# A child pulls a box with a force of  at an angle of $60°$above the horizontal. Then the horizontal <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> and vertical components of the force will be:                1. 100 N, 175 N 2.  86.6 N, 100 N   3.  100 N, 86.6 N 4. 100 N, 0 N

Subtopic:  Resolution of Vectors |
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A man rows a boat at a speed of  in the northwest direction. The shoreline makes an angle of $15°$ south of west. The component of the velocity of the boat along the shoreline is:

1.

2.

3.

4.

Subtopic:  Resolution of Vectors |
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The linear velocity of a rotating body is given by $\stackrel{\to }{\mathrm{v}}=\stackrel{\to }{\mathrm{\omega }}×\stackrel{\to }{\mathrm{r}}$, where $\mathrm{\omega }$ is the angular velocity and r is the radius vector. The angular velocity of a body, $\stackrel{\to }{\mathrm{\omega }}=\stackrel{^}{\mathrm{i}}-2\stackrel{^}{\mathrm{j}}+2\stackrel{^}{\mathrm{k}}$ and their radius vector is   will be:

1.

2.

3.

4.

Subtopic:  Vector Product |
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The displacement of a particle is given by $\mathrm{y}=\mathrm{a}+\mathrm{bt}+{\mathrm{ct}}^{2}-{\mathrm{dt}}^{4}$. The initial velocity and initial acceleration, respectively, are: ($$Given: v=\frac{dx}{dt}~and~a=\frac{d^2x}{dt^2}$$)

1.  b, -4d

2.  -d, 2c

3.  b, 2c

4.  2c, -4d

Subtopic:  Differentiation |
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The position x of the particle varies with time t as $\mathrm{x}={\mathrm{at}}^{2}-{\mathrm{bt}}^{3}$ The acceleration of the particle will be zero at a time equal to: ($$Given: a=\frac{d^2x}{dt^2}$$)

1.  $\frac{\mathrm{a}}{\mathrm{b}}$

2.  $\frac{2\mathrm{a}}{\mathrm{b}}$

3.  $\frac{\mathrm{a}}{3\mathrm{b}}$

4.  Zero

Subtopic:  Differentiation |
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A body is moving according to the equation $\mathrm{x}=\mathrm{at}+{\mathrm{bt}}^{2}-{\mathrm{ct}}^{3}$ where x represents displacement and a, b and c are constants. The acceleration of the body is: ($$Given: a=\frac{d^2x}{dt^2}$$)

1.  $\mathrm{a}+2\mathrm{bt}$

2.  $2\mathrm{b}+6\mathrm{ct}$

3.  $2\mathrm{b}-6\mathrm{ct}$

4.  $3\mathrm{b}-6{\mathrm{ct}}^{2}$

Subtopic:  Differentiation |
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A particle moves along the X-axis so that its X coordinate varies with time t according to the equation $\mathrm{x}=\left(2-5\mathrm{t}+6{\mathrm{t}}^{2}\right)\mathrm{m}$. The initial velocity of the particle is: ($$Given; v=\frac{dx}{dt}$$)

1.  -5 m/s

2.  6 m/s

3.  3 m/s

4.  4 m/s

Subtopic:  Differentiation |
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The maximum value of the function $7+6\mathrm{x}-9{\mathrm{x}}^{2}$ is:

1.  8

2.  -8

3.  4

4.  -4

Subtopic:  Differentiation |
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If $\mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^{2}-2\mathrm{x}+4$, then f(x) has:

1.  a minimum at x=1.

2.  a maximum at x=1.

3.  no extreme point.

4.  no minimum.

Subtopic:  Differentiation |
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The resultant of the forces $\stackrel{\to }{\mathrm{P}}$ and $\stackrel{\to }{\mathrm{Q}}$ is $\stackrel{\to }{\mathrm{R}}$. If $\stackrel{\to }{\mathrm{Q}}$ is doubled, then the resultant also doubles in magnitude. Find the angle between $\stackrel{\to }{\mathrm{P}}$ and $\stackrel{\to }{\mathrm{Q}}$.

1.

2.

3.

4.

Subtopic:  Resultant of Vectors |
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