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The energy of ground electronic state of hydrogen atom is -13.6 eV. The energy of the first excited state will be:

A solid sphere, disc, and solid cylinder all of the same mass and made up of the same material are allowed to roll down (from rest) on an inclined plane, then:

The photon radiated from hydrogen corresponding to the second line of Lyman series is absorbed by a hydrogen-like atom X in the second excited state. As a result the hydrogen-like atom X makes a transition to nth orbit. Then:

Three objects, $A$ (a solid sphere), $B$ (a thin circular disk) and $C$ (a circular ring), each have the same mass $M$ and radius $R$. They all spin with the same angular speed about their own symmetry axes. The amount of work ($W$) required to bring them to rest, would satisfy the relation:

Which amine reacts with Hinsberg's reagent to produce an alkali insoluble product?

The total energy of an electron in the first excited state of hydrogen is about -3.4 eV. Its kinetic energy in this state is:

Point masses $m_1$ and $m_2$ are placed at the opposite ends of a rigid rod of length $L$ and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point P on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity $\omega_0$ is minimum, is given by:

A disc and a solid sphere of the same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

Dihedral angle of least stable conformer of ethane is :

A circular disk of moment of inertia $I_t$ is rotating in a horizontal plane, about its symmetry axis, with a constant angular speed $\omega_i$. Another disk of moment of inertia $I_b$ is dropped coaxially onto the rotating disk. Initially the second disk has zero angular speed. Eventually both the disks rotate with a constant angular speed $\omega_f$. The energy lost by the initially rotating disc to friction is:

Which of the following ecological pyramids is generally inverted?

What would be the torque about the origin when a force $3\hat{j} \text{ N}$ acts on a particle whose position vector is $2\hat{k} \text{ m}$?

A system consists of three masses $m_1$, $m_2$ and $m_3$ connected by a string passing over a pulley P. The mass $m_1$ hangs freely and $m_2$ and $m_3$ are on a rough horizontal table (the coefficient of friction = $\mu$). The pulley is frictionless and of negligible mass. The downward acceleration of mass $m_1$ is: (Assume $m_1=m_2=m_3=m$)

A force $\vec{F} = \alpha\hat{i} + 3\hat{j} + 6\hat{k}$ is acting at a point $\vec{r} = 2\hat{i} - 6\hat{j} - 12\hat{k}$. The value of $\alpha$ for which angular momentum is conserved about the origin is:

The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom if the coefficient of friction between the block and lower half of the plane is given by:

From a disc of radius $R$ and mass $M$, a circular hole of diameter $R$, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre?

A string is wrapped along the rim of a wheel of the moment of inertia $0.10 \text{ kg-m}^2$ and radius $10 \text{ cm}$. If the string is now pulled by a force of $10 \text{ N}$, then the wheel starts to rotate about its axis from rest. The angular velocity of the wheel after $2 \text{ s}$ will be:

The angular acceleration of a body moving along the circumference of a circle is:

Which one of the following vitamins is water-soluble?

A person of mass $60 \text{ kg}$ is inside a lift of mass $940 \text{ kg}$ and presses the button on the control panel. The lift starts moving upwards with an acceleration of $1.0 \text{ m/s}^2$. If $g=10 \text{ m/s}^2$, the tension in the supporting cable is: