JEE Main 2026 · 2 Apr · Shift 2 · Mathematics Q18

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MathematicsSingle correct+4 / -1Question 18 of 75

Let $f(x)$ be a polynomial of degree 5, and have extrema at $x=1$ and $x=-1$ . If $\displaystyle\lim_{x\to0}\left(\frac{f(x)}{x^3}\right)=-5$ , then $f(2)-f(-2)$ is equal to :

112

Answer and worked solution

Official answer: D

Form of f. $\lim\frac{f}{x^3}=-5$ means $f=-5x^3+ax^4+bx^5$ .

Extrema at ±1. $f'=-15x^2+4ax^3+5bx^4$ ; $f'(1)=f'(-1)=0$ gives $a=0$ , $b=3$ , so $f=3x^5-5x^3$ (odd).

Value. $f(2)-f(-2)=2(96-40)=112$ .

(D)

Topics:Maxima and minima Limits

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JEE Main 2026 · 2 Apr · Shift 2, Mathematics question 18