IAT (IISER) 2023

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 the following is an example of genetic diversity?

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)

Quate...

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

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

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 ...

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 best describes peptones?

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

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








Column I



Column II





P.

Sertoli cells

(i)

Secretion of chorionic gonadotropin





Q.

Follicle stimulating hormone

(ii)

Carri...

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

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

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...

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

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

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

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








Column I



Column II





P.

Squamous epithelium

(i)

The nucleus is at the basal side of the cell; also helps in movement of particles an...

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

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

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

\(\text { Which amongst the following are aromatic? }\)

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

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

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

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

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

Which of the following is an ore of iron?

Which parameters are plotted in the Ellingham diagram?

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

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

Related to the Freundlich adsorption isotherm, which one of the following statements is NOT correct?

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?

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

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 $y^2=1$ ?

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

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

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 $f: \mathbf{R} \rightarrow(0, \infty)$ 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 ...

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

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

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?

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}\...

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

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 e...

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 $p(x)=0$ ?

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...

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 $\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma$ ?

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 be...

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 flowin...

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

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?

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 follow...