An electron is moving along the positive \(x\)-axis. If the uniform magnetic field is applied parallel to the negative \(z\)-axis. then \(A.\) The electron will experience magnetic force along positive \(y\)-axis \(B.\) The electron will experience magnetic force along negative \(y\)-axis \(C.\) The electron will not experience any force in magnetic field \(D.\) The electron will continue to move along the positive \(x\)-axis \(E.\) The electron will move along circular path in magnetic field Choose the correct answer from the options given below:

A sample contains \(10^{-2}\, kg\) each of two substances A and \(B\) with half lives \(4 \,s\) and \(8 \,s\) respectively. The ratio of then atomic weights is \(1: 2\) The ratio of the amounts of \(A\) and \(B\) after \(16 \,s\) is \(\frac{x}{100}\). the value of \(x\) is........

Two plane polarized light waves combine at a certain point whose electric field components are :
\(\begin{aligned} & \mathrm{E}_1=\mathrm{E}_0 \sin \omega \mathrm{t} \\ & \mathrm{E}_2=\mathrm{E}_0 \sin \left(\omega \mathrm{t}+\frac{\pi}{3}\right)\end{aligned}\)
Find the amplitude of the resultant wave.

A particle undergoing simple harmonic motion has time dependent displacement given by \(x(t)\, = \,A\,\sin \,\frac{{\pi t}}{{90}}\). The ratio of kinetic to potential energy \(o\) the particle at \(t=210\,s\) will be

You are asked to design a shaving mirror assuming that a person keeps it \(10\,cm\) from his face and views the magnified image of the face at the closest comfortable distance of \(25\,cm.\) The radius of curvature of the mirror would then be.....\(cm\)

The equilateral triangle \(ABC\) is cut from a thin solid sheet of wood. (See figure) \(D, E\) and \(F\) are the mid points of its sides as shown and \(G\) is the centre of the triangle. The moment of inertia of the triangle about an axis passing through \(G\) and perpendicular to the plane of the triangle is \(I_0.\) If the smaller triangle \(DEF\) is removed from \(ABC,\) the moment of inertia of the remaining figure about the same axis is \(I.\) Then

In a semiconductor p-n diode, the doping concentrations on p-side and n-side are \(10^{15}\text{ atoms/cm}^3\) and \(10^{18}\text{ atoms/cm}^3\), respectively. Which one of the following statements is true ?

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

Two resistances are given as \(R _1=(10 \pm 0.5)\,\Omega\) and \(R_2=(15 \pm 0.5)\, \Omega\). The percentage error in the measurement of equivalent resistance when they are connected in parallel is

Two planets have masses \(M\) and \(16\, M\) and their radii are \(a\) and \(2\, a\) respectively. The separation between the centres of the planets is \(10\, a.\) A body of mass \(m\) is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firing speed needed is

Let \(A=\{0,3,4,6,7,8,9,10\} \quad\) and \(R\) be the relation defined on A such that \(R =\{( x , y ) \in A \times A : x - y \quad\) is odd positive integer or \(x-y=2\}\). The minimum number of elements that must be added to the relation \(R\), so that it is a symmetric relation, is equal to \(...........\).

There are two identical chambers, completely thermally insulated from surroundings. Both chambers have a partition wall dividing the chambers in two compartments. Compartment \(1\) is filled with an ideal gas and Compartment \(3\) is filled with a real gas. Compartments \(2\) and \(4\) are vacuum . A small hole (orifice) is made in the partition walls and the gases are allowed to expand in vacuum Statement \(-1\) : No change in the temperature of the gas takes place when ideal gas expands in vacuum. However, the temperature of real gas goes down (cooling) when it expands in vacuum Statement \(-2\) : The internal energy of an ideal gas is only kinetic. The internal energy of a real gas is kinetic as well as potential

The displacement of simple harmonic oscillator after \(3\) seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is \(\dots \; s\)