Let $$\mathrm{ABCDEF}$$ be a regular hexagon, with the vertices taken in order. The resultant of the vectors: $$\overrightarrow{AB},~\overrightarrow{BC},~\overrightarrow{CD},~\overrightarrow{DE}$$ equals, in magnitude, the vector:
1. $$\overrightarrow{AB}$$
2. $$\overrightarrow{AD}$$
3. $$\sqrt2\overrightarrow{AB}$$
4. $$\sqrt3\overrightarrow{AB}$$

Subtopic:  Resultant of Vectors |
From NCERT
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If the magnitude of the sum of two vectors is equal to the magnitude of the difference between the two vectors, the angle between these vectors is?
1. $$90^\circ$$
2. $$45^\circ$$
3. $$180^\circ$$
4. $$0^\circ$$
Subtopic:  Resultant of Vectors |
82%
From NCERT
NEET - 2016
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Let $$\overrightarrow{\mathrm{C}}=\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}},$$ then:

 1 $$|\overrightarrow{\mathrm{C}}|$$ is always greater than $$|\overrightarrow{\mathrm{A}}|$$ 2 It is possible to have $$|\overrightarrow{\mathrm{C}}|<|\overrightarrow{\mathrm{A}}|$$ 3 $$|\overrightarrow{\mathrm{C}}|$$ is always equal to $$|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|$$ 4 $$|\overrightarrow{\mathrm{C}}|$$ is never equal to $$|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|$$
Subtopic:  Resultant of Vectors |
57%
From NCERT
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A particle starting from the origin $$(0,0)$$ moves in a straight line in the $$(x,y)$$ plane. Its coordinates at a later time are ($\sqrt{3}$, $$3).$$ The path of the particle makes an angle of __________ with the $$x$$-axis:
1. $$30^\circ$$
2. $$45^\circ$$
3. $$60^\circ$$
4. $$0$$

Subtopic:  Position & Displacement |
76%
From NCERT
AIPMT - 2007
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The position of a moving particle at time $$t$$ is $$\overrightarrow{r}=3\hat{i}+4t^{2}\hat{j}-t^{3}\hat{k}.$$ Its displacement during the time interval $$t=1$$ s to $$t=3$$ s will be:

 1 $$\hat{j}-\hat{k}$$ 2 $$3\hat{i}-4\hat{j}-\hat{k}$$ 3 $$9\hat{i}+36\hat{j}-27\hat{k}$$ 4 $$32\hat{j}-26\hat{k}$$
Subtopic:  Position & Displacement |
80%
From NCERT
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Three girls skating on a circular ice ground of radius $$200$$ m start from a point $$P$$ on the edge of the ground and reach a point $$Q$$ diametrically opposite to $$P$$ following different paths as shown in the figure. The correct relationship among the magnitude of the displacement vector for three girls will be:

1. $$A > B > C$$
2. $$C > A > B$$
3. $$B > A > C$$
4. $$A = B = C$$

Subtopic:  Position & Displacement |
84%
From NCERT
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A cat is situated at point $$A$$ ($$0,3,4$$) and a rat is situated at point $$B$$ ($$5,3,-8$$). The cat is free to move but the rat is always at rest. The minimum distance travelled by the cat to catch the rat is:
1. $$5$$ unit
2. $$12$$ unit
3. $$13$$ unit
4. $$17$$ unit

Subtopic:  Position & Displacement |
75%
From NCERT
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A particle is moving on a circular path of radius $$R.$$ When the particle moves from point $$A$$ to $$B$$ (angle $$\theta$$), the ratio of the distance to that of the magnitude of the displacement will be:

 1 $\frac{\mathrm{\theta }}{\mathrm{sin}\frac{\mathrm{\theta }}{2}}$ 2 $\frac{\mathrm{\theta }}{2\mathrm{sin}\frac{\mathrm{\theta }}{2}}$ 3 $\frac{\mathrm{\theta }}{2\mathrm{cos}\frac{\mathrm{\theta }}{2}}$ 4 $\frac{\mathrm{\theta }}{\mathrm{cos}\frac{\mathrm{\theta }}{2}}$ 
Subtopic:  Position & Displacement |
74%
From NCERT
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A particle is moving such that its position coordinates $$(x,y)$$ are $$(2$$ m, $$3$$ m) at time $$t=0,$$ $$(6$$ m, $$7$$ m) at time $$t=2$$ s and $$(13$$ m, $$14$$ m) at time $$t=5$$ s. Average velocity vector $$(v_{avg})$$ from $$t=0$$ to $$t=5$$ s is:

 1 $$\frac{1}{5}\left ( 13\hat{i}+14\hat{j} \right )$$ 2 $$\frac{7}{3}\left ( \hat{i}+\hat{j} \right )$$ 3 $$2\left ( \hat{i}+\hat{j} \right )$$ 4 $$\frac{11}{5}\left ( \hat{i}+\hat{j} \right )$$
Subtopic:  Speed & Velocity |
81%
From NCERT
NEET - 2014
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The position of a particle is given by;
$$\overrightarrow{r}=(3.0t\hat{i}-2.0t^{2}\hat{j}+4.0\hat{k})$$ m $\stackrel{}{\mathrm{}}$
where $$t$$ is in seconds and the coefficients have the proper units for $$r$$ to be in meters. The magnitude and direction of $$\overrightarrow{v}(t)$$ at $$t=1.0$$ s are:

 1 $$4$$ m/s, $$53^\circ$$ with $$x$$-axis 2 $$4$$  m/s, $$37^\circ$$ with $$x$$-axis 3 $$5$$ m/s, $$53^\circ$$ with $$y$$-axis 4 $$5$$  m/s, $$53^\circ$$ with $$x$$-axis
Subtopic:  Speed & Velocity |
67%
From NCERT
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