1
WB JEE 2024
+1
-0.25

Let $$\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$$ be given by $$\mathrm{f}(x)=\left|x^2-1\right|$$, then

A
f has a local minima at $$x= \pm 1$$ but no local maxima
B
f has a local maxima at $$x=0$$, but no local minima
C
$$\mathrm{f}$$ has a local minima at $$x= \pm 1$$ and a local maxima at $$x=0$$
D
f has neither any local maxima nor any local minima
2
WB JEE 2024
+2
-0.5

Consider the function $$\mathrm{f}(x)=x(x-1)(x-2) \ldots(x-100)$$. Which one of the following is correct?

A
This function has 100 local maxima
B
This function has 50 local maxima
C
This function has 51 local maxima
D
Local minima do not exist for this function
3
WB JEE 2023
+1
-0.25

A missile is fired from the ground level rises x meters vertically upwards in t sec, where $$x = 100t - {{25} \over 2}{t^2}$$. The maximum height reached is

A
100 m
B
300 m
C
200 m
D
125 m
4
WB JEE 2023
+2
-0.5

The portion of the tangent to the curve $${x^{{2 \over 3}}} + {y^{{2 \over 3}}} = {a^{{2 \over 3}}},a > 0$$ at any point of it, intercepted between the axes

A
varies as abscissa
B
varies as ordinate
C
is constant
D
varies as the product of abscissa and ordinate
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