A \(25\,cm\) long solenoid has radius \(2\,cm\) and \(500\) total number of turns. It carries a current of \(15\,A.\) If it is equivalent to a magnet of the same size and magnetization \(\vec M\) ( magnetic moment/ volume), then \(\left| {\vec M} \right|\)  is

The wavelength of light, while it is passing through water is 540 nm. The refractive index of water is \(\frac{4}{3}\).The wavelength of the same light when it is passing through a transparent medium having refractive index of \(\frac{3}{2}\) is __________ nm.

An inclined plane is bent in such a way that the vertical cross-section is given by \(y =\frac{ x ^{2}}{4}\) where \(y\) is in vertical and \(x\) in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction \(\mu=0.5,\) the maximum height in \(cm\) at which a stationary block will not slip downward is............\(cm\)

\(LED\) is constructed from \(Ga-As-P\) semiconducting material. The energy gap of this \(LED\) is \(1.9\, eV\). Calculate the wavelength of light emitted and its colour. \(\left[ h =6.63 \times 10^{-34} \;Js \right.\) and \(\left. c =3 \times 10^{8}\; ms ^{-1}\right]\)

A river of width 200 m is flowing from west to east with a speed of \(18 km / h\). A boat, moving with speed of \(36 km / h\) in still water, is made to travel one-round trip (bank to bank of the river). Minimum time taken by the boat for this journey and also the displacement along the river bank are _________ and _________ respectively.

A projectile is given an initial velocity of \((\hat i + 2\hat j)\ ms^{-1}\), where \(\hat i\) is along the ground and \(\hat j\) is along the vertical. If \(g = 10\ m/s^2\) , the equation of its trajectory is

The electric current in the circuit is given as \(i=i_{ o }(t / T)\). The r.m.s current for the period \(t=0\) to \(t=T\) is ___________

Three capacitors each of \(4\,\,\mu F\)  are to be connected in such a way that the effective capacitance is \(6\,\,\mu F.\)  This can be done by connecting thern

Two bodies are having kinetic energies in the ratio \(16: 9\). If they have same linear momentum, the ratio of their masses respectively is

A body \(A,\) of mass \(m=0.1\; kg\) has an initial velocity of \(3 \hat{\mathrm{i}}\; \mathrm{ms}^{-1} .\) It collides elastically with another body, \(\mathrm{B}\) of the same mass which has an initial velocity of \(5 \hat{\mathrm{j}} \;\mathrm{ms}^{-1}\). After collision. A moves with a velocity \(\overline{\mathrm{v}}=4(\hat{\mathrm{i}}+\hat{\mathrm{j}})\). The energy of \(\mathrm{B}\) after collision is written as \(\frac{\mathrm{x}}{10} \;\mathrm{J}\) The value of \(x\) is

In a double slit experiment, at a certain point on the screen the path difference between the two interfering waves is \(\frac{1}{8} ^{th}\) of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is

While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is \(1 \mathrm{~mm}\) and circular scale reading is equal to \(42\) divisions. Pitch of screw gauge is \(1 \mathrm{~mm}\) and it has \(100\) divisions on circular scale. The diameter of the wire is \(\frac{x}{50} \mathrm{~mm}\). The value of \(x\) is _______.