A particle moves in the XY plane and at time t is at the point whose coordinates are t2, t3-2t. Then at what instant of time, will its velocity and acceleration vectors be perpendicular to each other?

(1)  1/3 sec

(2)  2/3 sec

(3)  3/2 sec

(4)  never

Subtopic:  Scalar Product |
 61%
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints

A motor boat of mass m moving along a lake with velocity V0. 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? Hint: Fx=mVdVdx=-rV

(1)  mV0/r

(2)  3 mV0/2r

(3)  mV0/2r

(4)  2mV0/r

Subtopic:  Integration |
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints

A particle is moving along positive x-axis. Its position varies as x=t3-3t2+12t+20, where x is in meters and t is in seconds.

Velocity of the particle when its acceleration zero is

(1)  1 m/s

(2)  3 m/s

(3)  6 m/s

(4)  9 m/s

Subtopic:  Differentiation |
 71%
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints

Two forces F1=2i^+2j^ N and F2=3j^+4k^ N are acting on a particle.

The resultant force acting on particle is:

(A)  2i^+5j^+4k^

(B)  2i^-5j^-4k^

(C)  i^-3j^-2k^

(D)  i^-j^-k^

Subtopic:  Resultant of Vectors |
 84%
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints

A=4i+4j-4k and B=3i+j+4k, then angle between vectors A and B is:

(1)  180°

(2)  90°

(3)  45°

(4)  0°

Subtopic:  Resultant of Vectors |
 77%
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints

If vectors \(\overrightarrow{{A}}=\cos \omega t \hat{{i}}+\sin \omega t \hat{j}\) and \(\overrightarrow{{B}}=\cos \left(\frac{\omega t}{2}\right)\hat{{i}}+\sin \left(\frac{\omega t}{2}\right) \hat{j}\) are functions of time. Then, at what value of \(t\) are they orthogonal to one another?
1. \(t = \frac{\pi}{4\omega}\)
2. \(t = \frac{\pi}{2\omega}\)
3. \(t = \frac{\pi}{\omega}\)
4. \(t = 0\)

Subtopic:  Scalar Product |
 59%
From NCERT
NEET - 2015
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

Six vectors a through f have the magnitudes and directions indicated in the figure. Which of the following statements is true? 

1. b+c=f

2. d+c=f

3. d+e=f

4. b+e=f

Subtopic:  Resultant of Vectors |
 74%
From NCERT
AIPMT - 2010
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

A and B are two vectors and θ is the angle between them. If A×B=3A.B, then the value of θ will be:

1. 60o

2. 45o

3. 30o

4. 90o

Subtopic:  Scalar Product | Vector Product |
 80%
From NCERT
AIPMT - 2007
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh

If a curve is governed by the equation y=sinx, then the area enclosed by the curve and x-axis between x =0 and x =π is (shaded region) :

              

1. 1 unit

2. 2 units

3. 3 units

4. 4 units

Subtopic:  Integration |
 58%
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints

The acceleration of a particle starting from rest varies with time according to relation, a=α t+β. The velocity of the particle at time instant t is: (\(Here, a=\frac{dv}{dt}\))

1. αt2+βt

2. αt2+βt2

3. αt22+βt

4. 2αt2+βt

Subtopic:  Integration |
 85%
From NCERT
To view explanation, please take trial in the course.
NEET 2023 - Target Batch - Aryan Raj Singh
Hints
Links