The equation of a wave travelling on a string is \(\mathrm{y}=\sin [20 \pi \mathrm{x}+10 \pi \mathrm{t}]\), where x and t are distance and time in SI units. The minimum distance between two points having the same oscillating speed is :

A series \(L C R\) circuit has \(L=0.01\,H, R=10\,\Omega\) and \(C =1\,\mu F\) and it is connected to ac voltage of amplitude \(\left( V _{ m }\right) 50\,V\). At frequency \(60 \%\) lower than resonant frequency, the amplitude of current will be approximately \(...............\,mA\)

A pole is vertically submerged in swimming pool, such that it gives a length of shadow \(2.15 \,m\) within water when sunlight is incident at an angle of \(30^{\circ}\) with the surface of water. If swimming pool is filled to a height of \(1.5\,m\), then the height of the pole above the water surface in centimetres is \(\left(\eta_W=4 / 3\right)........\)

If the wavelength of the first member of Lyman series of hydrogen is \(\lambda\). The wavelength of the second member will be _______.

A string \(A\) of length \(0.314\) m and Young's modulus \(2 \times 10^{10}\) N/m\(^2\) is connected to another string \(B\) of length and Young's modulus both twice of those of \(A\). This series combination of strings is then suspended from a rigid support and its free end is fixed to a load of mass \(0.8\) kg. The net change in length of the combination is _____ mm. (radius of both the strings is \(0.2\) mm and acceleration due to gravity \(= 10\) m/s\(^2\)) (Mass of both strings is to be neglected as compared to the mass of load)

The radius of third stationary orbit of electron for Bohr's atom is \(R\). The radius of fourth stationary orbit will be what?

Four bulbs \(B_1 , B_2, B_3\) and \(B_4\) of \(100\, W\) each are connected to \(220\, V\) main as shown in the figure. The reading in an ideal ammeter will be ............... \(A\)

In the given figure the magnetic flux through the loop increases according to the relation \(\phi_{B}(t)=10 t^{2}+20 t\), where \(\phi_{B}\) is in milliwebers and \(t\) is in seconds. The magnitude of current through \({R}=2 \,\Omega\) resistor at \({t}=5\, {s}\) is \(....\,{mA}\).

A spherical mirror is obtained as shown in the figure from a hollow glass sphere. If an object is positioned in front of the mirror, what will be the nature and magnification of the image of the object ? (Figure drawn as schematic and not to scale)

A rod of length \(50\,cm\) is pivoted at one end. It is raised such that if makes an angle of \(30^o\) fro the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal (in \(rad\,s^{-1}\) ) will be \((g = 10\,ms^{-2})\)