1
WB JEE 2024
+1
-0.25

$$f(x)=\cos x-1+\frac{x^2}{2!}, x \in \mathbb{R}$$ Then $$\mathrm{f}(x)$$ is

A
decreasing function
B
increasing function
C
neither increasing nor decreasing
D
constant $$\forall x>0$$
2
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 $$60^{\circ}$$
3
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
$$4a$$
4
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
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