IAT (IISER) 2023 | IAT (IISER) Year Wise Previous Years Questions

Biology

1. $$ \text { Match the entries in Column I with their functions described in Column II. } $$ Column I Column II 2. Which one of the following best describes peptones? 3. Match the biomolecules given in Column I with their corresponding chemical nature given in Column II. Column I 4. A mitotic drug inhibits microtubule formation. Which one of the following stages of karyokinesis will be the first to g 5. Which one of the following statements regarding seed structure is INCORRECT? 6. Which one of the following anatomical features of wood can be used to estimate the age of a tree growing in a temperate 7. Which one of these statements is CORRECT about biological nitrogen fixation in plants? 8. Which one of the following is an example of genetic diversity? 9. When the ribosome encounters a stop codon in the mRNA, during translation, which one of the following binds to the stop 10. $$ \text { Match the terms in column I with their physiological roles given in Column II. } $$ Column I Colum 11. For which one of the following diseases does the causative agent require the splicing of their hnRNA to generate mature 12. $$ \text { The diagram represents an enzyme, its substrate and potential inhibitors }(P, Q, R, S, T) \text {. } $$ Whic 13. In an island with 10,000 individuals, four have sickle cell anemia, a recessive autosomal disease. Assuming that the loc 14. A 1000 base-pair DNA fragment was cloned between Hind III and EcoRI sites of the plasmid vector (plAT) of size 3500 base 15. The following pedigree chart shows the inheritance of a genetic disorder. I-2 and III-2 are the only affected individual

Chemistry

1. $$ \text { How many radial nodes does } \mathrm{Ca}^{+} \text {have in its } 4 \text { s orbital? } $$ 2. Amongst $\mathrm{O}_2, \mathrm{~N}_2, \mathrm{~F}_2$, and $\mathrm{B}_2$, which molecules will be attracted to an extern 3. What is the smallest P-P-P bond angle in the highly reactive allotrope of phosphorus? 4. Which of the following is an ore of iron? 5. Which parameters are plotted in the Ellingham diagram? 6. Which of the following compounds will NOT undergo the Finkelstein reaction with NaI via $S_N 2$ pathway? 7. Which one amongst the following is the most efficient way of synthesizing $n$-propyl benzene? 8. $$ \text { Which amongst the following are chiral compounds? } $$ 9. $$ \text { Which one amongst the following bases is NOT present in RNA? } $$ 10. $$ \text { Which amongst the following are aromatic? } $$ 11. Why is it harder to compress liquids and solids relative to gases? 12. Related to the Freundlich adsorption isotherm, which one of the following statements is NOT correct? 13. Consider the following reaction: $\mathrm{CH}_4(\mathrm{~g}) \rightarrow \mathrm{C}(\mathrm{g})+4 \mathrm{H}(\mathrm{g}) 14. In two solutions $X$ (hexane and benzene) and $Y$ (water and HCl ), what types of deviations from Raoult's law are obser 15. In aqueous solution, the hydronium ion gets further hydrated to give which of the following species?

Mathematics

1. Let $f: \mathbf{R} \rightarrow(0, \infty)$ be a continuous decreasing function. Suppose $f(0), \dot{f}(1), \ldots, f(10) 2. Let $M$ be a $3 \times 3$ matrix with real entries such that $$ \left\{\left[\begin{array}{l} x_1 \\ x_2 \\ x_3 \end{arr 3. What is the locus of the center of circles passing through the origin $(0,0)$ with fixed radius? 4. Let $\alpha$ be a real number. What is the total number of distinct point(s) of intersection between the parabola $y=x^2 5. Let $L$ be a straight line passing through the origin, and it makes angles $\alpha, \beta$ and $\gamma$ with the positi 6. $$ \text { What is the total number of distinct divisors of } 2^9 \times 3^{19} \text { ? } $$ 7. Suppose the mean and the standard deviation of the data $\left\{x_1, x_2, \cdots, x_9\right\}$ are $\mu$ and $\sigma(\ne 8. Consider three biased coins. Let the probability of getting head be $\frac{1}{3}$ and the probability of getting tail be 9. Which of the following differential equations has $y=e^x$ as one of its particular solutions? 10. What is the area of the region $\left\{(x, y): 0 \leq y \leq x e^{x^2}, 0 \leq x \leq 1\right\}$ ? 11. Consider the objective function $Z=x-y$ subject to the constraints $$ \begin{aligned} & x+2 y \leq 10 \\ & x+y \geq 2 \\ 12. 42. Let $p(x)=x^2+b x+c$ be quadratic polynomial with real coefficients $b$ and $c$. Suppose $p(1)=5$ and $p(-1)=3$. Wha 13. Let $f:(-1,2) \rightarrow \mathbf{R}$ be a differentiable function such that $f^{\prime}(x)=\frac{2}{x^2-5}$ and $f(0)= 14. Let $f(x)=\sin (3 x), x \in\left[0, \frac{\pi}{2}\right]$. Which of the following statements is true 15. Which one of the following functions is differentiable at $x=0$ ?

