A motor boat of mass m moving along a lake with velocity ${\mathrm{V}}_{0}$. At t=0, the engine of the boat is shut down. Magnitude of resistance force offered to the boat is equal to rV. (V is instantaneous speed). What is the total distance covered till it stops completely?

(A)  ${\mathrm{mV}}_{0}/\mathrm{r}$

(B)

(C)  ${\mathrm{mV}}_{0}/2\mathrm{r}$

(D)  $2{\mathrm{mV}}_{0}/\mathrm{r}$

Concept Questions :-

Integration
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A particle is moving along positive x-axis. Its position varies as $\mathrm{x}={\mathrm{t}}^{3}-3{\mathrm{t}}^{2}+12\mathrm{t}+20$, where x is in meters and t is in seconds.

Initial velocity of the particle is

(A)  1 m/s

(B)  3 m/s

(C)  12 m/s

(D)  20 m/s

Concept Questions :-

Differentiation
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A particle is moving along positive x-axis. Its position varies as $\mathrm{x}={\mathrm{t}}^{3}-3{\mathrm{t}}^{2}+12\mathrm{t}+20$, where x is in meters and t is in seconds.

Initial acceleration of the particle is

(A)  Zero

(B)

(C)

(D)

Concept Questions :-

Differentiation
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A particle is moving along positive x-axis. Its position varies as $\mathrm{x}={\mathrm{t}}^{3}-3{\mathrm{t}}^{2}+12\mathrm{t}+20$, where x is in meters and t is in seconds.

Velocity of the particle when its acceleration zero is

(A)  1 m/s

(B)  3 m/s

(C)  6 m/s

(D)  9 m/s

Concept Questions :-

Differentiation
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Two forces  and  are acting on a particle.

The resultant force acting on particle is:

(A)  $2\stackrel{^}{\mathrm{i}}+5\stackrel{^}{\mathrm{j}}+4\stackrel{^}{\mathrm{k}}$

(B)  $2\stackrel{^}{\mathrm{i}}-5\stackrel{^}{\mathrm{j}}-4\stackrel{^}{\mathrm{k}}$

(C)  $\stackrel{^}{\mathrm{i}}-3\stackrel{^}{\mathrm{j}}-2\stackrel{^}{\mathrm{k}}$

(D)  $\stackrel{^}{\mathrm{i}}-\stackrel{^}{\mathrm{j}}-\stackrel{^}{\mathrm{k}}$

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Two forces  and  are acting on a particle.

The angle between  is:

(A)  $\mathrm{\theta }={\mathrm{cos}}^{-1}\left(\frac{3}{2\sqrt{5}}\right)$

(B)  $\mathrm{\theta }={\mathrm{cos}}^{-1}\left(\frac{3}{5\sqrt{2}}\right)$

(C)  $\mathrm{\theta }={\mathrm{cos}}^{-1}\left(\frac{2}{3\sqrt{5}}\right)$

(D)  $\mathrm{\theta }={\mathrm{cos}}^{-1}\left(\frac{\sqrt{3}}{5}\right)$

Concept Questions :-

Resultant of Vectors
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Two forces  and  are acting on a particle.

The magnitude of the component of force ${\stackrel{\to }{\mathrm{F}}}_{1}$ along force ${\stackrel{\to }{\mathrm{F}}}_{2}$ is:

(A)  $\frac{5}{6}$

(B)  $\frac{5}{3}$

(C)  $\frac{6}{5}$

(D)  $\frac{5}{2}$

Concept Questions :-

Resultant of Vectors
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$\mathrm{A}=4\mathrm{i}+4\mathrm{j}-4\mathrm{k}$ and $\mathrm{B}=3\mathrm{i}+\mathrm{j}+4\mathrm{k}$, then angle between vectors A and B is:

(A)  $180°$

(B)  $90°$

(C)  $45°$

(D)  $0°$

Concept Questions :-

Resultant of Vectors
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A curve is governed by the equation y=sinx, then what is the area enclosed by the curve and x-axis between x =0 and x =$\mathrm{\pi }$ is (shaded region)

1. 1 units

2. 2 units

3. 3 units

4. 4 units

Concept Questions :-

Integration
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Calculate the area of disk of radius 'a' using integration

1. $\frac{{\mathrm{\pi a}}^{2}}{2}$

2. ${\mathrm{\pi a}}^{2}$

3. $\frac{3}{2{\mathrm{\pi a}}^{2}}$

4. $2{\mathrm{\pi a}}^{2}$

Concept Questions :-

Integration
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Difficulty Level: