IISER IAT 2022 question paper with solutions

1. i and u; ii and r; iii and s; iv and p
2. i and t; ii and r; iii and s; iv and q
3. i and $𝑢$; ii and r; iii and q; iv and p
4. i and r; ii and t; iii and s; iv and q

Transcription note: Retyped the damaged matching table against the 2022 paper.

1. i; ii; iii; iv
2. i; iii; iv; ii
3. ii; i; iii; iv
4. ii; iii; i; iv

Transcription note: Removed repeated numerals in a distractor using the 2022 paper.

1. Brown seeds with $𝑊𝑤$ embryo
2. White seeds with $𝑊𝑤$ embryo
3. Brown seeds with ww embryo
4. White seeds with ww embryo

1. Single stranded RNA
2. Single stranded DNA
3. Double stranded RNA
4. Double stranded DNA

1. Fat digested in the intestine is absorbed through the lymph.
2. It is the interstitial fluid generated by the passage of liquid between the cells of the capillary.
3. It is colourless and has similar mineral composition as of plasma.
4. It remains as an interstitial fluid and is never put back into circulation.

1. Dorsal root ganglion
2. White matter
3. Gray matter
4. Muscle spindle

1. They stimulate renin production to induce vasoconstriction and increase blood pressure
2. They stimulate pituitary gland to facilitate the secretion of mineralocorticoids to adjust the changes in mineral composition of the body fluid.
3. They stimulate atrial wall to release atrial natriuretic factor to induce vasodilation and reduce blood pressure.
4. They stimulate hypothalamus to facilitate the release of the anti-diuretic hormone and increase water reabsorption.

1. Incomplete dominance
2. Pleiotropy
3. Linkage
4. Partial dominance

1. 0
2. 25
3. 100
4. 200

1. Arthropoda
2. Mollusca
3. Platyhelminthes
4. Hemichordata

1. $P>Q>S>R$
2. $𝑃>𝑆>𝑄>𝑅$
3. $𝑄>𝑃>𝑆>𝑅$
4. $𝑅>𝑄>𝑆>𝑃$

1. 0.7 and 0.3
2. 0.9 and 0.1
3. 0.3 and 0.7
4. 0.1 and 0.9

1. The replication fork is formed and DNA ligase activity of the Taq polymerase joins the discontinuous fragments.
2. The replication fork is formed and Taq polymerase extends DNA in both $3^{\prime }$ to $5^{\prime }$ and $5^{\prime }$ to $3^{\prime }$ direction.
3. Denaturation step in PCR substitutes for the replication fork and Taq polymerase extends DNA only in the $3^{\prime }$ to $5^{\prime }$ direction.
4. Denaturation step in PCR substitutes for the replication fork and Taq polymerase extends DNA only in the $5^{\prime }$ to $3^{\prime }$ direction.

1. Early anaphase
2. Early metaphase
3. Late anaphase
4. Metaphase

Transcription note: Normalised quotation marks around X; this is a distance, not a derivative.

1. $K_3\left[\mathrm{Fe}\right(\mathrm{CN}{)}_6]$ and KOH
2. $K_3\left[\mathrm{Fe}\right(\mathrm{CN}{)}_6]$ and $H_{2}O$
3. K₃[Fe(CN)₆], H₂O and O₂
4. $K_4\left[\mathrm{Fe}\right(\mathrm{CN}{)}_5\left(\mathrm{OH}\right)]$ and HCN

Transcription note: Restored O2 in the distractor from the 2022 paper.

1. ${\left({𝑡}_{2𝑔}\right)}^3{\left({𝑒}_{𝑔}\right)}^0$
2. ${\left({𝑡}_{2𝑔}\right)}^6{\left({𝑒}_{𝑔}\right)}^4$
3. ${\left({𝑡}_{2𝑔}\right)}^6{\left({𝑒}_{𝑔}\right)}^2$
4. ${\left({𝑡}_{2𝑔}\right)}^4{\left({𝑒}_{𝑔}\right)}^2$

1. 6-membered rings are fused with 5-membered rings ONLY.
2. 6-membered rings are fused with 6-membered rings ONLY.
3. 5-membered rings are fused with 6-membered rings ONLY.
4. 5-membered rings are fused with both 5-membered and 6-membered rings.

1. 1,4
2. 3,4
3. 3,5
4. 4,5

Which of the following expressions represents the hydrogen atom wave function $𝜓\left(𝑟\right)$ shown in the figure below? ( $𝑟$ is the distance of the electron from the nucleus and ${𝑎}_0$ is a constant)

1. $\cdot \frac{1}{\sqrt{𝜋}}{\left(\frac{1}{{𝑎}_0}\right)}^{3/2}{𝑒}^{-𝑟/2{𝑎}_0}$
2. $\frac{1}{\sqrt{6𝜋}}{\left(\frac{1}{{𝑎}_0}\right)}^{3/2}\left(\frac{𝑟}{{𝑎}_0}\right){𝑒}^{-𝑟/2{𝑎}_0}$
3. $\frac{1}{4\sqrt{2𝜋}}{\left(\frac{1}{{𝑎}_0}\right)}^{3/2}(2-\frac{𝑟}{{𝑎}_0}){𝑒}^{-𝑟/2{𝑎}_0}$
4. $\frac{1}{\sqrt{3𝜋}}{\left(\frac{1}{{𝑎}_0}\right)}^{3/2}(3-\frac{2𝑟}{{𝑎}_0}+\frac{2{𝑟}^2}{9{𝑎}_0^2}){𝑒}^{-𝑟/3{𝑎}_0}$

$\text{ Which of the following molecules are aromatic? }$

1. M and O only
2. N and P only
3. M, N and O only
4. M, N, O, and P

Which of the following are aryl bromides?

