IAT (IISER) 2023 | IAT (IISER) Paper Questions with Solutions

IAT (IISER) 2023

Paper was held on Sat, Jun 17, 2023 3:30 AM

Biology

$$ \text { Match the entries in Column I with their functions described in Column II. } $$

	Column I		Column II
P.	Squamous epithelium	(i)	The nucleus is at the basal side of the cell; also helps in movement of particles and mucous.
Q.	Cuboidal epithelium	(ii)	The nucleus is at the basal side of the cell; also helps in secretion and absorption.
R.	Columnar epithelium	(iii)	The nucleus is at the center of the cell; also helps in secretion and absorption.
S.	Ciliated epithelium	(iv)	It serves as a diffusion barrier.

Which one of the following best describes peptones?

Match the biomolecules given in Column I with their corresponding chemical nature given in Column II.

	Column I		Column II
P.	Insulin	(i)	Secondary metabolite
Q.	Inulin	(ii)	Homopolymer
R.	Lectin	(iii)	Quaternary ammonium derivative
S.	Lecithin	(iv)	Hetropolymer

A mitotic drug inhibits microtubule formation. Which one of the following stages of karyokinesis will be the first to get affected by the drug?

Which one of the following statements regarding seed structure is INCORRECT?

Which one of the following anatomical features of wood can be used to estimate the age of a tree growing in a temperate climate?

Which one of these statements is CORRECT about biological nitrogen fixation in plants?

Which one of the following is an example of genetic diversity?

When the ribosome encounters a stop codon in the mRNA, during translation, which one of the following binds to the stop codon?

$$ \text { Match the terms in column I with their physiological roles given in Column II. } $$

	Column I		Column II
P.	Sertoli cells	(i)	Secretion of chorionic gonadotropin
Q.	Follicle stimulating hormone	(ii)	Carries urine away from bladder
R.	Placenta	(iii)	Carries urine away from kidney
S.	Urethra	(iv)	Provides nutrition to developing spermatozoa
		(v)	Triggers ovulation

Which one of the following combinations is correct?

For which one of the following diseases does the causative agent require the splicing of their hnRNA to generate mature mRNA?

$$ \text { The diagram represents an enzyme, its substrate and potential inhibitors }(P, Q, R, S, T) \text {. } $$

IAT (IISER) 2023 Biology - Biomolecules Question 1 English

Which one of the following combinations is the best pair of competitive inhibitors for the enzyme?

In an island with 10,000 individuals, four have sickle cell anemia, a recessive autosomal disease. Assuming that the locus is in Hardy-Weinberg equilibrium, how many individuals in that island are expected to be heterozygous for the disease allele?

A 1000 base-pair DNA fragment was cloned between Hind III and EcoRI sites of the plasmid vector (plAT) of size 3500 base-pair. The cloned fragment had a Not I site as shown in the figure. In order to confirm the presence of the insert, the recombinant plasmid was digested completely with (a) Not I and EcoR I, and (b) Not I and Hind III.

In lane 1 the products of the digestion by Not I and EcoRI was loaded. In lane 2 the products of the digestion by Not I and Hind III was loaded. Which one of the following correctly represents the agarose gel electrophoresis profile of the digested recombinant plasmid for (a) and (b), respectively?

The following pedigree chart shows the inheritance of a genetic disorder. I-2 and III-2 are the only affected individuals.

IAT (IISER) 2023 Biology - Principles of Inheritance and Variation Question 1 English

Which one of the following is the correct pattern of inheritance of the disorder, and the genotype of the II- 3 individual?

Chemistry

$$ \text { How many radial nodes does } \mathrm{Ca}^{+} \text {have in its } 4 \text { s orbital? } $$

Amongst $\mathrm{O}_2, \mathrm{~N}_2, \mathrm{~F}_2$, and $\mathrm{B}_2$, which molecules will be attracted to an external magnetic field?

What is the smallest P-P-P bond angle in the highly reactive allotrope of phosphorus?

Which of the following is an ore of iron?

Which parameters are plotted in the Ellingham diagram?

Which of the following compounds will NOT undergo the Finkelstein reaction with NaI via $S_N 2$ pathway?

