List of top Questions asked in IISER

Which of the following schematics correctly depict a lac operon that can be negatively regulated?

Which one of the following correctly describes the sequence of events leading to muscle contraction following acetylcholine release at the neuromuscular junction?

Which one of the following is the correct sequence of the coding strand of the given gene?

If cell wall was used as the only criterion for classifying organisms, then Mycoplasma would have belonged to which one of the following groups?

Which one of the following correctly describes the mode of action of Follicle Stimulating Hormone (FSH) and estrogen?

The pBR322 cloning vector has genes coding for tetracycline and ampicillin resistance. A foreign DNA to be cloned is inserted into the tetracycline resistance gene and the recombinant plasmid is then transformed into E. coli cells. Which one of the following choices is the most likely outcome of this cloning reaction?

For which one of the following enzyme activity plots, will the K$_m$ of the enzyme for substrate ‘S' be 20? [S] indicates substrate concentration.

Which one of the following choices matches the organs in column I with their vascular system arrangement described in column II?

Which of the following processes result in development of a proton gradient across the thylakoid membrane during photosynthesis?
i. Release of protons into the lumen of the thylakoid by plastoquinone
ii. Consumption of protons in the stroma during the reduction of NADP$^+$
iii. Release of protons into the lumen of the thylakoid by ATP synthase
iv. Release of protons into the lumen of the thylakoid by water splitting reaction

The graphs below depict the number of individuals of two organisms, named P and Q, when grown independently, and together. Based on these growth patterns, which one of the following statements is correct?

An electron in the ground state (with energy $E_1$) of a hydrogen atom, absorbs a photon of energy $E_a$, and gets excited to a higher energy level of principal quantum number $n$. What is the value of $n$?

Consider an equilateral prism of refractive index 1.5 and a parallelepiped block of refractive index 2.0 arranged as shown in the figure such that their adjacent faces are parallel. A light ray enters the prism from air at an angle of incidence such that the ray travels through the prism parallel to its base. What is the angle of emergence $\theta$?

A source produces a light beam of intensity $I_0$ polarized along the $x$-direction. The beam is sent along the $z$-direction. It enters a polaroid $P_1$ with its polaroid axis aligned along the $y$-direction so that no light exits the polaroid. When another polaroid $P_2$ is placed in between the source and $P_1$, the intensity measured after $P_1$ is $3I_0/16$. Which among the following is a possible value of $\theta$, the angle of the polaroid axis measured from the $x$-axis?

What is the potential difference between the points $P$ and $Q$ in the circuit shown below, once the capacitors are fully charged?

A particle of mass $m$ and charge $q$ moving with a velocity $\vec{v} = v_0(\hat{i} + \hat{j} - \hat{k})$ is placed in a uniform magnetic field $\vec{B} = B_0(\hat{i} + \hat{j} + \hat{k})$. It executes a helical trajectory of radius $r$ and pitch $p$. Which of the following options is correct?

A charged particle is moving in a circular orbit with radius $r$ and orbital angular frequency $\omega$ in the presence of a magnetic field. The orbit is enclosed within a larger circular metallic frame. The frame is concentric and coplanar with the orbit. The radius of the frame is now gradually decreased. Assuming that the particle remains within the frame at all times, what changes to the trajectory of the particle will occur as the frame is being shrunk?

A circular disk of mass $M$ and radius $R$ is rotating clockwise with a uniform angular velocity $\omega$ about an axis passing through the centre, normal to the disk. At time $t = 0$, a torque $T$ is applied along the same axis to oppose the rotation of the disk. What is the angular displacement $\theta$ (measured from $t = 0$ in the clockwise direction) that the disk attains before it starts rotating counterclockwise?

A particle of charge $q = 1e$ and mass $m$ with kinetic energy $K$ enters an electric field set up by two parallel plates of length $l$ as illustrated in the figure. The potential difference between the two plates is $1\text{ V}$ and their separation is $d$. What is the minimum value of $K$ (in $\text{eV}$) for which the particle will not hit either of the plates? [$e$ is the charge of the electron.]}

A metallic cube initially kept at a temperature $T$ is emitting black body radiation with a power $P$ (energy emitted per unit time). If $T$ is increased by $1\%$, the power being radiated increases by $4.5\%$. What is the approximate percentage increase in the volume of the cube in this process?

Consider two pipes $A$ and $B$ of identical length. $A$ has one end closed and one end open. $B$ has both ends open. Each tube is immersed in a closed chamber of ideal gas having volume $V$. The chamber containing tube $A$ is at temperature $T_A$ and the chamber containing tube $B$ is at temperature $T_B$. The sound frequencies corresponding to the $n_A$-th harmonic in tube $A$ and the $n_B$-th harmonic in tube $B$ are the same. What is the relation between the temperatures $T_A$ and $T_B$?

Consider two waves, which are given by $y_1(x, t) = A \sin(kx - \omega t)$ and $y_2(x, t) = \sqrt{3}A \cos(kx - \omega t)$, where $k$ is the wave number and $\omega$ is the angular frequency. The amplitude of the resultant waveform obtained by the superposition of the two waves is $A_s$ and its phase difference with $y_1$ is $\phi_s$. What are $A_s$ and $\phi_s$?

Which one of the following is the solution of the differential equation
\[ x^2 \frac{dy}{dx} + 9xy = x^4 \quad (\text{for } x > 0) \]
given that $y = 0$ when $x = 1$?

Consider an elastic collision between two particles $A$ and $B$ of same mass, moving in the same direction. Particle $A$ is moving at speed $v_A$ and particle $B$ is moving at speed $v_B$. In the figures shown, the solid lines represent the motion before the collision and the dotted lines represent the motion after the collision. Which of the following describes the motion of these two particles most accurately?

A block of mass $M$ lies at rest connected to a massless spring of spring constant $k$ on a frictionless surface. A bullet of mass $m$ hits the block horizontally with speed $v$ as shown in the figure and is completely stuck to the block. What is the maximum compression in the spring resulting from this impact (assuming that at this point the spring is still not fully compressed)?

What is the value of $\int_{0}^{\pi} x |\cos x| \sin x \, dx$?