Physics, Chemistry, and Math Exam

The radius of curvature $r$ of a spherical convex mirror is related to its focal length $f$ by which of the following?

What quantity remains invariant when a longitudinal wave propagates through a medium, causing particles to execute simple harmonic oscillations?

An object of mass 5 kg is thrown vertically upwards. Air resistance provides a constant retarding force of 10 N. What is the ratio of ascent time to descent time? (Use $g = 10 m/s^2$)

Two temperature scales, P and Q, have a linear relationship. Scale P has 150 equal divisions and scale Q has 100 equal divisions between the upper and lower fixed points. The conversion formula is:

In a uranium radioactive series, $^{238}{92}U$ decays to $^{206}{82}Pb$. How many alpha and beta particles are emitted in this process?

A vessel contains 1 mole of oxygen and 2 moles of nitrogen at 300 K. What is the ratio of the average rotational kinetic energy per O₂ molecule to that per N₂ molecule?

Two organ pipes of the same length and material have different radii. When emitting fundamental notes, which statement is correct?

An electron moves along the x-axis with position $x = 20te^{-t}$ m, where t is in seconds. How far is the electron from the origin when it momentarily stops?

The electric potential at point P due to a point charge of $5 \times 10^{-9} C$ is 50 V. What is the distance of point P from the charge? (Assume $\frac{1}{4\pi\epsilon_0}=9 \times 10^9 Nm^2C^{-2}$)

In Young's double slit experiment, the intensity at a point is $\frac{1}{4}$ of the maximum intensity. What is the angular position of this point?

A projectile is launched at 30° from the horizontal with initial velocity 40 m/s. What is the velocity of the projectile at t = 2 s? (Given $g = 10 m/s^2$)

The displacement of a particle is $y = 3\cos(\frac{\pi}{4} - 2\omega t)$. What is the nature and period of the motion?

A monochromatic neon lamp with wavelength 670.5 nm illuminates a photo-sensitive material with stopping voltage 0.48 V. If the lamp is replaced with another source of wavelength 474.6 nm, what is the new stopping voltage?

A stone of mass $m$ is tied to a string of length $l$ and rotated in a circle at constant speed $v$. What is the torque on the stone?

An ideal spring with constant $\textit{k}$ is hung vertically, and mass $M$ is attached. When released with the spring unstretched, what is the spring's maximum extension?

If $E$, $L$, $M$, and $G$ denote energy, angular momentum, mass, and gravitational constant respectively, what is the dimension of $P$ in $P = EL^2M^{-5}G^{-2}$?

A 70 kg garden roller is pushed with a 200 N force at 30° to the horizontal. Given $g = 10 m/s^2$, what is the normal reaction on the roller?

A convex lens in contact with a concave lens has combined focal length 30 cm. The ratio of their powers is $\frac{2}{3}$. What are their focal lengths?

A capillary is dipped in a water vessel in a lift going up at 2$g$. The water will...

A particle moves under force $F = Cx$ from $\textit{x} = 0$ to $\textit{x} = x_1$. The work done is...

What is the apparent depth of a vessel of depth d which is half oil ($n_1$) and half water ($n_2$)?

One metallic sphere A receives positive charge and an identical sphere B receives identical negative charge. What happens?

An insect at the bottom of a hemispherical ditch of radius 1 m crawls upward, and slips after height $h$. If coefficient of friction is 0.75, what is $h$?

What is the equivalent capacitance of the given combination?

Eight drops of mercury with equal radii and charge combine into one big drop. How does the capacitance of the bigger drop compare?

A ball of mass \textit{M} strikes a ball of mass \textit{m} at rest. They separate perpendicularly. The impact coefficient \textit{e} is...

Pressure of gas changes liniarly with volume, from A to B. If no heat is extracted, change in internal energy is...

Ionization potential of hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are excited by monochromatic radiation of energy 12.1 eV. The spectral lines will be...

If two circular rings A and B are of the same mass, but having radii $r$ and $2r$. The moment of inertia of A compared to B is...

A planet having mass 9M and radius 4R, where \textit{M} and \textit{R} are mass/radius of earth, has an escape velocity in km/s...

In Wheatstone's bridge three resistances P, Q and R connected in the three arms and fourth is $S_1$ and $S_2$ is parallel. Condition for balance is...

The magnitude of the position vector of COM of a system with masses 1 kg and 3 kg having positon $\hat i+2\hat j+\hat k$ and $-3\hat i-2\hat j+\hat k$ is similar to...

$\textit{B}$= magnetic induction and R is the path radius, the energy of a charged particle coming out of a cyclotron is...

The intensity of a laser is 53.10 W/m². Find the amplitude of electric field.

The potential energy of a satellite of mass $m$ at height 6.4 x $10^6$ m from surface of earth is...

The frequency of revolution of an electron with energy 0.1 keV at a right angle to magnetic field of 1x$10^{-4}$ Wb/m² is...

An infinitely long cylinder is kept parallel to a uniform magnetic field. The direction of the induced current as seen from the z-axis is...

The magnetic flux linked with a vector area \textit{\textbf{A}} in a uniform magnetic field \textit{\textbf{B}} is...

A LCR circuit contains 110$\Omega$ and 220 V supply at 300 rad/s. if capacitance is removed, lags are 45°. If inductor is removed, lead are 45° . The rms current flowing is:

Two spheres have the same material, radius $R$ and $3R$, allowed to fall vertically through a liquid. Their velocity is...

In order for cooking the food, most suitable utensil would have