List of practice Questions

The errors in the measurement of mass and length of the cube is $1.5%$ and $2.5%$ respectively. The percentage error in the measurement of density of a cube is

Water is flowing through a horizontal pipe of non-uniform cross-section. In the region of narrowest part inside the pipe, the water will have

A pendulum is oscillating with frequency $n$ on the surface of earth. It is taken to depth $\dfrac{R{2}$ below the surface of earth where $R$ is radius of earth. The new frequency of oscillations at depth $\dfrac{R}{2}$ is}

A stationary wave is formed having 4 nodes along the $120\,\text{cm$ length of the string. The wavelength of the wave is}

Two small drops of liquid of same radius coalesce to form a big drop. The ratio of the total surface energies after and before the change is

For a particle performing S.H.M., the displacement–time graph is as shown.

In biprism experiment, a source of monochromatic light is used for a certain distance between slit and eyepiece. When the distance between two virtual sources is changed from $d_A$ to $d_B$, then the fringe width is changed from $Z_A$ to $Z_B$. The ratio $Z_A$ to $Z_B$ is

A parallel beam of monochromatic light of wavelength $5\times10^{-7\,\text{m}$ is incident normally on a single narrow slit of width $10^{-3}\,\text{mm}$. At what angle of diffraction, the first minima is observed?}

Two identical thin bar magnets are placed mutually at right angles such that the north pole of one touches the south pole of the other. The length of each bar magnet is $\ell$. The magnitude of resultant magnetic moment of the system is
$\left[m = \text{pole strength of the magnet}\right]$

A string of mass $0.1\,\text{kg$ is under a tension $1.6\,\text{N}$. The length of the string is $1\,\text{m}$. A transverse wave starts from one end of the string. The time taken by the wave to reach the other end is}

Relative permeability of an iron is $5500$, then its magnetic susceptibility will be

The excess pressure inside a spherical drop of water is three times that of another drop of water. The ratio of their surface area is

Two concentric circular coils having radii $r_1$ and $r_2$ $(r_2 \ll r_1)$ are placed co-axially with centres coinciding. The mutual induction of the arrangement is (Both coils have single turn, $\mu_0$ = permeability of free space)

If the potential difference used to accelerate electrons is doubled, by what factor does the de-Broglie wavelength associated with the electrons change?

A solid sphere of mass $M$ and radius $R$ is rotating about its diameter. A disc of same mass and radius is also rotating about an axis passing through its centre and perpendicular to the plane but angular speed is twice that of the sphere. The ratio of kinetic energy of disc to that of sphere is

Two progressive waves $Y_1=\sin 2\pi\left(\dfrac{t}{4}-\dfrac{x}{4}\right)$ and $Y_2=\sin 2\pi\left(\dfrac{t}{4}+\dfrac{x}{4}\right)$ superpose to form a standing wave. $Y_1$ and $Y_2$ are in SI system. Amplitude of the particle at $x=0.5\,\text{m$ is}
$\left[\sin 45^\circ=\cos 45^\circ=\dfrac{1}{\sqrt{2}}\right]$

Earth revolves round the sun in a circular orbit of radius $R$. The angular momentum of the revolving earth is directly proportional to

Let the two forces have equal magnitude $A$. If the magnitude of the resultant is $\dfrac{2A{3}$, then the angle between those two forces is}

A graph of magnetic flux $\phi$ versus current $(I)$ is shown for four inductors A, B, C, D. Smaller value of self inductance is for inductor

The equation of a normal to the curve \[ x = 4\sec\theta,\qquad y = 4\tan^2\theta \] at \( \theta = \frac{\pi}{4} \) is

If the function \[ f(x)= \begin{cases} \dfrac{1-\sin2x+\cos2x}{1+\sin2x+\cos2x}, & x\neq \dfrac{\pi}{2}
k, & x=\dfrac{\pi}{2} \end{cases} \] is continuous at \( x=\dfrac{\pi}{2} \), then \( k \) is

Two spheres $S_1$ and $S_2$ have radii $R$ and $3R$, temperature $T$ K and $\dfrac{T{\sqrt{3}}$ K respectively. If they are coated with a material of same emissivity, rate of radiation of $S_1$ is $E$ then rate of radiation of $S_2$ is}

In the experiment to determine the internal resistance of a cell ($E_1$) using potentiometer, the resistance drawn from the resistance box is $R$. The potential difference across the balancing length of the wire is equal to the terminal potential difference $(V)$ of the cell. The value of internal resistance $(r)$ of the cell is

If \( \log_{10}\!\left(\dfrac{x^3-y^3}{x^3+y^3}\right)=2 \), then find \( \dfrac{dx}{dy} \).

If \( \vec{AB} = 3\hat{i} + 5\hat{j} + 4\hat{k} \), \( \vec{AC} = 5\hat{i} - 5\hat{j} + 2\hat{k} \) represent the sides of triangle \( ABC \), then the length of the median through \( A \) is