IAT (IISER) 2020
Paper was held on Fri, Sep 18, 2020 3:30 AM
View Questions

Biology

1

Which of the following root modifications is observed in maize?

2
Which of the following chemical intermediates are products of light in photosynthesis?
3
Which of the following organisms produce Cry proteins?
4
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 1000 plants were found to be white-flowered, how many of the red-flowered plants will be heterozygous?
5
Troponin controls binding of actin to myosin motor, thereby regulating muscle contraction. Binding of which metal ions to troponin is crucial for this purpose?
6

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 population?

7
Which of the following is the correct description of interferon?
8
Which of the following products are expected when lipase acts on diglycerides?
9
Radial symmetry is NOT found in which of the following taxa?
10
Reabsorption of which of these molecules in kidney occurs via passive transport?
11

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

Column I Column II
(a) Col$$G_2 \text { phase cells }
$$
(i) 46
(b) $$
G_1 \text { phase cells }
$$
(ii) 92
(c) Spermatogonia (pre-replication)
(iii) 23
(d) Ovum
12
Which of the following processes is NOT involved in functionalisation of mRNA (from hnRNA) in eukaryotes?
13
Which of the following processes increases the uptake of water and minerals by roots in legumes?
14
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?
15
Which of the following processes gives rise to new organisms from unfertilized ova in some species of plants and animals?

Chemistry

1

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

2
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 ( $\mathrm{mol} \mathrm{L}^{-1}$ )?
3

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

4
Common disaccharide sucrose is held together by a glycosidic linkage between
5
Select the correct option based on the increasing order of boiling point of the molecules given below. IAT (IISER) 2020 Chemistry - General Organic Chemistry Question 1 English
6
Identify the major product that forms easily and faster in the following reaction. (Tetrahydrofuran= solvent) IAT (IISER) 2020 Chemistry - Carboxylic Acids and Its Derivatives Question 1 English
7
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?
8
The total number of nodes for a given principal quantum number $n$, and azimuthal quantum number $\ell$, are
9
Which among the following is NOT correct?
10
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 $S$ ?
11
Which one of the following aqueous solutions gives the most intense colour?
12
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)
13

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

14

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

IAT (IISER) 2020 Chemistry - Alcohol, Phenols and Ethers Question 1 English
15

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

IAT (IISER) 2020 Chemistry - Haloalkanes and Haloarenes Question 1 English

Mathematics

1
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?
2
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
3
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?
4

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:

5
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?
6
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:
7

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

8

    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:

9

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 following statements is correct?

10

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

11

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 $C$ ?

12
For what value of $t$ does $f(x)=x^3+t x^2+(2-t) x-3$ have only real roots?
13
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 $\lim \limits_{x \rightarrow 0} f^{\prime}(x)$ ?
14

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 :

15
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?

Physics

1

The potential energy of a point particle of mass $m$ undergoing rectilinear motion along the $x$-axis is given by

$$ V(x)=A x+B x^2 $$

What is the maximum speed attained by the particle if it starts from rest at $x=\frac{A}{B}$ ?

2

Two identical containers kept at the same temperature carry the same gas with different molecular mean free paths $l_1$ and $l_2$. The gas from the first container is completely transferred into the second at the same temperature. What is the molecular mean free path of the resultant mixture in the second container?

3

Consider the circuit with a Zener diode whose breakdown voltage $V_z=4 \mathrm{~V}$. What is the voltage $V_0$ if $V_i=20 \mathrm{~V}$ ?

IAT (IISER) 2020 Physics - Semiconductor Devices and Logic Gates Question 1 English
4

Consider a mass-pulley system as shown in the figure. There is a wedge of mass $M$ and equal wedge angles $\theta$ lying on a rigid horizontal table. The coefficient of friction between the wedge and the table is $\mu$. There are two blocks of mass $m_1$ and $m_2$ lying on the incline of the wedge. The coefficients of friction between the blocks and wedge are $\mu_1$ and $\mu_2$ as shown in the figure. Consider $m_1>m_2$ and the coefficients of friction ( $\mu, \mu_1$ and $\mu_2$ ) to be less than $\tan \theta$. Gravity is acting downwards with acceleration due to gravity $g$. What should be the value of $\frac{m_1}{m_2}$ so that the system is in equilibrium?

IAT (IISER) 2020 Physics - Laws of Motion Question 1 English
5

What is the maximum angle of incidence $\theta_i$ in the figure for which the ray would satisfy the condition for total internal reflection at the boundary of media of refractive indices $n_1$ and $n_2$, where $n_1>n_2$ ?

+ IAT (IISER) 2020 Physics - Ray Optics Question 1 English
6

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

IAT (IISER) 2020 Physics - Current Electricity Question 1 English
7
Consider a solid rod of mass $m$ and uniform density resting against a vertical wall and horizontal floor as shown in the figure. The coefficients of friction of the rod with the wall and with the floor are given to be $\mu_1$ and $\mu_2$ respectively. Gravity is acting downwards with acceleration due to gravity $g$. What should be the value of the inclination angle $\alpha$ so that the rod stays in equilibrium? IAT (IISER) 2020 Physics - Rotational Motion Question 1 English
8
The charge distribution inside a sphere of radius $R=2 a / b$ is given by the volume charge density $\rho=a r^2-b r^3$, where $a$ and $b$ are constants and $r$ is the radial distance from the center of the sphere. At what distance from the center of the sphere, will the electric field go to zero?
9

The acceleration due to earth's gravity on a point particle at a height $h$ above the surface of the earth is denoted by $g_o(h)$ and at a depth $d$ below the surface of the earth is denoted by $g_i(d)$. Consider the earth to be a sphere of radius $R$ with uniform mass density. Which of the following correctly represents the ratio $g_i(d) / g_o(d)$ ?

10

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 square loop is then moved rightwards with a uniform speed as shown in the figure. What is the induced emf in the loop as a function of time $t$ ?

IAT (IISER) 2020 Physics - Electromagnetic Induction Question 1 English

11

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

12

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 $M_e=m_e c^2=0.51 \times 10^6 \mathrm{eV}$, where $c$ is the velocity of light in a vacuum. It is given that $\frac{e^2}{2 \epsilon_0 h c}=1 / 137$. The Planck's constant h is given as $4.13 \times 10^{-15} \mathrm{eV}-\mathrm{sec}$. The electron makes a transition from $n^{\text {th }}$ orbit to the ground state of the atom. What is the frequency of the emitted photon?

13
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?
14
An ideal rigid diatomic gas undergoes expansion at constant pressure when $\Delta Q$ heat is added to it. What is the ratio of the change in the internal energy $\Delta U$ to the heat supplied $\Delta Q$ ?
15
The fundamental constants are given to be permittivity constant $\left(\epsilon_0\right)$, Planck's constant $(h)$, velocity of light $(c)$, Newton's constant $(G)$ and Boltzmann's constant $\left(k_B\right)$. Which of the following quantities constructed out of the above constant has the dimensions of an electric charge?
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12