Biology
1. $$ \text { Match the entries in column I and column II. } $$
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.tg td 2. Chromosomes are classified as metacentric, sub-metacentric, acrocentric and telocentric. This classification is based on 3. Which one of the following options describes a triglyceride? 4. Which one of the following statements about a plant carotenoid is FALSE? 5. A cell suspension of actively respiring mitochondria is treated with either chemical X (experiment 1) or chemical Y (exp 6. Which one of the following autoregulatory mechanisms is employed by the kidney when glomerular filtration rate is reduce 7. Which one of the following conditions will favour maximum dissociation of oxygen from the oxyhaemoglobin in the tissues? 8. Which one of the following statements is correct?
9. Which one of the following organisms produces the female gamete by mitosis of haploid cells? 10. Which amino acid will be charged on the tRNA with anticodon $5^{\prime}$-GUU- $3^{\prime}$ ? 11. Two double heterozygous plants ( PpQq ), derived from two different pairs of true-breeding parents of unknown genotype, 12. What are retroviruses? 13. The given picture was obtained from an agarose gel electrophoresis of a plasmid after digestion with restriction enzymes 14. Honey bee males are haploid and females are diploid. Which one of the following statements is INCORRECT about honey bees 15. Which one of the following statements is FALSE?
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
1
IAT (IISER) 2025
MCQ (Single Correct Answer)
+4
-1
$$ \text { What are the correct orders of stability for the following compounds? } $$
A
$$ \mathrm{VF}_5>\mathrm{VCl}_5 ; \mathrm{CuCl}_2>\mathrm{CuI}_2 $$
B
$$ \mathrm{VCl}_5>\mathrm{VF}_5 ; \mathrm{CuCl}_2>\mathrm{CuI}_2 $$
C
$$ \mathrm{VCl}_5>\mathrm{VF}_5 ; \mathrm{CuI}_2>\mathrm{CuCl}_2 $$
D
$$ \mathrm{VF}_5>\mathrm{VCl}_5 ; \mathrm{CuI}_2>\mathrm{CuCl}_2 $$
2
IAT (IISER) 2025
MCQ (Single Correct Answer)
+4
-1
$$ \text { Consider the following reaction scheme: } $$
$$ \text { Which among the following statements is correct? } $$
A
$\mathbf{P}$ shows geometrical isomerism and absorbs light of higher wavelength than that of $\mathbf{Q}$.
B
Both $\mathbf{P}$ and $\mathbf{Q}$ show geometrical isomerism and $\mathbf{P}$ absorbs light of higher wavelength than that of $\mathbf{Q}$.
C
Q shows geometrical isomerism and absorbs light of higher wavelength than that of $\mathbf{P}$.
D
$\mathbf{P}$ shows geometrical isomerism and absorbs light of lower wavelength than that of $\mathbf{Q}$.
3
IAT (IISER) 2025
MCQ (Single Correct Answer)
+4
-1
$$ \text { How many } \beta \text {-hydrogen is/are present in 2-methyl-3-phenyl-pentan-1-al? } $$
A
4
B
1
C
3
D
2
4
IAT (IISER) 2025
MCQ (Single Correct Answer)
+4
-1
$$ \text { Which of the following reactions do NOT provide an aldehyde as a product? } $$
A
B
C
D
Paper Analysis
Total Questions
Biology 15
Chemistry 15
Mathematics 15
Physics 15
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