1. N and P only
2. N and O only
3. M, O and P only
4. N, O and P only

1. $𝑀{𝐿}^2{𝑇}^{-1}$
2. $𝑀{𝐿}^{-1}{𝑇}^{-2}$
3. $𝑀𝐿{𝑇}^{-2}$
4. $𝑀{𝐿}^2{𝑇}^{-2}$

1. Only Y
2. $24\%𝑋$ and $76\%𝑌$ by weight
3. Only X
4. $98\%𝑋$ and $2\%𝑌$ by weight

1. 0.605
2. 605.0
3. 0.688
4. 688.0

Transcription note: Restored the para-difluoro structure from the 2022 paper; the secondary diagram showed different para substituents.

1. $7/13$
2. $8/13$
3. 9/13
4. $19/26$

1. $2^{33}$
2. $2^{31}$
3. $-2^{33}$
4. $-2^{31}$

1. 25
2. 35
3. 55
4. 105

1. 8 elements
2. 2 elements
3. 4 elements
4. Infinitely many elements

1. ${15.049}^{\circ }C$
2. ${17.298}^{\circ }C$
3. ${17.135}^{\circ }C$
4. ${17.471}^{\circ }C$

1. $𝑅$ is reflexive and symmetric but not transitive
2. $𝑅$ is reflexive and transitive but not symmetric
3. $𝑅$ is symmetric and transitive but not reflexive
4. $𝑅$ is an equivalance relation

1. $1/2$
2. $1/3$
3. $1/6$
4. $1/12$

Transcription note: Restored the subscript n+1 from the paper.

1. 0
2. $1/2$
3. 1
4. 2

1. Local maxima at $𝑥=𝑎$ if $𝑎>0$
2. Local maxima at $𝑥=𝑎$ if $𝑎<0$
3. Local minima at $𝑥=𝑎$ if $𝑎>0$
4. A point of inflection at $𝑥=𝑎$

1. 0
2. 1
3. -1
4. $(-1{)}^{𝑘}$

1. 0,2
2. $-2,2$
3. $7/2,0$
4. $4,-2$

1. $\frac{𝜋}{4}$
2. $\frac{3𝜋}{4}$
3. $\frac{5𝜋}{6}$
4. $\frac{𝜋}{6}$

1. Increasing on the interval $(0,2)$
2. Decreasing on the interval $(-3,0)$
3. Increasing on the interval $(2,3)$
4. Decreasing on the interval $(3,\infty )$

1. $\log \left(\frac{{100}^{98}}{98!}\right)$
2. $\log \left(\frac{{100}^{99}}{98!}\right)$
3. $\log \left(\frac{{100}^{98}}{99!}\right)$
4. $\log \left(\frac{{100}^{99}}{99!}\right)$

1. ${𝑦}^{\prime \prime }-2{𝑦}^{\prime }+𝑦=0$
2. ${𝑦}^{\prime \prime }-{𝑦}^{\prime }+𝑦=0$
3. ${𝑦}^{\prime \prime }-2{𝑦}^{\prime }-𝑦=0$
4. ${𝑦}^{\prime \prime }-{𝑦}^{\prime }-𝑦=0$

1. $\frac{{𝑆}_{13}}{{𝑆}_{12}}=\frac{\log \left[𝛼({𝑡}_3-{𝑡}_1)\right]}{\log \left[𝛼({𝑡}_2-{𝑡}_1)\right]}$
2. $\frac{{𝑆}_{13}}{{𝑆}_{12}}=\frac{\exp \left[𝛼({𝑡}_3-{𝑡}_1)\right]}{\exp \left[𝛼({𝑡}_2-{𝑡}_1)\right]}$
3. $\frac{{𝑆}_{13}}{{𝑆}_{12}}=\frac{\exp \left[𝛼({𝑡}_3-{𝑡}_1)\right]-1}{\exp \left[𝛼({𝑡}_2-{𝑡}_1)\right]-1}$

4. $\frac{{𝑆}_{13}}{{𝑆}_{12}}=\frac{\log \left[𝛼({𝑡}_3-{𝑡}_1)\right]-1}{\log \left[𝛼({𝑡}_2-{𝑡}_1)\right]-1}$

1. $\sqrt{6𝑔𝑅}$
2. $\sqrt{7𝑔𝑅}$
3. $\sqrt{(7/2)𝑔𝑅}$
4. $4\sqrt{𝑔𝑅}$

1. $𝜇=\cot \left(𝜃\right)$
2. $𝜇=\cot \left(\frac{𝜃}{2}\right)$
3. $𝜇=\tan \left(𝜃\right)$
4. $𝜇=\tan (𝜃/2)$

As shown in the figure a block is resting on a frictionless floor and is attached to the free end of a spring. The right edge of the block in equilibrium is at a distance $𝑑$ from the wall. When the spring is compressed by a distance $𝑑/2$ and released, the time-period of the motion is $𝑇$. Similarly, when compressed by a distance $2𝑑$ and released, the time-period is ${𝑇}_0$. Considering elastic collision between the block and the wall, what is the value of the quantity ${𝑇}_0/𝑇$ ?

