1
WB JEE 2010
+1
-0.25

The co-ordinates of the point on the curve $$y = {x^2} - 3x + 2$$ where the tangent is perpendicular to the straight line y = x are

A
(0, 2)
B
(1, 0)
C
($$-$$1, 6)
D
(2, $$-$$2)
2
WB JEE 2011
+1
-0.25

The acceleration of a particle starting from rest moving in a straight line with uniform acceleration is 8m/sec2. The time taken by the particle to move the second metre is

A
$${{\sqrt 2 - 1} \over 2}$$ sec
B
$${{\sqrt 2 + 1} \over 2}$$ sec
C
$$(1 + \sqrt 2 )$$ sec
D
$$(\sqrt 2 - 1)$$ sec
3
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 $$\forall x>0$$
4
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 $$60^{\circ}$$
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