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JEE Main 29-Jan-2025 Paper - Shift 2 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 29-Jan-2025 Paper - Shift 24 Marks
MCQ
Let the function $f(x)=\left(x^2-1\right)\left|x^2-a x+2\right|+\cos |x|$ be not differentiable at the two points $x =\alpha=2$ and $x=\beta$. Then the distance of the point $(\alpha, \beta)$ from the line $12 x+5 y+10=0$ is equal to :
  • ✓
    3
  • B
    4
  • C
    2
  • D
    5
✓

Answer

Correct option: A.
3
(A) 3
Sol. $\cos | x |$ is always differentiable
$\therefore$ we have to check only for $\left| x ^2- ax +2\right|$
$\therefore$ Not differentiable at
$
x^2-a x+2=0
$
One root is given, $\alpha=2$
$
\begin{aligned}
\therefore & 4-2 a+2=0 \\
& a=3
\end{aligned}
$$\therefore$
other root $\beta=1$
but for $x=1 f(x)$ is differentiable
(Drop)

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