1. $1/4$
2. 1
3. $3/4$
4. $2/3$

A liquid of density $𝜌$ in a container weighs $𝑊$. A cubic block of side $𝐿$ and density ${𝜌}_{𝑏}<𝜌$ is pushed by a stick to completely submerge the block in the liquid without touching the bottom. If $𝑔$ is the acceleration due to the gravity and liquid displaced by the stick is negligible, what is the new weight of the container as registered by the weighing machine below?

1. $𝑊+𝜌𝑔{𝐿}^3$
2. $𝑊+{𝜌}_{𝑏}𝑔{𝐿}^3$
3. $𝑊+(𝜌-{𝜌}_{𝑏})𝑔{𝐿}^3$
4. $𝑊+({𝜌}_{𝑏}-𝜌)𝑔{𝐿}^3$

1. $𝑃$
2. $2𝑃$
3. $4𝑃$
4. $𝑃/2$

A uniform taut string with two point charges $𝑞$ and $-𝑞$ attached to its ends passes over two massless pullies kept $𝐿$ distance apart as shown in the fgure. If $𝑓$ is the fundamental frequency of the part of the string over pullies, which of the following statements is correct?

1. $𝑓\propto {𝐿}^{-2}$
2. $𝑓\propto {𝐿}^{-1}$
3. $𝑓\propto 𝐿$
4. $𝑓\propto {𝐿}^2$

Consider a very long cylinder of radius $𝑎$ having a uniform positive charge density $𝜌$. A sphere of radius $𝑎$ has been carved out (see figure), leaving no charge in that region. The distance radially outward to the cylinder, as measured from the center of the sphere is $𝑥$. At what value of $𝑥$ will the electric field be maximum?

1. $𝑎$
2. $(2/3)𝑎$
3. $(3/2)𝑎$
4. $(4/3)𝑎$

1. 60.0 g
2. 0.5 kg
3. 1 kg
4. 10 kg

In the given circuit, the box $𝐵$ either contains a capacitor, or an inductor or a resistor. The current $𝐼$ versus time $𝑡$ plots for three cases $({𝑎}_1,{𝑎}_2,{𝑎}_3)$ are shown in figures. The switch $𝑆$ is closed at time $𝑡=0$. Which of the following is correct?

1. ${𝑎}_1$ corresponds to an inductor, ${𝑎}_2$ corresponds to a capacitor, ${𝑎}_3$ correspond to a resistor.
2. ${𝑎}_1$ corresponds to a resistor, ${𝑎}_2$ corresponds to an inductor, ${𝑎}_3$ corresponds to capacitor
3. ${𝑎}_1$ corresponds to an inductor, ${𝑎}_2$ corresponds to a resistor, ${𝑎}_3$ corresponds to capacitor.
4. ${𝑎}_1$ corresponds to a resistor, ${𝑎}_2$ corresponds to a capacitor, ${𝑎}_3$ corresponds to inductor.

In the given circuit each of the resistors is of $1k\Omega$ resistance and each of the capacitors has $4𝜇F$ capacitance. What is the charge in the capacitor between the points B and F ?

1. $10𝜇𝐶$
2. $15𝜇𝐶$
3. $(40/7)𝜇𝐶$
4. $(60/7)𝜇𝐶$

A thin lens made of material of refractive index $n_l$ forms the image at the position I of a point object held at O on the central axis of the lens, as is shown in the ray diagram below. Consider that the refractive index of the medium is $n_m$ and $n_l>n_m$ for the figure given. Where does the image form when $n_l<n_m$?

1. At point A
2. At point B
3. At point $𝐶$
4. At point D

Transcription note: Restored the missing ray diagram and damaged inequality from the 2022 paper. This is Physics question 12 in that PDF; numbering here follows the supplied year-wise collection.

A conducting sphere of radius $𝑎$ initially contains a uniform volume charge density $𝜌$. What is the electric flux $\Phi$ through a spherical surface of radius $2𝑎$ centered at a point on the surface of the charged sphere (see figure) at a later time $𝑡$ ? ( ${𝜖}_0$ is the permittivity of free space.)

1. $\Phi =\frac{16}{{𝜖}_0}𝜋{𝑎}^2𝜌$
2. $\Phi =\frac{4}{3{𝜖}_0}𝜋{𝑎}^3𝜌$
3. $\Phi =\frac{32}{3{𝜖}_0}𝜋{𝑎}^3𝜌$
4. $\Phi =\frac{4}{{𝜖}_0}𝜋{𝑎}^2𝜌$