Past Years NEET

Unspecified year 13 questions

1. If vectors $\vec{A} = \cos \omega t\hat{i} + \sin \omega t\hat{j}$ and $\vec{B} = \cos (\omega t/2)\hat{i} + \sin (\omega t/2)\hat{j}$ are functions of time, then the value of t at which they are orthogonal to each other is:
2. The position vector of a particle $\vec{R}$ as a function of time is given by: $\vec{R} = 4 \sin (2\pi t)\hat{i} + 4 \cos (2\pi t)\hat{j}$,Where R is in meter, t in seconds and $\hat{i}$ and $\hat{j}$ denote unit vectors along x-and y-directions, respectively. Which one of the following statements is wrong for the motion of particle?
3. A ship A is moving Westwards with a speed of $10 km h^{-1}$ and a ship B 100 km South of A, is moving Northwards with a speed of $10 km h^{-1}$. The time after which the distance between them becomes shortest, is
4. A particle moves so that its position vector is given by $\vec{r} = \cos \omega t\hat{x} + \sin \omega t\hat{y}$. Where $\omega$ is a constant. Which of the following is true?
5. If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is:
6. The x and y coordinates of the particle at any time are $x = 5t - 2t^{2}$ and $y = 10t$ respectively, where x and y are in meters and t in seconds. The acceleration of the particle at $t = 2s$ is
7. The moment of the force, $\vec{F} = 4\hat{i} + 5\hat{j} - 6\hat{k}$ at (2,0,-3), about the point (2,-2,-2), is given by
8. When an object is shot from the bottom of a long smooth inclined plane kept at an angle $60^{\circ}$ with horizontal, it can travel a distance $x_{1}$ along the plane. But when the inclination is decreased to $30^{\circ}$ and the same object is shot with the same velocity, it can travel $x_{2}$ distance. Then $x_{1}$: $x_{2}$ will be:
9. A car starts from rest and accelerates at $5 m/s^{2}$. At $t = 4 s$, a ball is dropped out of a window by a person sitting in the car. What is the velocity and acceleration of the ball at $t = 6 s$? (Take $g = 10 m/s^{2}$)
10. A particle moving in a circle of radius R with a uniform speed takes a time T to complete one revolution. If this particle were projected with the same speed at an angle ' $\theta$ ' to the horizontal, the maximum height attained by it equals 4R. The angle of projection, $\theta$, is then given by:
11. A ball is projected with a velocity, $10 ms^{-1}$, at an angle of $60^{\circ}$ with the vertical direction. Its speed at the highest point of its trajectory will be:
12. The angular speed on a fly wheel moving with uniform angular acceleration changes from 1200rpm to 3120rpm in 16 seconds. The angular acceleration in $rad/s^{2}$ is:
13. A bullet is fired from a gun at the speed of $280 m s^{-1}$ in the direction $30^{\circ}$ above the horizontal. The maximum height attained by the bullet is ($g = 9.8 m s^{-2}$, $\sin 30^{\circ} = 0.5$)