Two parallel long current carrying wire separated by a distance \(2 \mathrm{r}\) are shown in the figure. The ratio of magnetic field at \(\mathrm{A}\) to the magnetic field produced at \(C\) is \(\frac{x}{7}\). The value of \(x\) is _______.

Four particles \(A, B, C\) and \(D\) with masses \(m_A=m, m_B=2m, m_C=3m\) and \(m_D=4m\) are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is

For a nucleus \({ }_Z^A X\) having mass number \(A\) and atomic number \(Z\) \(A.\) The surface energy per nucleon \(\left(b_s\right)=a_1 A^{2 / 3}\) \(B.\) The Coulomb contribution to the binding energy \(b_c=-a_2 \frac{Z(Z-1)}{A^{4 / 3}}\) \(C.\) The volume energy \(b_v=a_3 A\) \(D.\) Decrease in the binding energy is proportional to surface area. \(E.\) While estimating the surface energy, it is assumed that each nucleon interacts with \(12\) nucleons, \(\left(a_1, a_2\right.\) and \(a _3\) are constants) Choose the most appropriate answer from the options given below:

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping the distance between wedge point and 200 gm weight as 25 cm. Initially the masses were not at balance. A beaker is placed beneath the unknown mass and water is added slowly to it. At given point the masses were in balance and half volume of the unknown mass was inside the water.
(Take the density of unknown mass is more than that of the water, the mass did not absorb water and water density is \(1 \mathrm{gm} / \mathrm{cm}^3\).) The unknown mass is ________ kg.

An oscillating \(LC\) circuit consists of a \(75\,mH\) inductor and a \(1.2\,\mu F\) capacitor. If the maximum charge to the capacitor is \(2.7\,\mu C\). The maximum current in the circuit will be \(...........\,mA\).

A concave mirror produces an image of an object such that the distance between the object and image is 20 cm . If the magnification of the image is ' -3 ', then the magnitude of the radius of curvature of the mirror is :

With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer is \((A)\) directly proportional to the length of the potentiometer wire \((B)\) directly proportional to the potential gradient of the wire \((C)\) inversely proportional to the potential gradient of the wire \((D)\) inversely proportional to the length of the potentiometer wire Choose the correct option for the above statements:

A Copper \((Cu)\) rod of length \(25\, {cm}\) and cross- sectional area \(3\, {mm}^{2}\) is joined with a similar Aluminium \((Al)\) rod as shown in figure. Find the resistance of the combination between the ends \(A\) and \(B\) (in \({m} \Omega\)) (Take Resistivity of Copper \(=1.7 \times 10^{-8}\, \Omega \,{m}\), Resistivity of Aluminium \(=2.6 \times 10^{-8}\, \Omega \,{m}\) )

If the foci of a hyperbola are same as that of the ellipse \(\frac{x^2}{9}+\frac{y^2}{25}=1\) and the eccentricity of the hyperbola is \(\frac{15}{8}\) times the eccentricity of the ellipse, then the smaller focal distance of the point \(\left(\sqrt{2}, \frac{14}{3} \sqrt{\frac{2}{5}}\right)\) on the hyperbola, is equal to

In the figure shown, a circuit contains two identical resistors with resistance \(R = 5\,\Omega \) and an inductance with \(L = 2\, mH\). An ideal battery of \(15\, V\) is connected in the circuit. What will be the current through the battery long after the switch is closed?......\(A\)

An organization awarded \(48\) medals in event '\(A\)',\(25\) in event '\(B\) ' and \(18\) in event ' \(C\) '. If these medals went to total \(60\) men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?

The energy equivalent of \(1 \mathrm{~g}\) of substance is _______.

Imagine that the electron in a hydrogen atom is replaced by a muon \((\mu) .\) The mass of muon particle is \(207\) times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be ............. \(eV\)