Consider an electron in a hydrogen atom, revolving in its second excited state (having radius \(4.65\, \mathop A\limits^o \)). The de-Broglie wavelength of this electron is....\(\mathop A\limits^o \)

A mixture of hydrogen and oxygen has volume \(2000 \; cm ^{3}\), temperature \(300 \; K\), pressure \(100 \; kPa\) and mass \(0.76 \; g\) The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be

Water is flowing at a speed of \(1.5\, ms^{-1}\) through a horizontal tube of cross-sectional area  \(10^{-2}\, m^2\) and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm. the minimum force that you must exert should be ......... \(N\) (density of water \(= 10^3\, kgm^{-3}\))

A stone of mass \(900 \mathrm{~g}\) is tied to a string and moved in a vertical circle of radius \(1 \mathrm{~m}\) making \(10\  \mathrm{rpm}\). The tension in the string, when the stone is at the lowest point is _______. (if \(\pi^2=9.8\) and \(g=9.8 \mathrm{~m} / \mathrm{s}^2\) )

A capacitor of capacitance \(900\,\mu F\) is charged by a \(100\,V\) battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as \(x \times 10^{-2}\,J\). The value of \(x\) is \(..............\)

Arrange the four graphs in descending order of total work done; where \(W _{1}, W _{2}, W _{3}\) and \(W _{4}\) are the work done corresponding to figure \(a , b , c\) and d respectively.

A thin bar of length \(L\) has a mass per unit length \(\lambda \), that increases linearly with distance from one end. If its total mass is \(M\) and its mass per unit length at the lighter end is \(\lambda_0\), then the distance of the centre of mass from the lighter end is

Match List\(-I\) with List\(-II\)

List\(-I\)	List\(-II\)
\((a)\) Isothermal	\((i)\) Pressure constant
\((b)\) Isochoric	\((ii)\) Temperature constant
\((c)\) Adiabatic	\((iii)\) Volume constant
\((d)\) Isobaric	\((iv)\) Heat content is constant

Choose the correct answer from the options given below

A wire carrying current \(I\) is tied between points \(P\) and \(Q\) and is in the shape of a circular arc of radius \(R\) due to a uniform magnetic field \(B\) (perpendicular to the plane of the paper, shown by \(\times \times \times \)) in the vicinity of the wire. If the wire subtends an angle \(2\theta_0\) at the centre of the circle (of which it forms an arc) then the tension in the wire is

A circular coil having \(N\,turns\) and radius \(r\) carries a current. It is held in the \(XZ\) plane in a magnetic field \(B\hat i\) . The torque on the coil due to the magnetic field is

\(\sigma\) is the uniform surface charge density of a thin spherical shell of radius \(R\). The electric field at any point on the surface of the spherical shell is _______.

A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is \(y \pi \times 10^{-2} \mathrm{~s}\), where the value of \(y\) is ________.
(Acceleration due to gravity, \(g=10 \mathrm{~m} / \mathrm{s}^2\), density of water \(=10^3 \mathrm{~kg} / \mathrm{m}^3\) )

Vectors \(a \hat{i}+b \hat{j}+\hat{k}\) and \(2 \hat{i}-3 \hat{j}+4 \hat{k}\) are perpendicular to each other when \(3 a+2 b=7\), the ratio of a to \(b\) is \(\frac{x}{2}\). The value of \(x\) is \(..............\)