Temperature of a body varies with time as , where ${\mathrm{T}}_{0}$ is the temperature in Kelvin at , then the rate of change of temperature $\left(\frac{\mathrm{dT}}{\mathrm{dt}}\right)$ at  is-

1.

2.

3.

4.

Concept Questions :-

Differentiation
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Difficulty Level:

If the distance 's' travelled by a body in time 't' is given by $\mathrm{s}=\frac{\mathrm{a}}{\mathrm{t}}+{\mathrm{bt}}^{2}$ then the acceleration equals

(A)  $\frac{2\mathrm{a}}{{\mathrm{t}}^{3}}+2\mathrm{b}$

(B)  $\frac{2\mathrm{s}}{{\mathrm{t}}^{3}}$

(C)  $2\mathrm{b}-\frac{2\mathrm{a}}{{\mathrm{t}}^{3}}$

(D)  $\frac{\mathrm{s}}{{\mathrm{t}}^{2}}$

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Difficulty Level:

The velocity of a particle moving on the x-axis is given by $\mathrm{v}={\mathrm{x}}^{2}+\mathrm{x}$ where v is in m/s and x is in m. Find its acceleration in $\mathrm{m}/{\mathrm{s}}^{2}$ when passing through the point x=2m.

1.  0

2.  5

3.  11

4.  30

Concept Questions :-

Integration
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Difficulty Level:

A particle moves in the XY plane and at time t is at the point whose coordinates are . Then at what instant of time, will its velocity and acceleration vectors be perpendicular to each other?

(A)  1/3 sec

(B)  2/3 sec

(C)  3/2 sec

(D)  never

Concept Questions :-

Differentiation
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Difficulty Level:

A particle moves in the x-y plane with velocity ${\mathrm{v}}_{\mathrm{x}}=8\mathrm{t}-2$ and ${\mathrm{v}}_{\mathrm{y}}=2$. If it passes through the point x=14 and y=4 at t=2 sec. The equation of the path is

(A)  $\mathrm{x}={\mathrm{y}}^{2}-\mathrm{y}+2$

(B)  $\mathrm{x}=\mathrm{y}+2$

(C)  $\mathrm{x}={\mathrm{y}}^{2}+2$

(D)  $\mathrm{x}={\mathrm{y}}^{2}+\mathrm{y}+2$

Concept Questions :-

Integration
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Difficulty Level:

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

Difficulty Level:

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
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

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

Difficulty Level:

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

Difficulty Level:

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