 π x|(x-a)(2 x-b)(3 x-c)| is non-derivable is

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 π x|(x-a)(2 x-b)(3 x-c)| is non-derivable is (A) (1/6) (B) (5/6) (C) (1/2) (D) (2/3)

Tardigrade Admin · Accepted Answer

For the function to be derivable a =1,2,3,4,5,6 ; b =2,4,6 ; c =3,6 ∴ Probability that f ( x ) is derivable =(6 × 3 × 2/6 × 6 × 6)=(1/6) ∴ Probability that f ( x ) is non-derivable =1-(1/6)=(5/6)

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

$\frac{1}{6}$

$\frac{5}{6}$

$\frac{1}{2}$

$\frac{2}{3}$

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

Q. A fair dice is thrown three times. If a,b,c are the numbers obtained on the dice then the probability that f(x)=sinπx∣(x−a)(2x−b)(3x−c)∣ is non-derivable is

61​

65​

21​

32​