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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:

In an experiment, four quantities $a$, $b$, $c$ and $d$ are measured with percentage error $1\%$, $2\%$, $3\%$ and $4\%$ respectively. Quantity $P$ is calculated as follows: $P=\frac{a^3b^2}{cd}$. Percentage error in $P$ is:

If $n_1, n_2$ and $n_3$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by

In which of the following devices, the eddy current effect is not used?

Two point charges A and B, having charges +Q and −Q respectively, are placed at a certain distance apart and the force acting between them is F. If 25% charge of A is transferred to B, then the force between the charges becomes:

The current in an inductor of self-inductance $4 \text{ H}$ changes from $4 \text{ A}$ to $2 \text{ A}$ in $1 \text{ s}$. The emf induced in the coil is:

Dimensional formula for volume elasticity is

What is the flux of electric field $\vec{E} = 3 \times 10^3 \hat{i}$ N/C through a square of 10 cm on a side whose plane is parallel to the yz-plane?

A point charge +10 μC is at a distance 5 cm directly above the centre of a square of side 10 cm, as shown in the figure. What is the magnitude of the electric flux through the square?

Each of the two strings of lengths $51.6 \text{ cm}$ and $49.1 \text{ cm}$ is tensioned separately by $20 \text{ N}$ of force. The mass per unit length of both strings is the same and equals $1 \text{ g/m}$. When both the strings vibrate simultaneously, the number of beats is:

The force between two small charged spheres having charges of $2 \times 10^{-7}$ C and $3 \times 10^{-7}$ C placed 30 cm apart in the air is:

The velocity $v$ of a particle at time $t$ is given by $v = at + \frac{b}{t+c}$, where $a$, $b$ and $c$ are constants. The dimensions of $a$, $b$ and $c$ are respectively:

Which one has the dimensions different from the remaining three?

Six charges +q, -q, +q, -q, +q and -q are fixed at the corners of a hexagon of side d as shown in the figure. The work done in bringing a charge q₀ to the centre of the hexagon from infinity is: (ε₀ - permittivity of free space)

pH of a saturated solution of $Ca(OH)_2$ is 9. The solubility product ($K_{sp}$) of $Ca(OH)_2$ is:

A tuning fork with a frequency of $800 \text{ Hz}$ produces resonance in a resonance column tube with the upper end open and the lower end closed by the water surface. Successive resonances are observed at lengths of $9.75 \text{ cm}$, $31.25 \text{ cm}$, and $52.75 \text{ cm}$. The speed of the sound in the air is:

Taking into account the significant figures, what is the value of $9.99\text{ m} - 0.0099\text{ m}$?

Of the following quantities, which one has dimensions different from the remaining three?

In the above diagram, a strong bar magnet is moving towards solenoid-2 from solenoid-1. The direction of induced current in solenoid-1 and that in solenoid-2, respectively, are through the directions:

A body of mass $1\text{ kg}$ is thrown upwards with a velocity $20\text{ ms}^{-1}$. It momentarily comes to rest after attaining a height of $18\text{ m}$. How much energy is lost due to air friction? ($g=10\text{ ms}^{-2}$)