As per the given circuit, the value of current through the battery will be \(\dots \; A\).

Consider a water tank as shown in the figure. It's cross-sectional area is \(0.4\, m ^{2}\). The tank has an opening \(B\) near the bottom whose cross-section area is \(1\, cm ^{2}\). A load of \(24\, kg\) is applied on the water at the top when the height of the water level is \(40\, cm\) above the bottom, the velocity of water coming out the opening \(B\) is \(v\, ms ^{-1}\). The value of \(v\), to the nearest integer, is ......\(m/s\). [Take value of \(g\) to be \(10 \,ms ^{-2}\) ]

A Zener of breakdown voltage \(V_{z}=8\,V\) and maximum zener current, \(I _{ ZM }=10\,mA\) is subjected to an input voltage \(V _{ i }=10\,V\) with series resistance \(R=100\,\Omega\). In the given circuit \(R_{L}\) represents the variable load resistance. The ratio of maximum and minimum value of \(R_{L}\) is

Half lives of two radioactive nuclei \(A\) and \(B\) are \(10\, minutes\) and \(20\, minutes\), respectively. If, initially a sample has equal number of nuclei, then after \(60\) \(minutes\) , the ratio of decayed numbers of nuclei \(A\) and \(B\) will be

If \(\vec{E}\) and \(\vec{K}\) represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by : \((\omega-\) angular frequency) :

Consider the efficiency of Carnot's engine is given by \(\eta=\frac{\alpha \beta}{\sin \theta} \log _{e} \frac{\beta x}{k T}\), where \(\alpha\) and \(\beta\) are constants. If \(T\) is temperature, \(k\) is Boltzman constant, \(\theta\) is angular displacement and \(x\) has the dimensions of length. Then, choose the incorrect option.

A parallel plate capacitor with plate area \(A\) and plate separation \(d =2 \,m\) has a capacitance of \(4 \,\mu F\). The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant \(K =3\) (as shown in figure) will be .........\( \mu \,F\)

A uniform electric field of \(10\,N / C\) is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy \(0.5\,eV\). The length of each plate is \(10\,cm\). The angle \((\theta)\) of deviation of the path of electron as it comes out of the field is  \(.........\)(in degree).

Consider a mixture of gas molecule of types \(A, B\) and \(C\) having masses \(m_{A}\,<\,m_{B}\,<\,m_{C}\) ratio of their root mean square speeds at normal temperature and pressure is :

A particle is moving \(5\) times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is \(1.878 \times 10^{-4}\). The mass of the particle is close to

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The Bohr model is applicable to hydrogen and hydrogen-like atoms only.
Reason R : The formulation of Bohr model does not include repulsive force between electrons.
In the light of the above statements, choose the correct answer from the options given below :

The de-Broglie wavelength of a particle having kinetic energy \(E\) is \(\lambda\). How much extra energy must be given to this particle so that the de-Broglie wavelength reduces to \(75 \,\%\) of the initial value ?

In a Young's double slit experiment set up, the two slits are kept 0.4 mm apart and screen is placed at 1 m from slits. If a thin transparent sheet of thickness \(20 \mu m\) is introduced in front of one of the slits then centre bring fringe shifts by 20 mm on the screen. The refractive index of transparent sheet is given by \(\frac{\alpha}{10}\), where \(\alpha\) is _________ .