Two particles \(\mathrm{X}\) and \(\mathrm{Y}\) having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radius \(R_1\) and \(R_2\) respectively. The mass ratio of \(\mathrm{X}\) and \(\mathrm{Y}\) is _______.

In a reflecting telescope, a secondary mirror is used to:

The electric field of an electromagnetic wave travelling through a medium is given by \(\overline{E}(x,t) = 25\ sin(2.0 \times 10^{15}t - 10^{7}x)\hat{n}\) then the refractive index of the medium is ___________.
(All given measurement are in SI units)

A thermally insulted vessel contains \(150\, g\) of water at \(0\,^oC\). Then the air from the vessel is pumped out a adiabatically. A fraction of water turns into ice and the rest evaporates at \(0\,^oC\) itself. The mass of evaporated water will be closes to ....... \(g\) (Latent heat of vaporization of water \(= 2.10 \times10^6\, Jkg^{-1}\) and Laten heat of Fusion of water \( = 3.36 \times10^5\,Jkg^{-1}\) )

The projectile motion of a particle of mass \(5\, g\) is shown in the figure. The initial velocity of the particle is \(5 \sqrt{2}\, ms ^{-1}\) and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points \(A\) and \(B\) is \(x \times 10^{-2}\, kgms ^{-1} .\) The value of \(x ,\) to the nearest integer, is ...... .

A galvanometer of resistance \(100 \Omega\) when connected in series with \(400 \Omega\) measures a voltage of upto \(10 \mathrm{~V}\). The value of resistance required to convert the galvanometer into ammeter to read upto \(10 \mathrm{~A}\) is \(\mathrm{x} \times 10^{-2} \Omega\). The value of \(\mathrm{x}\) is _______.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R .
Assertion A : If oxygen ion \(\left(\mathrm{O}^{-2}\right)\) and Hydrogen ion \(\left(\mathrm{H}^{+}\right)\)enter normal to the magnetic field with equal momentum, then the path of \(\mathrm{O}^{-2}\) ion has a smaller curvature than that of \(\mathrm{H}^{+}\).
Reason R : A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly.
In the light of the above statements, choose the correct answer from the options given below :

In a meter bridge experiment null point is obtained at \(40\, cm\) from one end of the wire when resistance \(X\) is balanced against another resistance \(Y\). If \(X < Y\), then the new position of the null point from the same end, if one decides to balance a resistance of \(3X\) against \(Y\), will be close to .............. \(cm\)

The angular frequency of alternating current in a \(L-C-R\) circuit is \(100\, rad / s\). The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.