A body is moving according to the equation $\mathrm{x}=\mathrm{at}+{\mathrm{bt}}^{2}-{\mathrm{ct}}^{3}$ where x = displacement and a, b and c are constants. The acceleration of the body is

(A)  $\mathrm{a}+2\mathrm{bt}$

(B)  $2\mathrm{b}+6\mathrm{ct}$

(C)  $2\mathrm{b}-6\mathrm{ct}$

(D)  $3\mathrm{b}-6{\mathrm{ct}}^{2}$

Concept Questions :-

Differentiation
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

A particle moves along X-axis in such a way 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

(A)  -5 m/s

(B)  6 m/s

(C)  3 m/s

(D)  3 m/s

Concept Questions :-

Differentiation
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

If the momentum of a particle is given by P=(180-8t) kg m/s, then its force will be

(A)  Zero

(B)  8 N

(C)  -8 N

(D)  4 N

Concept Questions :-

Differentiation
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

A particle moves along x-axis as $\mathrm{x}=4\left(\mathrm{t}-2\right)+\mathrm{a}{\left(\mathrm{t}-2\right)}^{2}$

Which of the following is true?

1.  The initial velocity of the particle is 4.

2.  The acceleration of the particle is 2a.

3.  The particle is at the origin at t=0.

4.  None of these

Concept Questions :-

Differentiation

Difficulty Level:

The maximum value of $7+6\mathrm{x}-9{\mathrm{x}}^{2}$ is

(A)  8

(B)  -8

(C)  4

(D)  -4

Concept Questions :-

Differentiation
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

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

Concept Questions :-

Differentiation
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

A particle is moving along x-axis. The velocity v of particle varies with its position x as $\mathrm{v}=\frac{1}{\mathrm{x}}$. Find velocity of particle as a function of time t given that at t=0, x=1 .

1.  $\mathrm{v}=\sqrt{2\mathrm{t}+1}$

2.  $\mathrm{v}=\frac{1}{\sqrt{2\mathrm{t}+1}}$

3.  $\mathrm{v}=\frac{1}{\mathrm{t}}$

4.  None of these

Concept Questions :-

Integration
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

A vector $\stackrel{\to }{\mathrm{A}}$ is directed along $30°$ west of north direction and another vector $\stackrel{\to }{\mathrm{B}}$ along $15°$ south of east. Their resultant cannot be in ____________ direction.

(A)  North

(B)  East

(C)  North-East

(D)  South

Concept Questions :-

Resultant of Vectors
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

ABCD is a quadrilateral. Forces  act at a point. Their resultant is

(A)

(B)

(C)  zero vector

(D)

Concept Questions :-

Resultant of Vectors
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

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 double then the resultant also doubles in magnitude. Find the angle between $\stackrel{\to }{\mathrm{P}}$ and $\stackrel{\to }{\mathrm{Q}}$.

(A)

(B)

(C)

(D)

Concept Questions :-

Resultant of Vectors