Proton \((P)\) and electron \((e)\) will have same deBroglie wavelength when the ratio of their momentum is (assume, \(m _{ p }=1849\,m _{ e }\))

An inductor of \(0.5\,mH\), a capacitor of \(20\,\mu\,F\) and resistance of \(20\,\Omega\) are connected in series with a \(220\,V\) ac source. If the current is in phase with the emf, the amplitude of current of the circuit is \(\sqrt{x} A\). The value of \(x\) is -

As shown in the figure, a particle of mass \(10\) \(kg\) is placed at a point \(A\). When the particle is slightly displaced to its right, it starts moving and reaches the point \(B\). The speed of the particle at \(B\) is \(x\, m / s\). (Take \(\left. g =10\, m / s ^{2}\right)\) The value of \('x'\) to the nearest integer is.........

A plane electromagnetic wave propagating in \(\mathrm{x}\)-direction is described by \(\mathrm{E}_{\mathrm{y}}=\left(200\  \mathrm{Vm}^{-1}\right) \sin \left[1.5 \times 10^7 \mathrm{t}-0.05\  \mathrm{x}\right] \text {; }\) The intensity of the wave is :(Use \(\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}\) )

A parallel plate capacitor has capacitance C , when there is vacuum within the parallel plates.
A sheet having thickness \(\left(\frac{1}{3}\right)^{ rd }\) of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is :

A small square loop of side \('a'\) and one turn is placed inside a larger square loop of side \({b}\) and one turn \((b \gg a)\). The two loops are coplanar with thei centres coinciding. If a current \(I\) is passed in the square loop of side \('b',\) then the coefficient of mutual inductance between the two loops is

A charge \(q\)  is spread uniformly over an insulated loop of radius \(r\) . If it is rotated with an angular velocity \(\omega \) with respect to normal axis then the magnetic moment of the loop is

In an ammeter, \(5 \%\) of the main current passes through the galvanometer. If resistance of the galvanometer is G, the resistance of ammeter will be _______.

Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is \(V\). The potential difference between the points A and B (shown in the figure) is :

The de Broglie wavelengths of a proton and an \(\alpha\) particle are \(\lambda\) and \(2 \lambda\) respectively. The ratio of the velocities of proton and \(\alpha\) particle will be _______.

The disc of mass \(M\) with uniform surface mass density \(\sigma\) is shown in the figure. The centre of mass of the quarter disc (the shaded area) is at the position \(\frac{x}{3} \frac{a}{\pi}, \frac{x}{3} \frac{a}{\pi}\) where \(x\) is ....... . (Round off to the Nearest Integer) \([ a\) is an area as shown in the figure \(]\)

A car accelerates from rest at a constant rate \(\alpha\) for some time after which it decelerates at a constant rate \(\beta\) to come to rest. If the total time elapsed is \(t\) seconds, the total distance travelled is

The output of the given combination gates represents