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: Statement \(I\) : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit \(\left( E _{1}\right)\) to higher energy orbit \(\left( E _{2}\right)\), is given as \(hf = E _{1}- E _{2}\). Statement \(II\) : The jumping of electron from higher energy orbit \(\left(E_{2}\right)\) to lower energy orbit \(\left(E_{1}\right)\) is associated with frequency of radiation given as \(f\) \(=\left( E _{2}- E _{1}\right) / h\) This condition is Bohr's frequency condition. In the light of the above statements, choose the correct answer from the options given below

In a physical balance working on the principle of moments, when \(5\, mg\) weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?

The electric current in a circular coil of \(2\) turns produces a magnetic induction \(B _{1}\) at its centre. The coil is unwound and is rewound into a circular coil of \(5\) turns and the same current produces a magnetic induction \(B _{2}\) at its centre.The ratio of \(\frac{ B _{2}}{ B _{1}}\) is.

The distance between an object and a screen is \(100\, cm .\) A lens can produce real image of the object on the screen for two different positions between the screen and the object. The distance between these two positions is \(40\, cm .\) If the power of the lens is close to \(\left(\frac{ N }{100}\right) D\) where \(N\) is an integer, the value of \(N\) is.......

The position vector of the centre of mass \(\vec r\, cm\) of an asymmetric uniform bar of negligible area of cross-section as shown in figure is

A train blowing a whistle of frequency \(320\,Hz\) approaches an observer standing on the platform at a speed of \(66\,m / s\). The frequency observed by the observer will be (given speed of sound \(=330\,ms ^{-1}\) ) \(.............Hz\).

For some \(\mathrm{a}, \mathrm{b}\), let \(f(x)=\left|\begin{array}{ccc}\mathrm{a}+\frac{\sin x}{x} & 1 & \mathrm{~b} \\ \mathrm{a} & 1+\frac{\sin x}{x} & \mathrm{~b} \\ \mathrm{a} & 1 & \mathrm{~b}+\frac{\sin x}{x}\end{array}\right|, x \neq 0, \lim _{x \rightarrow 0} f(x)=\lambda+\mu \mathrm{a}+\nu \mathrm{b}\). Then \((\lambda+\mu+v)^2\) is equal to :

If a radioactive element having half-life of \(30\,min\) is undergoing beta decay, the fraction of radioactive element remains undecayed after \(90\,min\). will be :

A cylindrical wire of radius \(0.5 \,mm\) and conductivity \(5 \times 10^{7}\, S / m\) is subjected to an electric field of \(10 \,mV / m .\) The expected value of current in the wire will be \(x ^{3} \,\pi mA\). The value of \(x\) is ......

The rate of growth of bacteria in a culture is proportional to the number of bacteris present and the bacteria count is \(1000\) at initial time \(t =0 .\) The number of bacteria is increased by \(20 \%\) in \(2\) hours. If the population of bacteria is \(2000\) after \(\frac{ k }{\log _{ e }\left(\frac{6}{5}\right)}\) hours, then \(\left(\frac{ k }{\log _{ c } 2}\right)^{2}\) is equal to

Consider a sphere of radius \(\mathrm{R}\) which carries a uniform charge density \(\rho .\) If a sphere of radius \(\frac{\mathrm{R}}{2}\) is carved out of it, as shown, the ratio \(\frac{\left|\overrightarrow{\mathrm{E}}_{\mathrm{A}}\right|}{\left|\overrightarrow{\mathrm{E}}_{\mathrm{B}}\right|}\) of magnitude of electric field \(\overrightarrow{\mathrm{E}}_{\mathrm{A}}\) and \(\overrightarrow{\mathrm{E}}_{\mathrm{B}}\) respectively, at points \(\mathrm{A}\) and \(\mathrm{B}\) due to the remaining portion is

For \(x \in R\) , \(f\left( x \right) = \left| {\log 2 - \sin x} \right|\) and \(g\left( x \right) = f\left( {f\left( x \right)} \right)\) then ..  .