List of practice Questions

A particle of mass $8~\mu g$ collides with another stationary particle of mass $4~\mu g$. If the collision is perfectly elastic and one dimensional, the ratio of de Broglie wavelengths after collision is
The difference between the frequencies of the first and second Lyman lines of hydrogen atom is (R - Rydberg constant and c - speed of light in vacuum)
If the half-life of a radioactive element is $12.5$ hours, then the time taken to disintegrate $256~g$ of the substance into $1~g$ is (in hours)
If 27 charged water droplets, each of radius $10^{-6~\text{m}$ and charge $10^{-12}~\text{C}$ coalesce to form a single spherical drop, then the potential of the big drop is}
A straight wire of resistance $18~\Omega$ is bent in the form of an equilateral triangle. The effective resistance between any two vertices of the triangle is
The power dissipated by a uniform wire of resistance $100~\Omega$ when a potential difference of $120~\text{V$ is applied across its ends is}
If a straight current-carrying wire of linear density $0.12~\text{kg/m$ is suspended in mid-air by a uniform horizontal magnetic field of $0.5~\text{T}$ normal to the length of the wire, then the current through the wire is (Neglect earth’s magnetic field)}
Two concentric loops $A$ and $B$ of same radius $2\pi~\text{cm$ are placed at right angles to each other. If the currents flowing through $A$ and $B$ are $3~\text{A}$ and $4~\text{A}$ respectively, then the net magnetic field at their common center is}
If a gas of volume $400~\text{cc$ at an initial pressure $P$ is suddenly compressed to $100~\text{cc}$, then its final pressure is (The ratio of specific heats $\gamma = 1.5$)}
A Carnot engine having efficiency $60%$ receives heat from a source at temperature $600~\text{K$. For the same sink temperature, to increase its efficiency to $80%$, the temperature of the source is}
A gaseous mixture consists of $2$ moles of oxygen and $4$ moles of argon at temperature $T$. Neglecting all vibrational modes, the total internal energy of the mixture is
The average translational kinetic energy of oxygen molecules at a temperature of $127^\circ\text{C$ is (Boltzmann constant $= 1.38 \times 10^{-23}~\text{J/K}$)}
The speed of a stationary wave represented by the equation $y = 0.75 \sin\left(\dfrac{7\pi}{4}x\right)\cos(350\pi t)$ is
For an observer on the earth, if a spectral line of wavelength $6600~\mathring{A$ emitted by a star is found to be redshifted by $22~\mathring{A}$, then the star is}
The kinetic energy of a particle executing simple harmonic motion at a displacement of $3~\text{cm$ from the mean position is $4~\text{mJ}$. If the amplitude of the particle is $5~\text{cm}$, then the maximum force acting on the particle is}
A body of mass $1~\text{kg$ is attached to the lower end of a vertically suspended spring of force constant $600~\text{N/m}$. If another body of mass $0.5~\text{kg}$ moving vertically upward hits the suspended body with a velocity $3~\text{m/s}$ and is embedded in it, then the frequency of the oscillation is}
When a wire of length $L$ clamped at one end is pulled by a force $F$ from the other end, its length increases by $L'$. If the radius and the applied force are halved, then the increase in its length is
A liquid drop of diameter $D$ splits into $3375$ small identical drops. If $S$ is the surface tension of the liquid, then the change in the surface energy in the process is
If a particle of mass 'm' covers half of the horizontal circle with constant speed 'v', then the change in its kinetic energy is
The bob of a simple pendulum of length $200~\text{cm}$ is released from horizontal position.
If $10%$ of its initial energy is lost to air resistance, then the speed of bob at the mean position is
(Acceleration due to gravity $= 10~\text{m/s}^2$)
A steel sphere of radius $1.2~\text{cm}$ collides with another steel sphere at rest.
If the collision is elastic and the first sphere moves with $\dfrac{7}{9}$ of its initial velocity after collision,
then the radius of the second sphere is
Ratio of angular velocity of hour hand of a watch and the angular velocity of rotation of earth is
Evaluate the integral \[ \int_{\frac{1}{2}}^{\frac{\sqrt{3}}{2}} \frac{1}{\left(x + \sqrt{1 - x^2}\right) \cdot \left(1 - x^2\right)} \, dx = \]
The area of the region (in sq. units) enclosed between the curves \( y = |x| \), \( y = [x] \) and the ordinates \( x = -1, x = 0, x = 1 \) is
The general solution of the differential equation \((x+2y)^3\frac{dy}{dx} = y = 0, y>0\) is