JEE Main 2022 (29 Jun, Shift 2) Maths Q6: Maxima and Minima

Question

Let $f : \mathbb{R} 	o \mathbb{R}$ be a function defined by $f(x) = (x - 3)^{n_1}(x - 5)^{n_2}$, $n_1, n_2 \in \mathbb{N}$.
Then, which of the following is NOT true?

Accepted Answer

Option 3: For $n_1 = 3$, $n_2 = 5$, there exists $\alpha \in (3, 5)$ where $f$ attains local maxima.

Answer

For $n_1 = 3$, $n_2 = 4$, there exists $\alpha \in (3, 5)$ where $f$ attains local maxima.

Answer

For $n_1 = 4$, $n_2 = 3$, there exists $\alpha \in (3, 5)$ where $f$ attains local minima.

Answer

For $n_1 = 3$, $n_2 = 5$, there exists $\alpha \in (3, 5)$ where $f$ attains local maxima.

Answer

For $n_1 = 4$, $n_2 = 6$, there exists $\alpha \in (3, 5)$ where $f$ attains local maxima.

JEE Main 29 June 2022, Shift 2, Maths Q6

Same idea in other shifts