IAT (IISER) 2025 | IAT (IISER) Year Wise Previous Years Questions

Biology

Chemistry

1. Which one of the following statements best describes the acidic/basic/amphoteric nature of ZnO and CaO ? 2. Which among the following processes is/are associated with increasing bond order but no change in diamagnetic/paramagnet 3. What is the value of $E^{\circ}\left(\mathrm{Fe}^{3+} / \mathrm{Fe}^0\right)$ ? [The standard reduction potential values 4. $$ \text { What are the correct orders of stability for the following compounds? } $$ 5. $$ \text { Consider the following reaction scheme: } $$ $$ \text { Which among the following statements is correct? } $$ 6. $$ \text { How many } \beta \text {-hydrogen is/are present in 2-methyl-3-phenyl-pentan-1-al? } $$ 7. $$ \text { Which of the following reactions do NOT provide an aldehyde as a product? } $$ 8. $$ \text { What are the major products formed in the following reaction sequence? } $$ 9. $$ \text { What is the major product in the reaction sequence given below? } $$ 10. Compound $\mathbf{I}$ undergoes hydroboration-oxidation reaction with $\left(\mathrm{BH}_3\right)_2$ followed by treatme 11. The work done when one mole of an ideal gas expands at constant temperature $T$ from volume $V$ to $2 V$ (in two equal s 12. At a particular temperature, the magnitude of the rate constant of a reaction is $5 \times 10^{-5}$ and the unit of the 13. What is the time period of revolution of an electron in the fourth Bohr orbit of $\mathrm{He}^{+}$? [Bohr radius $=52.9$ 14. The dipole moments of three $\mathrm{AB}_3$-type molecules $\mathbf{I}, \mathbf{I I}$, and $\mathbf{I I I}$ are measured 15. During the charging and discharging of a lead-acid battery (a Pb anode, a grid of Pb packed with $\mathrm{PbO}_2$ as cat

Mathematics

1. How many three digit numbers divisible by 5 are there in which no digits are repeated? 2. Let $A$ be a $3 \times 3$ matrix with real entries such that $$ A=\left[\begin{array}{ccc} 4 & -1 & \cos x \\ -1 & 5 x & 3. Let $n=\sum\limits_{r=0}^{10}(-1)^r{ }^{10} C_r\left(\frac{2}{3}\right)^{2 r} 3^{20}$. Which one of the following statem 4. Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be the function given by $f(x)=\cos \left(\tan ^{-1} x\right)$. Which one of 5. Let $$ A=\left\{x \in \mathbf{R} \left\lvert\,-31 Which one of the following statements is TRUE? 6. Let $z_1, z_2$, and $z_3$ be complex numbers satisfying the following conditions $$ 2=\left|2 z_1\right|=\left|z_2-1\rig 7. Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be defined as $f(x)=\left|x^3-3 x\right|[x]$, where $[x]$ denotes the greates 8. Let $\ell$ be the tangent line to the ellipse $x^2+16 y^2=4$ at $\left(1, \frac{\sqrt{3}}{4}\right)$. What is the equati 9. Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}+\vec{b}|=15$ and $$ \vec{a} \times(3 \hat{i}-4 \hat{j}+5 10. What is the derivative of $\log \left(\sin ^2 x\right)$ with respect to $\sin x$ ? 11. Let $S_n$ denote the sum of the first $n$ terms of a sequence $a_1, a_2, a_3, \ldots$. If $S_{n+3}-S_n=13 n+7$ for all $ 12. Five fair coins are tossed independently. What is the probability that at least two heads appear? 13. Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be the function defined by $$ f(x)= \begin{cases}x^2-4 x-5 & \text { if } x \ 14. Which one of the following is the solution of the differential equation $$ x^2 \frac{d y}{d x}+9 x y=x^4(\text { for } x 15. What is the value of $\int_0^\pi x|\cos x| \sin x d x$ ?

Physics

1. Consider an elastic collision between two particles $A$ and $B$ of same mass, moving in the same direction. Particle $A$ 2. A block of mass $M$ lies at rest connected to a massless spring of spring constant $k$ on a frictionless surface. A bull 3. A cart of mass $M$ is released from $A$, the highest point of a frictionless track, as shown in the figure. The cart tra 4. A circular disk of mass $M$ and radius $R$ is rotating clockwise with a uniform angular velocity $\omega$ about an axis 5. A metallic cube initially kept at a temperature $T$ is emitting black body radiation with a power $P$ (energy emitted pe 6. Consider two pipes $A$ and $B$ of identical length. $A$ has one end closed and one end open. $B$ has both ends open. Eac 7. Consider two waves, which are given by $y_1(x, t)=A \sin (k x-\omega t)$ and $y_2(x, t)=\sqrt{3} A \cos (k x-\omega t)$, 8. A particle of charge $q=1 e$ and mass $m$ with kinetic energy $K$ enters an electric field set up by two parallel plates 9. What is the potential difference between the points $P$ and $Q$ in the circuit shown below, once the capacitors are full 10. 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 unifo 11. A charged particle is moving in a circular orbit with radius $r$ and orbital angular frequency $\omega$ in the presence 12. Consider an equilateral prism of refractive index 1.5 and a parallelepiped block of refractive index 2.0 arranged as sho 13. A source produces a light beam of intensity $I_0$ polarized along the $x$-direction. The beam is sent along the $z$-dire 14. An electron in the ground state (with energy $E_1$ ) of a hydrogen atom, absorbs a photon of energy $E_a$, and gets exci 15. A particle of mass $m$ and charge $q$ is accelerated through a distance $d_1$ by an electric field $\vec{E}$. Another pa

IAT (IISER) 2025

MCQ (Single Correct Answer)

-1

Which one of the following is the solution of the differential equation

$$ x^2 \frac{d y}{d x}+9 x y=x^4(\text { for } x>0) $$

given that $y=0$ when $x=1$ ?

$\quad 12 y=x^3-\frac{1}{x^9}$

$\quad 12 y=x^9-\frac{1}{x^3}$

$9 y=x^{21}-\frac{1}{x^3}$

$\quad 9 y=x^3-\frac{1}{x^{21}}$

IAT (IISER) 2025

MCQ (Single Correct Answer)

-1

What is the value of $\int_0^\pi x|\cos x| \sin x d x$ ?

$\frac{\pi}{2}$

$\frac{\pi}{4}$

$\pi$

$\frac{\pi}{6}$

IAT (IISER) 2025

MCQ (Single Correct Answer)

-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?

IAT (IISER) 2025 Physics - Center of Mass and Collision Question 1 English Option 1

IAT (IISER) 2025 Physics - Center of Mass and Collision Question 1 English Option 2

IAT (IISER) 2025

MCQ (Single Correct Answer)

-1

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)?