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A bullet is fired from a gun at the speed of $280 \text{ m s}^{-1}$ in the direction $30^{\circ}$ above the horizontal. The maximum height attained by the bullet is: ($g=9.8 \text{ m s}^{-2}, \sin 30^{\circ}=0.5$)

The motion of a particle along a straight line is described by the equation x = 8 + 12t - t³, where x is in metre and t is in second. The retardation of the particle when its velocity becomes zero is:

If a ball is thrown vertically upwards with speed $u$, the distance covered during the last $t$ seconds of its ascent is

A body starts from rest from the origin with an acceleration of $6 \text{ m/s}^2$ along the $x$-axis and $8 \text{ m/s}^2$ along the $y$-axis. Its distance from the origin after $4 \text{ seconds}$ will be:

A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 s is s₁ and that covered in the first 20 s is s₂, then

The potential energy of a long spring when stretched by $2 \text{ cm}$ is $U$. If the spring is stretched by $8 \text{ cm}$, potential energy stored in it will be

A scooter accelerates from rest for time $t_1$ at constant rate $a_1$ and then retards at constant rate $a_2$ for time $t_2$ and comes to rest. The correct value of $\frac{t_1}{t_2}$ will be:

For the velocity-time graph shown in the figure, the distance covered by the body in the last two seconds of its motion is what fraction of the total distance covered by it in all the seven seconds?

A rocket is fired upward from the earth's surface such that it creates an acceleration of $19.6 \text{ m/s}^2$. If after $5 \text{ s}$ its engine is switched off, the maximum height of the rocket from the earth's surface would be:

The speed of a car as a function of time is shown in the figure. The distance travelled by the car in 8 s is:

The incorrect statement about the property of a Zener diode is:

Water drops fall at regular intervals from a tap which is $5 \text{ m}$ above the ground. The third drop is leaving the tap at the instant the first drop touches the ground. How far above the ground is the second drop at that instant?

A particle is thrown vertically upwards. If its velocity at half of the maximum height is $10 \text{ m/s}$, then maximum height attained by it is (Take $g = 10 \text{ m/s}^2$):

The effective acceleration of a body, when thrown upwards with acceleration $a$ (in a frame moving with acceleration $a$) will be:

A galvanometer has a coil of resistance $100\Omega$ and gives a full scale deflection for $30 \text{ mA}$ current. If it is to work as a voltmeter of $30\text{ V}$ range, the resistance required to be added will be

Velocity of a body on reaching the point from which it was projected upwards, is:

A body is thrown vertically up from the ground. It reaches a maximum height of $100 \text{ m}$ in $5 \text{ s}$. After what time will it reach the ground from the position of maximum height?

A $120 \text{ m}$ long train is moving in a direction with speed $20 \text{ m/s}$. A train B moving with $30 \text{ m/s}$ in the opposite direction and $130 \text{ m}$ long crosses the first train in a time:

A particle having a mass of $10^{-2}$ kg carries a charge of $5 \times 10^{-8}$ C. The particle is given an initial horizontal velocity of $10^5$ ms$^{-1}$ in the presence of electric field $\vec{E}$ and magnetic field $\vec{B}$. To keep the particle moving in a horizontal direction, it is necessary that: (1) $\vec{B}$ should be perpendicular to the direction of velocity and $\vec{E}$ should be along the direction of velocity. (2) Both $\vec{B}$ and $\vec{E}$ should be along the direction of velocity. (3) Both $\vec{B}$ and $\vec{E}$ are mutually perpendicular and perpendicular to the direction of velocity. (4) $\vec{B}$ should be along the direction of velocity and $\vec{E}$ should be perpendicular to the direction of velocity. Which one of the following pairs of statements are possible?

For a parallel beam of monochromatic light of wavelength $\lambda$, diffraction is produced by a single slit whose width $a$ is much greater than the wavelength of the light. If $D$ is the distance of the screen from the slit, the width of the central maxima will be: