JEE Main 2022 · 28 Jun · Shift 2 · Mathematics Q24

MathematicsInteger+4 / -1Question 24 of 90

If $\displaystyle\lim_{x\to1}\frac{\sin\left(3x^2-4x+1\right)-x^2+1}{2x^3-7x^2+ax+b}=-2$ , then the value of $(a-b)$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 11

0/0 twice. The numerator and its derivative vanish at $x=1$ , so the denominator must too: $a+b=5$ and $6-14+a=0$ , giving $a=8$ , $b=-3$ .

Check. Second derivatives: numerator $6-2=4$ , denominator $-2$ , limit $-2$ .

$a-b=11$ .

Answer: 11

JEE Main 2022 · 28 Jun · Shift 2, Mathematics question 24