List of practice Questions

Two strings of same material having lengths as $L$, $2L$ and radii $2r$, $r$ respectively, are vibrating in the fundamental mode. Tension applied to both the strings is same. The ratio of their respective fundamental frequencies is
If $T$ is the half-life of a radioactive substance, then its instantaneous rate of change of activity is proportional to
A wheel of radius $2\,\text{cm$ is at rest on the horizontal surface. A point $P$ on the circumference of the wheel is in contact with the horizontal surface. When the wheel rolls without slipping on the surface, the displacement of point $P$ after half rotation of wheel is}
A straight wire of length $0.5\,\text{m$ and carrying current of $1.2\,\text{A}$ is placed in a uniform magnetic field of induction $2\,\text{T}$. The magnetic field is perpendicular to the length of the wire. What is the force acting on the wire? $\left[\sin 90^\circ = 1\right]$}
An elastic material with Young's modulus $Y$ is subjected to a tensile stress $S$. The elastic energy stored per unit volume of the material will be
The resonant frequency of a series LCR circuit is $f$. The circuit is now connected to the sinusoidally alternating e.m.f. of frequency $2f$. The new reactances $X'_L$ and $X'_C$ are related as
A light ray of frequency $\nu$ and wavelength $\lambda$ enters a liquid of refractive index $\dfrac{3{2}$. The ray travels in the liquid with}
Two black spheres $P$ and $Q$ have radii in the ratio $3:2$. The wavelengths of maximum intensity radiation are in the ratio $3:4$ respectively. The ratio of radiated power by $P$ to $Q$ is
Two waves with same amplitude and frequency superpose at a point. The ratio of resultant intensities when they arrive in phase to that when they arrive $90^\circ$ out of phase is $\left[\cos \frac{\pi}{2} = 0\right]$
Under isothermal conditions, two soap bubbles of radii $r_1$ and $r_2$ coalesce to form a big drop. The radius of the big drop is
The region near the junction of an unbiased p-n junction diode is known as depletion layer. The layer is depleted of
A plane wavefront is incident on a water surface at an angle of incidence $60^\circ$ then it gets refracted at $45^\circ$. The ratio of width of incident wavefront to that of refracted wavefront will be
$\left[\sin \frac{\pi}{4} = \cos \frac{\pi}{4} = \frac{1}{\sqrt{2}}, \; \sin 60^\circ = \frac{\sqrt{3}}{2}, \; \cos 60^\circ = \frac{1}{2}\right]$
The resultant gate and its Boolean expression for the given circuit is
Three particles each of mass $m_1$ are placed at the corners of an equilateral triangle of side $L$. A particle of mass $m_2$ is placed at the midpoint of any one side of the triangle. Due to the system of particles the force acting on $m_2$ is (G = universal constant of gravitation)
When a mercury drop of radius $R$ breaks into $n$ droplets of equal size, the radius $r$ of each droplet is
Sensitivity of a given potentiometer can be decreased by
If $\lambda_1$ and $\lambda_2$ are the wavelengths of de-Broglie waves for electrons in first and second Bohr orbits in hydrogen atom, then $\left(\dfrac{\lambda_1}{\lambda_2}\right)$ is equal to (Energy in 1st Bohr orbit = $-13.6\,\text{eV}$)
In Searle's method to find Young's modulus of a wire, when a force of $1.5$ kg-wt is applied at its free end, the length of wire is $a$. When force of $2.5$ kg-wt is applied, the length of wire is $b$. What would be its original length?
Kirchhoff's current law and voltage law respectively are based on the law of conservation of
Focal length of a convex lens will be maximum for
An electromagnetic wave of wavelength $\lambda$ is incident on a photosensitive surface of negligible work function. If the photoelectrons emitted from this surface have the de-Broglie wavelength $\lambda_1$, then
A pipe open at both ends has length 1 m. The air column in the pipe cannot resonate for a frequency (Neglect end correction, speed of sound in air = 340 m/s)
The period of seconds pendulum on a planet, whose mass and radius are three times that of earth, is
If three vectors have equal magnitude i.e. $A = B = C$, then the angle between $\vec{A$ and $\vec{C}$ is $\alpha$. If $\vec{A} + \vec{B} + \vec{C} = 0$, then the angle between $\vec{A}$ and $\vec{C}$ is $\beta$, then $\dfrac{\alpha}{\beta}$ is}
If the Cartesian equation of the line is \[ x - 1 = 2y + 3 = 3 - z, \] then its vector equation is