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If e, h, µ , and G denote electron charge, Plank's constant, permiability, and universal gravitational constant. Then write the product which gives speed of light in terms of dimensions.

On seeing a speed limit road sign, you apply brakes that bring your car from the speed of $30\text{m/s}$ to a speed of $20\text{m/s}$, covering a distance of $100\text{m}$ at a constant deceleration. How much time is required for the given decrease in speed?

A 10 cm long gas column is trapped by a 4 cm long column of mercury in a capillary tube, as shown below, when the tube is held horizontally in a room at an external pressure of 1 atm. The length of the air column when the tube is held vertically with the open end up is

Consider a uniformly charged ring of radius R. Find the point on the axis where the electric field is maximum.

A ball of mass $m$ is attached to one end of a light rod of length $l$, the other end being hinged. What minimum velocity $u$ should be imparted to the ball downwards, so that it can complete the circle?

The graph shown in the figure, represents the fall of temperature $\left(T\right)$ of two bodies $x$ and $y$ having the same surface area, with time $\left(t\right)$ due to radiation. Choose the correct relationship between emissive power $\left(E\right)$ and absorptive power $\left(a\right)$ of the two bodies.

The tidal waves in the sea are primarily due to

6 capacitors each of capacity $6\mu F$ are joined in 2 rows, each of 3 capacitors. The capacity of the combination is

If $\overrightarrow{R}=\overrightarrow{P}+\overrightarrow{Q}$, also $|\overrightarrow{R}|=25\text{N}$ and $|\overrightarrow{P}|=10\text{N}$. Find the angle $\theta$ made by $\overrightarrow{Q}$ with the positive x-axis.

In the given figure all the surfaces are smooth. Find the time taken by the block to reach from the free end to the pulley attached to the plank. Distance between free end and pulley is l.

A bob is hanging over a pulley inside a car through a string. The second end of the string is in the hand of a person standing in the car. The car is moving with constant acceleration $a$, directed horizontally as shown in figure. The other end of the string is being pulled with constant acceleration $a$ (relative to car) vertically downward. The tension in the string is equal to (assume $\theta$ remains constant)

In an NPN transistor circuit, the collector current is 10 mA. If 90% of the electrons emitted reach the collector, the emitter current (i_E) and base current (i_B) are given by

Water contained in a metallic water bottle is an example of:

Three solid spheres each of mass $m$ and diameter $d$ are stuck together such that the lines connecting the centres form an equilateral triangle of side of length $d$. The ratio $\frac{I_0}{I_A}$ of moment of inertia $I_0$ of the system about an axis passing the centroid and about centre of any of the spheres $I_A$ and perpendicular to the plane of the triangle, is:

A deuteron and an alpha particle, having equal kinetic energy , enter perpendicular into a magnetic field. Let $r_d$ and $r_{\alpha }$ be their respective radii of circular path. The value of $\frac{r_d}{r_{\alpha }}$ is equal to :

If $\overrightarrow{A}+\overrightarrow{B}$ is a unit vector along x - axis and $\overrightarrow{A}=\hat{i}-\hat{j}+\hat{k}$, then what is $\overrightarrow{B}$?

An electric motor exerts a force of 40 N on a cable and pulls it by a distance of 30 m in one minute. The power supplied by the motor (in Watts) is

A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength ${\lambda }_1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is ${\lambda }_2$. The ratio $\frac{{\lambda }_2}{{\lambda }_1}$ is

One end of a horizontal cylindrical glass rod $(\mu =1.5)$ of radius 5.0 cm is rounded in the shape of a hemisphere. An object 0.5 mm high is placed perpendicular to the axis of the rod at a distance of 20.0 cm from the rounded edge. Locate the image of the object and find its height.

State the underlying principle of a potentiometer. Write two factors by which current sensitivity of a potentiometer can be increased. Why is a potentiometer preferred over a voltmeter for measuring the emf of a cell?

Find the approximate volume of metal in a hollow spherical shell whose internal and external radii are 3 cm and 3.0005 cm, respectively.

Two metal rods $1$ and $2$ of same lengths have the same temperature difference between their ends. Their thermal conductivities are $K_1$ and $K_2$, and cross-sectional areas $A_1$ and $A_2$ respectively. If the rate of heat conduction in $1$ is four times that in $2$, then

A solid sphere of uniform density and radius 4 units is located with its centre at the origin O. Two spheres of equal radii 1 unit, with their centres at A (- 2, 0, 0) and B (2, 0, 0) respectively are taken out of the solid leaving behind spherical cavities as shown in the figure. Then choose the incorrect statement.

A tuning fork $A$ of unknown frequency produces $5\text{beats/s}$ with a fork of known frequency $340\text{Hz}$. When fork $A$ is filed, the beat frequency decreases to $2\text{beats/s}$. What is the frequency of fork $A$?

The de-Broglie wavelength of a vehicle is $\lambda$. Its load is changed such that its velocity and energy both are doubled. Its new wavelength will be

The wavelength of the first spectral line in the Balmer series of hydrogen atom is $6561\stackrel{\circ }{A}$. The wavelength of the second spectral line in the Balmer series of singly-ionized helium atom is

What is frame of reference