IAT (IISER) 2023 Chemistry - Haloalkanes and Haloarenes Question 1 English

Which one amongst the following is the most efficient way of synthesizing $n$-propyl benzene?

$$ \text { Which amongst the following are chiral compounds? } $$

IAT (IISER) 2023 Chemistry - Isomerism Question 1 English

$$ \text { Which one amongst the following bases is NOT present in RNA? } $$

IAT (IISER) 2023 Chemistry - Biomolecules Question 1 English

$$ \text { Which amongst the following are aromatic? } $$

IAT (IISER) 2023 Chemistry - General Organic Chemistry Question 1 English

Why is it harder to compress liquids and solids relative to gases?

Consider the following reaction: $\mathrm{CH}_4(\mathrm{~g}) \rightarrow \mathrm{C}(\mathrm{g})+4 \mathrm{H}(\mathrm{g}) ; \Delta_a H^0=1665 \mathrm{kJmol}^{-} 1$ Which of the statements is FALSE?

In two solutions $X$ (hexane and benzene) and $Y$ (water and HCl ), what types of deviations from Raoult's law are observed?

In aqueous solution, the hydronium ion gets further hydrated to give which of the following species?

Mathematics

Let $f: \mathbf{R} \rightarrow(0, \infty)$ be a continuous decreasing function. Suppose $f(0), \dot{f}(1), \ldots, f(10)$ are in a geometric progression with common ratio $\frac{1}{5}$. In which of the following intervals does the value of $\int_0^{10} f(x) d x$ lie?

Let $M$ be a $3 \times 3$ matrix with real entries such that

$$ \left\{\left[\begin{array}{l} x_1 \\ x_2 \\ x_3 \end{array}\right]: M\left[\begin{array}{l} x_1 \\ x_2 \\ x_3 \end{array}\right]=\left[\begin{array}{l} 0 \\ 0 \\ 0 \end{array}\right]\right\}=\left\{\left[\begin{array}{l} x_1 \\ x_2 \\ x_3 \end{array}\right]: x_1+x_2=0=x_2+x_3\right\} $$

What is the value of the determinant of M ?

What is the locus of the center of circles passing through the origin $(0,0)$ with fixed radius?

Let $\alpha$ be a real number. What is the total number of distinct point(s) of intersection between the parabola $y=x^2+4 x \sin \alpha+6$ and the pair of lines $y^2=1$ ?

Let $L$ be a straight line passing through the origin, and it makes angles $\alpha, \beta$ and $\gamma$ with the positive $X, Y$ and $Z$-axes, respectively. What is the value of $\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma$ ?

$$ \text { What is the total number of distinct divisors of } 2^9 \times 3^{19} \text { ? } $$

Suppose the mean and the standard deviation of the data $\left\{x_1, x_2, \cdots, x_9\right\}$ are $\mu$ and $\sigma(\neq 0)$, respectively. After including one more data value $x_{10}$, the mean of the data $\left\{x_1, x_2, \cdots, x_9, x_{10}\right\}$ remains $\mu$. What is the standard deviation of the data $\left\{x_1, x_2, \cdots, x_9, x_{10}\right\}$ ?

Consider three biased coins. Let the probability of getting head be $\frac{1}{3}$ and the probability of getting tail be $\frac{2}{3}$ in each of the coins. Consider the experiment of tossing the threee coins one by one, and the following events: $E$ :"At least two heads show up" F:"First coin shows tail". What is the conditional probability of $E$ given that $F$ has already occurred?

Which of the following differential equations has $y=e^x$ as one of its particular solutions?

What is the area of the region $\left\{(x, y): 0 \leq y \leq x e^{x^2}, 0 \leq x \leq 1\right\}$ ?

Consider the objective function $Z=x-y$ subject to the constraints

$$ \begin{aligned} & x+2 y \leq 10 \\ & x+y \geq 2 \\ & x \geq 0, y \geq 0 \end{aligned} $$

What is the minimum value of $Z$ subject to the above constraints?

42. Let $p(x)=x^2+b x+c$ be quadratic polynomial with real coefficients $b$ and $c$. Suppose $p(1)=5$ and $p(-1)=3$. What is the product of the roots of $p(x)=0$ ?

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?

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

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

Physics

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?

Two cubes $A$ and $B$ of same dimensions are made of different materials with densities $\rho_A$ and $\rho_{\mathrm{B}}$, respectively. Cube A floats in water with a fraction $\eta$ of its volume immersed. When cube $B$ is placed on top of cube $A$, it is found that cube $A$ is just entirely immersed, while cube $B$ is entirely above the surface of the water. What is the ratio $\rho_{\mathrm{B}} / \rho_{\mathrm{A}}$ ?

