IAT (IISER) 2025

\(\text { Match the entries in column I and column II. }\)


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Which one of the following options describes a triglyceride?

The given picture was obtained from an agarose gel electrophoresis of a plasmid after digestion with restriction enzymes either $\mathrm{X}, \mathrm{Y}$ or both X and Y.
Which one of the following diagrams correctly represents the position ...

Which one of the following conditions will favour maximum dissociation of oxygen from the oxyhaemoglobin in the tissues?

Chromosomes are classified as metacentric, sub-metacentric, acrocentric and telocentric. This classification is based on the position of which one of the following structures?

Which one of the following statements is FALSE?

Which one of the following autoregulatory mechanisms is employed by the kidney when glomerular filtration rate is reduced?

Which one of the following statements is correct?

What are retroviruses?

Which amino acid will be charged on the tRNA with anticodon $5^{\prime}$-GUU- $3^{\prime}$ ?

Which one of the following statements about a plant carotenoid is FALSE?

Honey bee males are haploid and females are diploid. Which one of the following statements is INCORRECT about honey bees?

Two double heterozygous plants ( PpQq ), derived from two different pairs of true-breeding parents of unknown genotype, produce gametes in the proportions as given below.
Which one of the following options correctly represents the genotype ...

A cell suspension of actively respiring mitochondria is treated with either chemical X (experiment 1) or chemical Y (experiment 2), or left untreated (experiment 3 ).
Chemical X selectively inhibits electron transport from Complex I to ubiq...

Which one of the following organisms produces the female gamete by mitosis of haploid cells?

\(\text { Which of the following reactions do NOT provide an aldehyde as a product? }\)

What is the time period of revolution of an electron in the fourth Bohr orbit of $\mathrm{He}^{+}$?
[Bohr radius $=52.9$ picometers, mass of an electron $=9.11 \times 10^{-31} \mathrm{~kg}$, Planck's constant $=6.626 \times 10^{-34} \mathrm...

The dipole moments of three $\mathrm{AB}_3$-type molecules $\mathbf{I}, \mathbf{I I}$, and $\mathbf{I I I}$ are measured to be $0.0 \mathrm{D}, 0.2 \mathrm{D}$, and 1.5 D , respectively. Which one of the following options is correct regardi...

Which among the following processes is/are associated with increasing bond order but no change in diamagnetic/paramagnetic behaviour?
(i) $\mathrm{N}_2 \rightarrow \mathrm{~N}_2^{+}+\mathrm{e}^{-}$
(ii) $\mathrm{O}_2 \rightarrow \mathrm{O}_...

At a particular temperature, the magnitude of the rate constant of a reaction is $5 \times 10^{-5}$ and the unit of the pre-exponential factor of the Arrhenius equation for this reaction is $\mathrm{mol} \mathrm{L}^{-1} \mathrm{~min}^{-1}$....

\(\text { What is the major product in the reaction sequence given below? }\)

Which one of the following statements best describes the acidic/basic/amphoteric nature of ZnO and CaO ?

\(\text { What are the correct orders of stability for the following compounds? }\)

What is the value of $E^{\circ}\left(\mathrm{Fe}^{3+} / \mathrm{Fe}^0\right)$ ?
[The standard reduction potential values are $E^{\circ}\left(\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+}\right)=0.77 \mathrm{~V}$, and $\left.E^{\circ}\left(\mathrm{Fe}...

During the charging and discharging of a lead-acid battery (a Pb anode, a grid of Pb packed with $\mathrm{PbO}_2$ as cathode, and an aqueous solution of $\mathrm{H}_2 \mathrm{SO}_4$ as an electrolyte), which of the following redox reactions...

\(\text { How many } \beta \text {-hydrogen is/are present in 2-methyl-3-phenyl-pentan-1-al? }\)

Compound $\mathbf{I}$ undergoes hydroboration-oxidation reaction with $\left(\mathrm{BH}_3\right)_2$ followed by treatment with $\mathrm{H}_2 \mathrm{O}_2$ and aqueous NaOH to produce another compound II, which upon oxidation with $\mathrm{...

\(\text { What are the major products formed in the following reaction sequence? }\)

\(\text { Consider the following reaction scheme: }\)
\(\text { Which among the following statements is correct? }\)

The work done when one mole of an ideal gas expands at constant temperature $T$ from volume $V$ to $2 V$ (in two equal steps of volume in a linear fashion) is $\frac{7}{12} R T$. How much more work would be done by the gas if it expands in ...

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 statements is TRUE?

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...

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

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 $x=1$ ?

What is the derivative of $\log \left(\sin ^2 x\right)$ with respect to $\sin x$ ?

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 equation of the line perpendicular to $\ell$ passing through $(2,0)$ ?

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be the function defined by
$$ f(x)= \begin{cases}x^2-4 x-5 & \text { if } x \geq 1, \\ 2 x & \text { if } x<1 .\end{cases} $$
Which one of the following statements is TRUE?

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?

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?

Let $A$ be a $3 \times 3$ matrix with real entries such that
$$ A=\left[\begin{array}{ccc} 4 & -1 & \cos x \\ -1 & 5 x & 25 \\ x^2+1 & 25 & 7 \end{array}\right] $$
For how many values of $x$, the matrix $A$ is symmetric?

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?

How many three digit numbers divisible by 5 are there in which no digits are repeated?

Five fair coins are tossed independently. What is the probability that at least two heads appear?

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 $n$, what is the value of $a_{13}-a_{10}$ ?

Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}+\vec{b}|=15$ and
\(\vec{a} \times(3 \hat{i}-4 \hat{j}+5 \hat{k})=(3 \hat{i}-4 \hat{j}+5 \hat{k}) \times \vec{b}\)
What is the value of $|(\vec{a}+\vec{b}) \cdot(2 \hat{i}+3 \h...

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 $n$ ?

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

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...

A particle of mass $m$ and charge $q$ is accelerated through a distance $d_1$ by an electric field $\vec{E}$. Another particle of mass $M$ and charge $q$ is accelerated by the same electric field through a distance $d_2$. Both the particles...

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...