IISER IAT 2024 question paper with solutions

1. $5^{\prime }$-GAGAAGCCUAGAC-3'
2. $5^{\prime }$-GUCUAGGCUUCUC- $3^{\prime }$
3. $5^{\prime }$-CAGAUCCGAAGAG-3'
4. $5^{\prime }$-CUCUUCGGAUCUG-3'

The following pedigree diagram shows the inheritance of a rare genetic disorder (filled shapes depict affected individuals). Which of the following is the most likely pattern of inheritance of the disorder?

1. X-linked recessive
2. X-linked dominant
3. Autosomal recessive
4. Autosomal dominant

1. Trypsin
2. Insulin
3. Myoglobin
4. Troponin

1. Subsidiary cells from rice leaf
2. Trichomes from maize leaf
3. Casparian strip from rice root
4. Bulliform cells from grass

1. $𝑃-\left(𝑖𝑣\right);𝑄-\left(𝑖𝑖𝑖\right);𝑅-\left(𝑖\right);𝑆-\left(𝑖𝑖\right)$
2. $𝑃-\left(𝑖𝑖𝑖\right);𝑄-\left(𝑖𝑣\right);𝑅-\left(𝑖\right);𝑆-\left(𝑖𝑖\right)$
3. $𝑃-\left(𝑖𝑖\right);𝑄-\left(𝑖𝑣\right);𝑅-\left(𝑖𝑖𝑖\right);𝑆-\left(𝑖\right)$
4. $𝑃-\left(𝑖𝑖\right);𝑄-\left(𝑖\right);𝑅-\left(𝑖𝑣\right);𝑆-\left(𝑖𝑖𝑖\right)$

1. The end products of meiosis II are haploid gametes.
2. The four products of meiosis are genetically different.
3. Meiotic recombination takes place in both males and females
4. In most flowering plants, only one of the four products of meiosis survives in females.

1. RT-PCR
2. ELISA
3. Gel electrophoresis
4. Widal test

1. 1
2. 0.05
3. 0.8
4. 0.4

Transcription note: Restored words missing from the secondary transcription using the 2024 paper.

1. $𝑃-\left(𝑖𝑖\right);𝑄-\left(𝑖𝑖𝑖\right);𝑅-\left(𝑖\right);𝑆-\left(𝑖𝑣\right)$
2. $𝑃-\left(𝑖𝑣\right);𝑄-\left(𝑖\right);𝑅-\left(𝑖𝑖𝑖\right);𝑆-\left(𝑖𝑖\right)$
3. $𝑃-\left(𝑖𝑖𝑖\right);𝑄-\left(𝑖𝑖\right);𝑅-\left(𝑖\right);𝑆-\left(𝑖𝑣\right)$
4. $𝑃-\left(𝑖𝑖𝑖\right);𝑄-\left(𝑖\right);𝑅-\left(𝑖𝑣\right);𝑆-\left(𝑖𝑖\right)$

Two species of a flowering plant, $𝑃(2𝑛=20$ chromosomes) and $𝑄$ ( $2𝑛=30$ chromosomes) are reciprocally crossed with each other as male or female as shown below to produce F1 seeds. Which of the following seed tissues from both the F1 seeds ( $𝑅$ and $𝑆$ ) will have the same chromosome numbers?

1. Endosperm
2. Embryo
3. Embryo and seed coat
4. Embryo and endosperm

1. 10 million
2. 0.66 billion
3. 1 million
4. 0.1 billion

1. Hemichordata is not a chordate sub-phylum because it has a water vascular system.
2. Hemichordata is a chordate sub-phylum with a proto-notochord called stomochord.
3. Hemichordata is a chordate sub-phylum with a proper notochord and gill slits.
4. Hemichordata is not a chordate sub-phylum, with a proto-notochord called stomochord.

Which of the following statements is correct about the oxygen $\left(O_2\right)$ dissociation curves A and C relative to curve B ?

