An electric field is given by \((6 \hat{i}+5 \hat{j}+3 \hat{k}) \ N / C\). The electric flux through a surface area \(30 \hat{\mathrm{i}}\; m^2\) lying in \(YZ-\)plane (in SI unit) is _______.

In Young's double slit experiment, monochromatic light of wavelength \(5000\) \(A\) is used. The slits are \(1.0 \mathrm{~mm}\) apart and screen is placed at \(1.0 \mathrm{~m}\) away from slits. The distance from the centre of the screen where intensity becomes half of the maximum intensity for the first time is _______ \(10^{-6} \mathrm{~m}\).

The amplitude of a particle executing \(SHM\) is \(3\,cm\). The displacement at which its kinetic energy will be \(25 \%\) more than the potential energy is: \(.............cm\).

In the reported figure of earth, the value of acceleration due to gravity is same at point \(A\) and \(C\) but it is smaller than that of its value at point \(B\) (surface of the earth). The value of OA \(: AB\) will be \(x : y .\) The value of \(x\) is \(\ldots \ldots \ldots\)

Two moles of helium are mixed with \(n\)  with moles of hydrogen. If \(\frac{{{C_P}}}{{{C_V}}}\, = \,\frac{3}{2}\)  for the mixture, then the value of \(n\)  is

A resistor develops \(300 \,J\) of thermal energy in \(15 \,s\), when a current of \(2\, A\) is passed through it. If the current increases to \(3 \,A\), the energy developed in \(10\,\,s\)  is........\(J.\)

For a certain metal, when monochromatic light of wavelength \(\lambda\) is incident, the stopping potential for photoelectrons is \(3V_0\). When the same metal is illuminated by light of wavelength \(2\lambda\), then the stopping potential becomes \(V_0\). The threshold wavelength for photoelectric emission for the given metal is \(\alpha\lambda\). The value of \(\alpha\) is _______.

A hemispherical vessel is completely filled with a liquid of refractive index \(\mu\). A small coin is kept at the lowest point \((\mathrm{O})\) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point E (at the level of the vessel) is _______.

A thin strip \(10\, cm\) long is on a \(U\) shaped wire of negligible resistance and it is connected to a spring of spring constant \(0.5\,Nm^{-1}\) (see figure). The assembly is kept in a uniform magnetic field of \(0.1\, T\). If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of \(e\) is \(N\). If the mass of the strip is \(50\, grams\), its resistance \(10\,\Omega \) and air drag negligible, \(N\) will be close to

When a polaroid sheet is rotated between two crossed polaroids then the transmitted light intensity will be maximum for a rotation of :