IAT (IISER) 2024 | IAT (IISER) Year Wise Previous Years Questions

Biology

1. What will be the sequence of RNA synthesized using the following DNA template strand? $5^{\prime}$-GTCTAGGCTTCTC- $3^{\p 2. The following pedigree diagram shows the inheritance of a rare genetic disorder (filled shapes depict affected individua 3. Which of the following proteins plays a direct role in muscle contraction? 4. Which of the following is NOT derived from the epidermal cell layer in plants? 5. $$ \text { Match the list of conditions with the list of affected physiological processes. } $$ .tg {border-collapse: 6. Which of the following statements about meiosis in sexually reproducing plants is INCORRECT? 7. Which of the following is routinely performed to detect typhoid? 8. A population with $N=400$ in asymptote at $K=500$ individuals, $K$ being the carrying capacity. Assuming the intrinsic r 9. Which of the following graphs represents the correct relationship between light intensity (Xaxis) and the rate of photos 10. $$ \text { Match the enzymes in Column I with the cellular compartments in Column II. } $$ Column I Column II 11. Two species of a flowering plant, $P(2 n=20$ chromosomes) and $Q$ ( $2 n=30$ chromosomes) are reciprocally crossed with 12. Which of the following plasmid vectors can be used for cloning of a gene, with restriction enzymes BamHI and EcoRI, and 13. Polymerase chain reaction (PCR) is used to amplify a gene of interest (GOI). If, after 30 cycles of PCR, 1 billion copie 14. Which one of the following statements is correct? 15. Which of the following statements is correct about the oxygen $\left(\mathrm{O}_2\right)$ dissociation curves A and C re

Chemistry

1. If an element with $Z=120$ is discovered, then which group of elements will it belong to? 2. Which one of the following statements is correct about $\mathrm{N}_2, \mathrm{CO}$, and $\mathrm{NO}^{+}$? 3. Which of the following complexes exhibit(s) magnetic moment close to 2 BM ? $$ \left[\mathrm{Fe}\left(\mathrm{H}_2 \mat 4. According to the VSEPR theory, what are the most stable shapes of $X_4 F_4$ and $\mathrm{SF}_4$, respectively? 5. The following complex ions absorb in the ultraviolet-visible region of light. Which one of these shows violet colour? $$ 6. $$ \text { What is the relationship between the structures depicted below? } $$ 7. $$ \text { What is the correct order of acidity for the following compounds? } $$ 8. $$ \text { What are the products } \mathrm{N} \text { and } \mathrm{Q} \text { in the following reaction sequences? } $$ 9. $$ \text { What are } X \text { and } Z \text { in the following sequence of reactions? } $$ 10. $$ \text { What are the correct structural descriptions for } M \text { and } N \text { ? } $$ 11. Consider an exothermic reaction: $2 \mathrm{~A}(\mathrm{~s}) \rightarrow \mathrm{B}(\mathrm{s})+\mathrm{C}(\mathrm{g})+\ 12. The minimum energy needed to remove an electron from a metal corresponds to a wavelength of 500 nm . What is the total k 13. For a reaction $R \rightarrow P$ with a rate constant of $3 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{- 14. Which one of these plots correctly describes the variation of osmotic pressure ( $\Pi$ ) of a fixed amount of a solute a 15. Consider the following data for KCl solution at a particular temperature. What is the value of the limiting molar conduc

Mathematics

1. Consider the following lines in the $X Y$-plane: $$ L_1: 5 x-2 y=1 $$ $L_2$ : The line passing through $(0,1)$ and $(100 2. Let $A$ be the set of points in the $X Y$-plane which are equidistant from $P(-1,0)$ and $Q(1,0)$. Let $B$ be the set of 3. Consider the lines $L_1$ and $L_2$ given below: $$ \begin{gathered} L 1: x=2+\lambda, y=3+2 \lambda, z=4+3 \lambda \\ L 4. Let $a_1, a_2, a_3, \ldots$ be a sequence of real numbers. Let $s_n=a_1+a_2+\cdots+a_n$. If $2 s_n=$ $n\left(c+a_n\right 5. Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a strictly decreasing function with $|f(t)| 6. Let $f, g: R \rightarrow R$ be functions. If $g$ is continuous, then which one of the following cases implies that $f$ i 7. What is the largest area of a rectangle, whose sides are parallel to the coordinate axes, that can be inscribed under th 8. Let $M$ be the set of all $3 \times 3$ matrices with real entries. Consider the relation $R$ on $M$ given by $R=\{(A, B 9. What is the value of ${ }^{23} C_0+{ }^{23} C_2+{ }^{23} C_4+\cdots+{ }^{23} C_{22}$ ? 10. Let $f: Q \rightarrow Q$ be a function such that $f(x+y)=f(x)+f(y)$ for all $x, y \in \mathbf{Q}$, and $f(1)=$ 10. Which 11. Let $I=\int_{e^{-\pi / 2}}^{e^{\pi / 2}}\left(\sin ^2(\log (x))+\sin \left(\log \left(x^2\right)\right)\right) d x$. Wha 12. Consider the following subset of the $X Y$-plane. $$ S=\left\{\left(|z-\mathrm{i} z|,|z|^2\right): \quad z \text { is a 13. A ship sets off on a voyage with three engines, labelled $A, B$, and $C$, which work independently. The ship can complet 14. Consider the differential equation $\cos (y) \frac{d y}{d x}+\frac{1}{x} \sin (y)=x, \quad(x>0)$; given that, $y=\frac{\ 15. In the given figure, the angles $\angle B A Q=\angle C P Q=\angle C B Q=\frac{\pi}{2}$; and the lengths $Q A=3$ units, $

