A series \(L C R\) circuit with \(L=\frac{100}{\pi} \mathrm{mH}, C=\frac{10^{-3}}{\pi} \mathrm{F}\) and \(R=10 \Omega\), is connected across an ac source of \(220 \mathrm{~V}, 50 \mathrm{~Hz}\) supply. The power factor of the circuit would be___________.

A Carnot engine operates between two reservoirs of temperatures \(900\; \mathrm{K}\) and \(300 \;\mathrm{K}\) The engine performs \(1200\; \mathrm{J}\) of work per cycle. The heat energy (in \(\mathrm{J}\) ) delivered by the engine to the low temperature reservoir, in a cycle. is

A \(27\, mW\) lager beam has a cross -sectional area of \(10\, mm^2\). The magnitude of the maximum electric field in this electromagnetic wave is given by:........\(kV/m\) [Given permittivity of space \({ \in _0} = 9 \times {10^{ - 12}}\, SI\, units\), speed of light \(c = 3 \times 10^8\, m/s\)]

A bicycle tyre is filled with air having pressure of \(270\,kPa\) at \(27^{\circ}\,C\). The approximate pressure of the air in the tyre when the temperature increases to \(36^{\circ}\,C\) is \(............kPa\)

The output of the circuit is low (zero) for:

(A) \(\mathrm{X}=0, \mathrm{Y}=0\)
(B) \(X=0, Y=1\)
(C) \(X=1, Y=0\)
(D) \(\mathrm{X}=1, \mathrm{Y}=1\)
Choose the correct answer from the options given below :

An \(AC\) source is connected to an inductance of \(100\,mH\) a capacitance of \(100\,\mu F\) and a resistance of \(120\,\Omega\) as shown in figure. The time in which the resistance having a thermal capacity \(2\,J^{\circ } C\) will get heated by \(16^{\circ} C\) is ..........\(S\)

In the hydrogen atom, the electron makes a transition from the higher orbit (\(i\)) to a lower orbit (\(f\)). The ratio of the radius of the orbits in given by \(r_i : r_f = 16 : 4\). The wavelength of photon emitted due to this transition is _____ nm.
(Given Rydberg constant \(= 1.0973 \times 10^7\) /m)

Two slabs with square cross section of different materials \((1,2)\) with equal sides \((l)\) and thickness \(\mathrm{d}_1\) and \(\mathrm{d}_2\) such that \(\mathrm{d}_2=2 \mathrm{~d}_1\) and \(l \gt \mathrm{d}_2\). Considering lower edges of these slabs are fixed to the floor, we apply equal shearing force on the narrow faces. The angle of deformation is \(\theta_2=2 \theta_1\). If the shear moduli of material 1 is \(4 \times 10^9 \mathrm{~N} / \mathrm{m}^2\), then shear moduli of material 2 is \(\mathrm{x} \times 10^9 \mathrm{~N} / \mathrm{m}^2\), where value of \(x\) is ________.

In a double slit experiment, when one of the slits is covered by a transparent mica sheet of refractive index \(1.56\), the central fringe shifts to the position of \(7^{th}\) bright fringe, obtained with both slits uncovered. If the light source wavelength is \(450\) nm, the thickness of mica sheet is \(\alpha \times 10^{-9}\) m. The value of \(\alpha\) is ______.

At room temperature \(\left(27^{\circ} \mathrm{C}\right)\), the resistance of a heating element is \(50 \Omega\). The temperature coefficient of the material is \(2.4 \times 10^{-4}{ }^{\circ} \mathrm{C}^1\). The temperature of the element, when its resistance is \(62 \Omega\) is _______ \({ }^{\circ} \mathrm{C}\).

A mass of \(50\,g\) of water in a closed vessel, with surroundings at a constant temperature takes \(2\, minutes\) to cool from \(30\,^oC\) to \(25\,^oC\). A mass of \(100\,g\) of another liquid in an identical vessel with identical surroundings takes the same time to cool from \(30\,^oC\) to \(25\,^o C\). The specific heat of the liquid is .......... \(kcal/kg\) (The water equivalent of the vessel is \(30\,g\).)

de-Broglie wavelength of an electron accelerated by a voltage of \(50\,\,V\) is close to ............. \(\mathop {\rm{A}}\limits^o \)  \((\left| e \right| = 1.6 \times {10^{ - 19}}\,\,C,\,\,{m_e} = 9.1 \times {10^{ - 31}}\,kg,\,\,h = 6.6 \times {10^{ - 34}}\,\,Js)\)