Physics

1. A ball is thrown vertically upwards with an initial speed $u$ from a height $h$ above the ground. The ball eventually hi 2. Two cubes $A$ and $B$ of same dimensions are made of different materials with densities $\rho_A$ and $\rho_{\mathrm{B}}$ 3. An object is placed in front of a convex lens. A real inverted image of double its size is formed. When the object is mo 4. The frequency of the whistle of a train moving with a constant speed is observed by a stationary detector on the platfor 5. A current $I$ flows through a cylindrical cable of length $L$ and uniform cross-sectional area $A$. The power dissipated 6. Particle A with charge $Q$ and particle B with charge $2 Q$ are fixed at positions $\vec{r}_A$ and $\vec{r}_B$, respecti 7. The magnetic fux $\phi_B(t)$ through a coil at a time $t$ is given by $\phi_B(t)=\phi_0 \cos \omega t$, where $0 \leq$ $ 8. The intrinsic electron and hole concentrations of a Si-based intrinsic semiconductor are $n_e^{(0)}$ and $n_h^{(0)}$, re 9. The velocity $v(t)$ of a particle moving in one dimension is given by: $$ v(t)= \begin{cases}\alpha t, & 0 \leq t \leq T 10. Two fixed point particles, each of charge $+q$, are separated by a distance $2 L$. Another point charge $+q$ of mass $m$ 11. $$ \text { What is the effective resistance between } A \text { and } B \text { in the circuit shown below? } $$ 12. 57. Consider a Carnot heat engine operating between a heat reservoir at temperature 600 K , and an external atmosphere a 13. Two spherical bodies A and B each of mass $M$ and radius $R$ are located such that their centers are apart by a distance 14. Consider the Bohr model of an atom where an electron of charge $-e$ revolves around a nucleus of charge $+e$ in an orbit 15. A quantity has been measured to have a value of 0.00230 in some units. How many significant figures does the measured va

IAT (IISER) 2023

MCQ (Single Correct Answer)

-1

Let $f:(-1,2) \rightarrow \mathbf{R}$ be a differentiable function such that $f^{\prime}(x)=\frac{2}{x^2-5}$ and $f(0)=0$. Then in which of the following intervals does $f(1)$ lie?

$(-\infty, 0)$

$(0,2)$

$(2,4)$

$(4, \infty)$

IAT (IISER) 2023

MCQ (Single Correct Answer)

-1

Let $f(x)=\sin (3 x), x \in\left[0, \frac{\pi}{2}\right]$. Which of the following statements is true

$f$ is increasing on $\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$.

$f$ is decreasing on $\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$

$f$ is increasing on $\left(\frac{\pi}{4}, \frac{\pi}{3}\right)$ and decreasing on $\left(\frac{\pi}{3}, \frac{\pi}{2}\right)$.

$f$ is decreasing on $\left(\frac{\pi}{4}, \frac{\pi}{3}\right)$ and increasing on $\left(\frac{\pi}{3}, \frac{\pi}{2}\right)$.

IAT (IISER) 2023

MCQ (Single Correct Answer)

-1

Which one of the following functions is differentiable at $x=0$ ?

$|x|$

$|x|^{\frac{1}{2}}$

$\sin |x|$

$\cos |x|$

IAT (IISER) 2023

MCQ (Single Correct Answer)

-1

A ball is thrown vertically upwards with an initial speed $u$ from a height $h$ above the ground. The ball eventually hits the ground with a speed $v$. The acceleration due to gravity is $g$ and air resistance is negligible. What is the average speed of the ball over its entire trajectory?

$\frac{g h}{2(u+v)}$

$\frac{u+v}{2}$

$\frac{u^2+v^2}{2(u+v)}$

$\frac{u^2+g h}{2(u+v)}$

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