Physics

1. On a circular track, two cyclists, Abhijit and Vani, start moving in opposite directions from a point. Abhijit moves wit 2. Consider a simple pendulum undergoing simple harmonic motion with a time period $T$, and a fixed amplitude $\theta_0$ of 3. An inextensible cord of negligible mass passes over the rim of a solid disc of mass $M$ and radius $R$. The disc is free 4. Consider the motion of a particle along the $x$-axis. The position of the particle varies with time as $x(t)=\sin ^2(\o 5. A solid bob of a material having density twice that of water is suspended with a massless and inextensible string of len 6. Consider a solid sphere of radius $R$ floating in a pond with half of the sphere submerged. The sphere is pushed vertic 7. One mole of an ideal gas of volume $V$ and temperature $T$ is allowed to expand adiabatically to volume $2 V$ while doin 8. Two identical boxes contain the same ideal gas. Let $\left(n_1, \lambda_1, T_1\right)$ and $\left(n_2, \lambda_2, T_2\ri 9. Consider two point charges $+q$ and $+2 q$ fixed on the $x-y$ plane at $(-\ell / 2,0)$ and $(+\ell / 2,0)$ respectively. 10. Consider the circuit diagram as shown in the figure. The source has a voltage $V=V_0 \sin \omega t$. Both the resistors 11. A conducting wire carrying a steady current $I$ is shaped as shown in the figure below. All connected graight segments m 12. Consider the shown circuit. The capacitors $C_1$ and $C_2$ have capacitances $2 \mu \mathrm{~F}$ and $8 \mu \mathrm{~F}$ 13. Atomic masses of two oxygen isotopes ${ }_8^{16} \mathrm{O}$ and ${ }_8^{18} \mathrm{O}$ are 15.99491 u and 17.99916 u , 14. The refractive indices $(n)$ of two transparent slabs are 2 and $2 / \sqrt{3}$. They are attached together and placed in 15. Two monochromatic sources emit light at wavelengths $\lambda$ and $\lambda / 2$. The stopping potentials for a photosens

IAT (IISER) 2024

MCQ (Single Correct Answer)

-1

A ship sets off on a voyage with three engines, labelled $A, B$, and $C$, which work independently. The ship can complete the voyage only if at least two of these engines keep working. The probability that engine $A$ breaks down is $1 / 4$, that engine $B$ breaks down is $1 / 4$, and that engine $C$ breaks down is $1 / 2$. What is the probability that the ship can complete the voyage?

3/4

$1 / 2$

$1 / 32$

$1 / 4$

IAT (IISER) 2024

MCQ (Single Correct Answer)

-1

Consider the differential equation $\cos (y) \frac{d y}{d x}+\frac{1}{x} \sin (y)=x, \quad(x>0)$; given that, $y=\frac{\pi}{2}$ at $x=\sqrt{3}$. Which one of the following is the value of $y$ at $x=\sqrt{\frac{3}{2}}$ ?

$\frac{\pi}{6}$

$\frac{\pi}{3}$

$\frac{\pi}{2}$

$\frac{\pi}{4}$

IAT (IISER) 2024

MCQ (Single Correct Answer)

-1

In the given figure, the angles $\angle B A Q=\angle C P Q=\angle C B Q=\frac{\pi}{2}$; and the lengths $Q A=3$ units, $A B=$ 4 units, and $B C=1$ unit. What is the length of $P Q$ ?

IAT (IISER) 2024 Mathematics - Properties of Triangles Question 1 English

2 unit

2.2 unit

$\sqrt{2}$ unit

$3-\sqrt{2}$ unit

IAT (IISER) 2024

MCQ (Single Correct Answer)

-1

On a circular track, two cyclists, Abhijit and Vani, start moving in opposite directions from a point. Abhijit moves with a constant speed. Vani starts with a constant acceleration from rest. They meet again on the track with the same speed. Which of the following is correct?

Abhijit travelled the same distance travelled by Vani.

Abhijit travelled half the distance travelled by Vani.

Abhijit travelled double the distance travelled by Vani.

Abhijit travelled $4 / 3$ of the distance travelled by Vani.

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