IAT (IISER) 2026

The three numbers: (number of protons, number of neutrons, the radius) characterize a nucleus. What is the value of $\dfrac{r_1}{r_2}$ for two nuclei characterized by $(1, 0, r_1)$ and $(4, 4, r_2)$?

An experimental study of the photoelectric effect involves a metal of work function $\phi_0$. What is the smallest wavelength of the incident photon to photoemit an electron of mass $m$ which has the same de Broglie wavelength as that of th...

Consider normal incidence of a monochromatic beam of photons of power $P$ on a flat surface. Of the incident beam, 10% gets absorbed, 10% gets transmitted, and the rest is reflected by the flat surface. If $c$ is the speed of light, what is...

An exotic spherical jellyfish has a bulk modulus $B$. Close to the surface of the sea (depth $d=0$), its radius is $R$. When it dives to a depth $d$ ($d \gg R$), its radius is reduced by $\Delta R > 0$. Given the density of the incompressib...

A long solenoid of initial radius $R_0$ is put in a region of uniform magnetic field $\mathbf{B}$ with the axis of the solenoid aligned along the magnetic field. The solenoid is a part of a closed circuit that has no initial current running...

Three infinite plane sheets which have uniform positive surface charge densities $\sigma$, $\sigma$ and $2\sigma$, are arranged parallel to each other with a separation of $d$ as shown in the figure. A spherical Gaussian surface $S$ of radi...

A particle of mass $m_1$ and electric charge $q$ starts from rest under the influence of a uniform external electric field $\mathbf{E}$ to travel a distance $d$ in time $t_1$. If the particle had mass $m_2$, it would take time $t_2$ to trav...

A planet is revolving in a circular orbit with a time period $T$ around the center of a star solely under the gravity of the star. Suppose the distance between the star and the planet is halved. The individual radii of the star and the plan...

Consider two Carnot engines of efficiencies $\eta_1$ and $\eta_2$. The first engine absorbs heat $Q_1$ from a heat reservoir $A$ and releases heat $Q_2$ to a heat reservoir $B$. The second engine takes heat $Q_2$ from $B$ and releases heat ...

A jar is filled with two monoatomic non-interacting gases $A$ and $B$ with total masses $M_A$ and $M_B$, respectively. The molar mass of $A$ is double the molar mass of $B$. If the jar is kept at temperature $T$, what is the ratio of the to...

A spherical concave mirror of focal length 10 cm and a double convex lens of focal length 5 cm are arranged on the common principal axis as shown in the figure. A small object is placed on the principal axis between the focal points $F_1$ a...

The position of a particle of mass 1 kg at time $t$ is given by $\mathbf{r} = t\,\hat{i} + \hat{j} + 2t^2\,\hat{k}$, where $t$ is in seconds and the coefficients have the proper units for $\mathbf{r}$ to be in metres. What is the component ...

A simple pendulum of length $L$, mass $m$ and electric charge $q$ on its bob is oscillating with a time period $T$ under uniform gravity which is in the $-\hat{z}$ direction. Upon applying a uniform electric field $|E|\hat{n}$ (where $\hat{...

A sphere and a cube of equal masses on a horizontal frictionless floor, are confined between two vertical walls, as shown in the figure. The cube is attached to the wall by a massless spring. At the equilibrium position of the spring, the s...

The acceleration of a point particle is given by the equation$\dfrac{d^2\mathbf{x}}{dt^2} = \alpha \dfrac{\mathbf{x}}{|\mathbf{x}|^7} + \beta \dfrac{d\mathbf{x}}{dt}$where $\mathbf{x}$ denotes position and $t$ denotes time. Which of the fol...