An object is placed in front of a convex lens. A real inverted image of double its size is formed. When the object is moved closer to the lens by a distance $d$, the image shifts away from the lens by a distance $8 d$ from its previous position. What is the magnitude of the magnification in the final setup?

The frequency of the whistle of a train moving with a constant speed is observed by a stationary detector on the platform to be $v_1$. The frequency of the same whistle is detected to be $v_2$ inside another train moving on a parallel track, at a speed $v$ towards the frst train. If the speed of sound in air is taken to be $v_s$ ound, what is the ratio $v / v_s$ ound?

A current $I$ flows through a cylindrical cable of length $L$ and uniform cross-sectional area $A$. The power dissipated due to the current is $P_1$. The cable is cut into two equal halves. If the cross-sectional area and the current flowing through the two halves remain unchanged and the power dissipated in each half is $P_2$, which of these options is correct?

Particle A with charge $Q$ and particle B with charge $2 Q$ are fixed at positions $\vec{r}_A$ and $\vec{r}_B$, respectively. The force on $A$ due to $B$ is $\vec{F}_{B A}$, and that on $B$ due to $A$ is $\vec{F}_{A B}$. Which of the following options is correct?

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 $0 \leq$ $\omega t \leq \pi$ and $\phi_0$ is a non-zero constant. At what time is the magnitude of the induced emf a maximum?

The intrinsic electron and hole concentrations of a Si-based intrinsic semiconductor are $n_e^{(0)}$ and $n_h^{(0)}$, respectively. Upon doping with trivalent impurities the respective carrier concentrations become $n_e$ and $n_h$. Which of the following options is true?

The velocity $v(t)$ of a particle moving in one dimension is given by:

$$ v(t)= \begin{cases}\alpha t, & 0 \leq t \leq T / 3 \\ \alpha T / 3, & T / 3 \leq t \leq 2 T / 3 \\ \alpha(T-t), & 2 T / 3 \leq t \leq T\end{cases} $$

where $\alpha(\neq 0)$ is a constant. What is the displacement of the particle from time $t=0$ to $T$ ?

Two fixed point particles, each of charge $+q$, are separated by a distance $2 L$. Another point charge $+q$ of mass $m$ is oscillating about its equilibrium position as indicated in the figure below. The time period of oscillation is given by $T=$ $2 \pi^{3 / 2} \alpha \sqrt{m} / q$. Given that $\epsilon_0$ is the

permittivity of free space, which of the following options is the dimensionally correct expression for $\alpha$ in SI units?

IAT (IISER) 2023 Physics - Units & Measurement and Dimensions Question 1 English

$$ \text { What is the effective resistance between } A \text { and } B \text { in the circuit shown below? } $$

IAT (IISER) 2023 Physics - Current Electricity Question 1 English

57. Consider a Carnot heat engine operating between a heat reservoir at temperature 600 K , and an external atmosphere at temperature 300 K . In one cycle, 1000 kJ of heat is extracted from the heat reservoir, and the associated work is input to a reversible refrigerator that operates between 200 K and the same external atmosphere at 300 K . The refrigerator completes one cycle and releases heat into the atmosphere. How much heat is released into the atmosphere at the end of one cycle of the combined system?

Two spherical bodies A and B each of mass $M$ and radius $R$ are located such that their centers are apart by a distance of $4 R$ as shown in the figure. An object $C$ of mass $m$ is thrown from the surface of A directly towards the center of B with a speed $v_0=2 v_{\text {min }}$, where $v_m$ in is the minimum speed needed for $C$ to reach the surface of $B$. Given that $G$ is the universal gravitational constant, how does the speed $v(x)$ of C change as a function of its distance from the center of A?

IAT (IISER) 2023 Physics - Gravitation Question 1 English

Consider the Bohr model of an atom where an electron of charge $-e$ revolves around a nucleus of charge $+e$ in an orbit of radius $r$. The electron has an orbital angular momentum $2 h$. If the nucleus had charge $+2 e$, what would have been the radius of the orbit of the electron with the same principal quantum number?

A quantity has been measured to have a value of 0.00230 in some units. How many significant figures does the measured value have?