IAT (IISER) 2020

Radial symmetry is NOT found in which of the following taxa?

\(\text { Match the human cell types or (column I) to the number of chromatids (column II) }\)


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Which of the following products are expected when lipase acts on diglycerides?

The following word diagram depicts a food chain in a forest.
\(\text { Trees (Aspen, willow) } \rightarrow \text { Herbivore (Elk) } \rightarrow \text { Predator (Wolf) }\)
Which is the most likely outcome of depletion in predator populat...

Reabsorption of which of these molecules in kidney occurs via passive transport?

Which of the following is the correct description of interferon?

Troponin controls binding of actin to myosin motor, thereby regulating muscle contraction. Binding of which metal ions to troponin is crucial for this purpose?

Which of the following organisms produce Cry proteins?

Which of the following processes increases the uptake of water and minerals by roots in legumes?

Which of the following processes is NOT involved in functionalisation of mRNA (from hnRNA) in eukaryotes?

Which of the following root modifications is observed in maize?

Which of the following graphs correctly represents the relationship between population growth rate $(\mathrm{dN} / \mathrm{dt})$ and population size $(\mathrm{N})$, if the population shows logistic growth?

Which of the following chemical intermediates are products of light in photosynthesis?

A hypothetical plant species shows two flower colour phenotypes- red and white. Red is dominant over white. In a population, this flower colour locus was found to be in HardyWeinberg equilibrium. If 490 out of a total population size of 100...

Which of the following processes gives rise to new organisms from unfertilized ova in some species of plants and animals?

\(\text { Select the most appropriate compound I and the reagents for the synthesis of compound II }\)

The total number of nodes for a given principal quantum number $n$, and azimuthal quantum number $\ell$, are

Common disaccharide sucrose is held together by a glycosidic linkage between

Identify the major product that forms easily and faster in the following reaction. (Tetrahydrofuran= solvent)

\(\text { What is the most appropriate Lewis structure of } \mathrm{NO}_2 \mathrm{~F} \text { ? }\)

A first-order reaction is found to have a half-life of one second (sec). What will be the time required for $99.9 \%$ completion of the reaction?

\(\text { The number of unpaired electron(s) in the square planar complex }[\text{Ni}(\text{CN})_4]^{2-} \text { is/are }\) :

Which one of the following aqueous solutions gives the most intense colour?

Select the correct option based on the increasing order of boiling point of the molecules given below.

\(\text { Identify the final major product III in the following reaction sequence: }\)

The molar conductivity of 0.00241 M acetic acid is $32.87 \mathrm{Scm}^2 \mathrm{~mol}^{-1}$. If the limiting molar conductivity at 298 K is $390.5 \mathrm{Scm}^2 \mathrm{~mol}^{-1}$, what is the dissociation constant ( $\mathrm{mol} \mathr...

Which among the following is NOT correct?

Which among the following is NOT correct regarding the first ionization potential $\left(\mathrm{IP}_1\right)$ of period $I I I$ elements $M g, A l, S i, P$ and $S$ ?

\(\text { How many atoms are present in a hexagonal close-packed unit cell? }\)

What is the correct relation between the heat capacity at constant volume $\left(C_v\right)$ and heat capacity at constant pressure $\left(C_p\right)$ for an ideal gas? ( $R=$ Universal gas constant)

Let $C$ be a circle which passes through $(-2,1)$ and $(0,3)$ and whose centre lies on the line $y-x=1$. Then which of the following points lies on $C$ ?

Let $a, b$ be nonzero real numbers. If $p(x)=x^n+c_{n-1} x^{n-1}+\cdots+c_0$, where $c_{n-1}, \ldots, c_0$ are integers and $n \geq 3$, then which of the following statements is correct?

$F(x)=\int_0^{e^x}\left(t^3+2 t^2-t-2\right) d t$, then for how many real numbers $x$ does $F^{\prime}(x)=0$ ?

If $p(t)=\frac{t(t-1) \cdots(t-2019)}{2019!}$, then the value of
\(\int_0^1\left(\frac{1}{t+1}+\frac{1}{t+2}+\cdots+\frac{1}{t+2020}\right) p(-t-1) d t\)
is:

Consider the differential equation $f^{\prime \prime}+p f^{\prime}+q f=0$ where $p$ and $q$ are constants, $p^2=4 q$ and $q \neq 0$. If y is a nonzero solution of the equation, then which of the following statements is correct?

For what value of $t$ does $f(x)=x^3+t x^2+(2-t) x-3$ have only real roots?

Let $[x]$ denote the greatest integer less than or equal to $x$. The number of positive integer solutions of the equation

\(\left[\frac{x}{19}\right]=\left[\frac{x}{20}\right]\)
are:

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ be two functions such that
$$ g \circ f(x)= \begin{cases}x^2, & \text { if } x \geq 0 \\ e^x-1, & \text { if } x<0\end{cases} $$
Then which of the followi...

If $f(x)=a x^2+b x+c$ and $f\left(\frac{1}{n}\right)=\frac{n+1}{n^2}$ for all $n \in N$, then what is the value of $\lim \limits_{x \rightarrow 0} f^{\prime}(x)$ ?

If $A=\left[\begin{array}{lll}1 & a & 0 \\ 0 & 1 & b \\ 0 & 0 & 1\end{array}\right]$, then the determinant of $I-A+A^2-A^3+A^4-\cdots+A^{2020}$ is

The number of skew-symmetric matrices $A=\left[a_i j\right]_{3 \times 3}$, where $a_i j \in\{-3,-2,-1,0,1,2,3\}$ is:

A bag contains 8 balls, of which 5 are green and 3 are red. The probability that two balls chosen at random are of the same colour is :

\(\text { Define binary operation * on } Q \text { by } a * b=a+b-3 \text {. The inverse of } 2 \text { with respect to * is }\)

Let $S=\{(a, b): a, b \in Q\}$ and $\ell$ be the line $y=m x+c$. Which of the following statements is not correct?

If S is the set of all points $(x, y)$ satisfying the equation $\sin x=\cos y$, then which of the following statements is correct?

An electron of mass $m_e$ has a speed $u_n$ in the $n^{\text {th }}$ Bohr orbit of a hydrogen atom. The normalized speed $V_n$ is given as $V_n=u_n / c=1 / 685$ and the mass of the electron in the units of energy is given as $M_e=m_e c^2=0....

\(\text { What is the equivalent resistance between the points } A \text { and } B \text { in the figure? }\)

In the photoelectric effect experiment, the frequency of the incident light is changed from red to blue while keeping the energy per unit area per unit time of the incident radiation fixed. What will happen to the saturation current?

Consider an infinite one-dimensional wire carrying a uniform current $I$ as shown in the figure. A square loop of side $a$ is initially placed such that the center of the loop is at a distance $R$ from the wire, where $R>\frac{a}{2}$. The s...

The electric field of an electromagnetic wave is given by $\vec{E}(x, t)=E_0 \hat{z} \cos (a x+b t)$
If $c$ is the speed of light, then the value of $b$ is