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
1
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1
Let $M$ be the set of all $3 \times 3$ matrices with real entries. Consider the relation $R$ on $M$ given by $R=\{(A, B) \in M \times M: \operatorname{det}(A-B)$ is an integer $\}$. Which one of the following statements is Correct?
A
$R$ is reflexive and symmetric, but not transitive.
B
$R$ is reflexive, but neither symmetric nor transitive.
C
$R$ is an equivalence relation.
D
$R$ is symmetric and transitive, but not reflexive.
2
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1
What is the value of ${ }^{23} C_0+{ }^{23} C_2+{ }^{23} C_4+\cdots+{ }^{23} C_{22}$ ?
A
$2^{23}$
B
$2^{22}-1$
C
$2^{23}+1$
D
$2^{22}$
3
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1
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 one of the following statements is Correct?
A
$f$ is neither injective nor surjective
B
$f$ is injective but not surjective
C
$f$ is surjective but not injective
D
$f$ is bijective
4
IAT (IISER) 2024
MCQ (Single Correct Answer)
+4
-1
Let $I=\int_{e^{-\pi / 2}}^{e^{\pi / 2}}\left(\sin ^2(\log (x))+\sin \left(\log \left(x^2\right)\right)\right) d x$. What is the value of $I$ ?
A
0
B
$\frac{\pi e^{\frac{\pi}{2}}}{2}$
C
$e^{\pi / 2}-e^{-\pi / 2}$
D
$e^\pi-1$
Paper analysis
Total Questions
Biology
15
Chemistry
15
Mathematics
15
Physics
15
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