A charge particle moving in magnetic field \(B\), has the components of velocity along \(B\) as well as perpendicular to \(B\). The path of the charge particle will be

Six point charges are kept \( 60^{\circ} \) apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the centre of the circle is __________ .
(\( \epsilon \) is permittivity of free space)

The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is \(I_{1}\). The same rod is bent into a ring and its moment of inertia about a diameter is \(I _{2}\). If \(\frac{ I _{1}}{ I _{2}}\) is \(\frac{ x \pi^{2}}{3}\), then the value of \(x\) will be ...............

As per the given figure, two plates \(A\) and \(B\) of thermal conductivity \(K\) and \(2 K\) are joined together to form a compound plate. The thickness of plates are \(4.0 \,cm\) and \(2.5 \,cm\) respectively and the area of cross-section is \(120 \,cm ^{2}\) for each plate. The equivalent thermal conductivity of the compound plate is \(\left(1+\frac{5}{\alpha}\right) K\), then the value of \(\alpha\) will be_______

In an experiment, brass and steel wires of length \(1\,m\) each with areas of cross section \(1\,mm^2\) are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress requires to produced a new elongation of \(0.2\,mm\) is [Given, the Young’s Modulus for steel and brass are respectively \(120\times 10^9\,N/m^2\) and \(60\times 10^9\,N/m^2\) ]

The drift velocity of electrons for a conductor connected in an electrical circuit is \(V _{ d }\). The conductor in now replaced by another conductor with same material and same length but double the area of cross section. The applied voltage remains same. The new drift velocity of electrons will be

In the circuit shown, a four wire potentiometer is made of a \(400\, cm\) long wire, which extends between \(A\) and \(B\). The resistance per unit length of the potentiometer wire is \(r = 0.01\, \Omega /cm\). If an ideal voltmeter is connected as shown with jockey \(J\) at \(50\, cm\) from end \(A\), the expected reading of the voltmeter will be: ............... \(V\)

A teacher in his physics laboratory allotted an experiment to determine the resistance \((G)\) of a galvanometer. Students took the observations for \(\frac{1}{3}\) deflection in the galvanometer. Which of the below is true for measuring value of \(G\) \(?\)

Amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass \(=500\, g\), Decay constant \(=20 \,g / s\) then ...... \(s\) time is required for the amplitude of the system to drop to half of its initial value ? \((\ln 2=0.693)\)

The Boolean expression \(\mathrm{Y}=\mathrm{A} \overline{\mathrm{B}} \mathrm{C}+\overline{\mathrm{A}} \overline{\mathrm{C}}\) can be realised with which of the following gate configurations.
A. One 3-input AND gate, 3 NOT gates and one 2input OR gate, One 2-input AND gate,
B. One 3-input AND gate, 1 NOT gate, One 2input NOR gate and one 2-input OR gate
C. 3-input OR gate, 3 NOT gates and one 2-input AND gate
Choose the correct answer from the options given below.

A ray of light passing through a prism \((\mu=\sqrt{3})\) suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is ..... . (in degrees)