1
WB JEE 2024
+1
-0.25

Let $$\mathrm{y}=\mathrm{f}(x)$$ be any curve on the $$\mathrm{X}-\mathrm{Y}$$ plane & $$\mathrm{P}$$ be a point on the curve. Let $$\mathrm{C}$$ be a fixed point not on the curve. The length $$\mathrm{PC}$$ is either a maximum or a minimum, then

A
$$\mathrm{PC}$$ is perpendicular to the tangent at $$\mathrm{P}$$
B
$$\mathrm{PC}$$ is parallel to the tangent at $$\mathrm{P}$$
C
PC meets the tangent at an angle of $$45^{\circ}$$
D
$$\mathrm{PC}$$ meets the tangent at an angle of $$60^{\circ}$$
2
WB JEE 2024
+1
-0.25

If a particle moves in a straight line according to the law $$x=a \sin (\sqrt{\lambda} t+b)$$, then the particle will come to rest at two points whose distance is [symbols have their usual meaning]

A
$$a$$
B
$$\frac{a}{2}$$
C
$$2a$$
D
$$4a$$
3
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
4
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
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