IAT (IISER) 2020 | IAT (IISER) Year Wise Previous Years Questions

Biology

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 cond 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. 6. Identify the major product that forms easily and faster in the following reaction. (Tetrahydrofuran= solvent) 7. A first-order reaction is found to have a half-life of one second (sec). What will be the time required for $99.9 \%$ co 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 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 consta 13. $$ \text { The number of unpaired electron(s) in the square planar complex }[\text{Ni}(\text{CN})_4]^{2-} \text { is/ar 14. $$ \text { Select the most appropriate compound I and the reagents for the synthesis of compound II } $$ 15. $$ \text { Identify the final major product III in the following reaction sequence: } $$

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 i 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. 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 $$ \int_0^1\left(\frac{1}{t+1}+\frac{1}{t+2}+\cdots+\fr 5. Let $a, b$ be nonzero real numbers. If $p(x)=x^n+c_{n-1} x^{n-1}+\cdots+c_0$, where $c_{n-1}, \ldots, c_0$ are integers 6. The number of skew-symmetric matrices $A=\left[a_i j\right]_{3 \times 3}$, where $a_i j \in\{-3,-2,-1,0,1,2,3\}$ is: 7. $$ \text { Define binary operation * on } Q \text { by } a * b=a+b-3 \text {. The inverse of } 2 \text { with respect t 8. Let $[x]$ denote the greatest integer less than or equal to $x$. The number of positive integer solutions of the equati 9. Let $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ be two functions such that $$ g \c 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 t 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 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 s 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

Physics

1. The potential energy of a point particle of mass $m$ undergoing rectilinear motion along the $x$-axis is given by $$ V(x 2. Two identical containers kept at the same temperature carry the same gas with different molecular mean free paths $l_1$ 3. Consider the circuit with a Zener diode whose breakdown voltage $V_z=4 \mathrm{~V}$. What is the voltage $V_0$ if $V_i=2 4. Consider a mass-pulley system as shown in the figure. There is a wedge of mass $M$ and equal wedge angles $\theta$ lying 5. What is the maximum angle of incidence $\theta_i$ in the figure for which the ray would satisfy the condition for total 6. $$ \text { What is the equivalent resistance between the points } A \text { and } B \text { in the figure? } $$ 7. Consider a solid rod of mass $m$ and uniform density resting against a vertical wall and horizontal floor as shown in th 8. The charge distribution inside a sphere of radius $R=2 a / b$ is given by the volume charge density $\rho=a r^2-b r^3$, 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 10. Consider an infinite one-dimensional wire carrying a uniform current $I$ as shown in the figure. A square loop of side $ 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 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 13. In the photoelectric effect experiment, the frequency of the incident light is changed from red to blue while keeping t 14. An ideal rigid diatomic gas undergoes expansion at constant pressure when $\Delta Q$ heat is added to it. What is the r 15. The fundamental constants are given to be permittivity constant $\left(\epsilon_0\right)$, Planck's constant $(h)$, velo

IAT (IISER) 2020

MCQ (Single Correct Answer)

-1

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

2020

$a^{2020}-b a^{2019}+\cdots-b^{2019} a+b^{2020}$

$2020^3$

IAT (IISER) 2020

MCQ (Single Correct Answer)

-1

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 $\ell$ passes through two points of $S$, then $m$ must be rational.

If $m$ is rational and $c$ is irrational, then $\ell$ passes through at least one point of $S$.

If $\ell$ passes through exactly one point of $S$, then $m$ must be irrational.

If $m$ is irrational and $c$ is rational, then $\ell$ passes through exactly one point of $S$.

IAT (IISER) 2020

MCQ (Single Correct Answer)

-1

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:

$2019^2$

2019

$2020^2$

2020

IAT (IISER) 2020

MCQ (Single Correct Answer)

-1

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?

If $a+i b$ is a root of $p(x)$, then $n$ must be even.

If $a$ is a root of $p(x)$, then $n$ must be odd.

If $a+i b$ is a root of $p(x)$, then $(a+i b)^2$ can never be a root of $p(x)$.

If $a$ is a root of $p(x)$, then $a$ must be an integer.

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