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

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be the function given by $f(x)=\cos \left(\tan ^{-1} x\right)$. Which one of the following statements is TRUE?

$f$ is decreasing for $x>0$

$f$ is decreasing for $x<0$

$f$ is decreasing on $\mathbf{R}$

$f$ is decreasing on the interval $(-1,1)$

IAT (IISER) 2025

MCQ (Single Correct Answer)

-1

Let

$$ A=\left\{x \in \mathbf{R} \left\lvert\,-31<\operatorname{det}\left[\begin{array}{cc} 3 x-1 & 2 \\ -2 & 5 \end{array}\right] \leq 29\right.\right\} $$

Which one of the following statements is TRUE?

$\quad A=(-2,2]$

$A=(-2,2)$

$A=[-2,2)$

$A=[-2,2]$

IAT (IISER) 2025

MCQ (Single Correct Answer)

-1

Let $z_1, z_2$, and $z_3$ be complex numbers satisfying the following conditions

$$ 2=\left|2 z_1\right|=\left|z_2-1\right|=\left|z_3+1\right|=\left|\frac{1}{z_1}+\frac{1}{z_2-1}+\frac{1}{z_3+1}\right| . $$

What is the value of $\left|4 z_1+z_2+z_3\right|$ ?

$\frac{1}{4}$

$\frac{1}{8}$

IAT (IISER) 2025

MCQ (Single Correct Answer)

-1

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be defined as $f(x)=\left|x^3-3 x\right|[x]$, where $[x]$ denotes the greatest integer less than or equal to $x$. Which one of the following statements is TRUE?

Every non-zero integer is a point of discontinuity of $f$

$\quad f$ is continuous at every real number

Every integer is a point of discontinuity of $f$

$f$ is continuous at every real number except for $0, \pm \sqrt{3}$

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