Physics

A radioactive simple is undergoing decay. At any time t₁, its activity is A and another time t₂, the activity is $\frac{A}{5}.$ What is the average life time for the sample?

The length of metallic wire is ${\mathcal{l}}_1$ when tension in it is $T_1$ . It is ${\mathcal{l}}_2$ when the tension is T₂. The original length of the wire will be

The trajectory of a projectile in an vertical plane is y = ax - bx², where a and b are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection q and the maximum height attained H are respectively given by

A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and the moment of inertial about it is I. A weight mg is attached to the cord at the end. The weight falls from rest. After falling through a distance 'h', the square of angular velocity of wheel will be

Two charged thin infinite plane sheets of uniform surface charge density ${\sigma }_{+}$ and ${\sigma }_{-}$ , where $\left|{\sigma }_{+}\right|>\left|{\sigma }_{-}\right|$ , intersect at right angle. Which of the following best represents the electric field lines for this system.

A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer G attached across the coil?

Three positions shown describe:

(a) The magnet's entry

(b) Magnet is completely inside and

(c) Magnet's exit

An infinitely long hollow conducting cylinder with radius R carries a uniform current along its surface. Choose the correct representation of magnetic field (B) as a function of radial distance (r) from the axis of cylinder.

Match the $C_p/C_V$ ratio for ideal gases with different type of molecules:

Match the correct option?

A two point charges $4q$ and $-q$ are fixed on the $x$ -axis at $x=-\frac{d}{2}$ and $x=\frac{d}{2}$ , respectively. If a third point charge ' $q$ ' is taken from the origin to $x=d$ along the semicircle as shown in the figure, the energy of the charge will:

Take the breakdown voltage of the zener diode used in the given circuit as $6\mathrm{V}$ . For the input voltage shown in figure below, the time variation of the output voltage is: (Graphs drawn are schematic and not to scale)