1
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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
MCQ (Single Correct Answer)
+1
-0.25
Change Language

A unit vector in XY-plane making an angle $$45^{\circ}$$ with $$\hat{i}+\hat{j}$$ and an angle $$60^{\circ}$$ with $$3 \hat{i}-4 \hat{j}$$ is

A
$$ \frac{13}{14} \hat{i}+\frac{1}{14} \hat{j} $$
B
$$ \frac{1}{14} \hat{i}+\frac{13}{14} \hat{j} $$
C
$$ \frac{13}{14} \hat{\mathrm{i}}-\frac{1}{14} \hat{\mathrm{j}} $$
D
$$ \frac{1}{14} \hat{i}-\frac{13}{14} \hat{j} $$
4
WB JEE 2024
MCQ (Single Correct Answer)
+1
-0.25
Change Language

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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