1. Curve C represents favourable $O_2$ association with haemoglobin at low ${\mathrm{pCO}}_2$.
2. Curve A represents favourable O₂ association with haemoglobin at low [H⁺].
3. Curve A represents favourable $O_2$ association with haemoglobin at low pH .
4. Curve C represents favourable $O_2$ association with haemoglobin at high ${\mathrm{pO}}_2$.

Transcription note: Restored low hydrogen-ion concentration in option B from the paper; the secondary source repeated the low-pH distractor.

1. Noble gases
2. Halogens
3. Alkali metals
4. Alkaline earth metals

1. These are isoelectronic and have identical bond order.
2. These are isoelectronic and have different bond orders.
3. These are not isoelectronic but have identical bond order.
4. These are neither isoelectronic nor have identical bond order.

1. $K_4\left[\mathrm{Mn}\right(\mathrm{CN}{)}_6]$ and $\left[\mathrm{Ni}\right(\mathrm{CO}{)}_4]$
2. ${𝐾}_2\left[{\mathrm{MnCl}}_4\right]$ and ${𝐾}_4\left[\mathrm{Mn}\right(\mathrm{CN}{)}_6]$
3. $\left[\mathrm{Fe}{\left(H_{2}O\right)}_6\right]{\left({\mathrm{NO}}_3\right)}_2$ and $K_2\left[{\mathrm{MnCl}}_4\right]$
4. Only ${𝐾}_4\left[\mathrm{Mn}\right(\mathrm{CN}{)}_6]$

1. See-saw and square planar
2. Both see-saw
3. Square planar and see-saw
4. Both square planar

Transcription note: Restored XeF4; the secondary transcription incorrectly displayed X4F4.

1. ${\left[\mathrm{Co}\left(H_{2}O\right){\left({\mathrm{NH}}_3\right)}_5\right]}^{3+}$
2. ${\left[\mathrm{CoCl}{\left({\mathrm{NH}}_3\right)}_5\right]}^{2+}$
3. ${\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_6\right]}^{3+}$
4. ${\left[\mathrm{Co}\right(\mathrm{CN}{)}_6]}^{3-}$

$\text{ What is the relationship between the structures depicted below? }$

1. Conformational isomers
2. Structural isomers
3. Enantiomers
4. Positional isomers

$\text{ What is the correct order of acidity for the following compounds? }$

1. $𝑁>𝑃>𝑄>𝑀$
2. $P>Q>N>M$
3. $N>P>M>Q$
4. $P>N>Q>M$

$\text{ What are the correct structural descriptions for }𝑀\text{ and }𝑁\text{ ? }$

1. M is $𝛽$-D-(+)-glucopyranose and N is $𝛽$-D-(-)-fructofuranose
2. M is $𝛼-D-(+)$-glucopyranose and N is $𝛽$-D-(-)-fructofuranose
3. M is $𝛼-D-(+)$-glucopyranose and N is $𝛼-D-(-)$-fructofuranose
4. M is $𝛼-D-(+)$-glucofuranose and N is $𝛽$-D-(-)-fructopyranose

1. Spontaneous only at very low temperatures
2. Spontaneous only at very high temperatures
3. Non-spontaneous at all temperatures
4. Spontaneous at all temperatures

1. $1.6\times {10}^{-19}J$
2. $2.6\times {10}^{-19}J$
3. 40 J
4. 80 J

Transcription note: Restored the minus sign in Planck’s constant, 6.6 × 10⁻³⁴ J s, from the paper.

1. $149.2S{\mathrm{cm}}^2{\mathrm{mol}}^{-1}$
2. $150.1S{\mathrm{cm}}^2{\mathrm{mol}}^{-1}$
3. $151.1S{\mathrm{cm}}^2{\mathrm{mol}}^{-1}$
4. $152.1S{\mathrm{cm}}^2{\mathrm{mol}}^{-1}$

1. 0
2. 1
3. 2
4. 3

1. 1
2. 4
3. 9
4. 16

1. $(3,4,3)$

2. $(3,4,4)$

3. $(5,4,5)$

4. $(4,4,4)$

1. ${𝑎}_1,2{𝑎}_2,3{𝑎}_3,\dots$ is an Arithmetic Progression.
2. ${𝑎}_1,{𝑎}_2,{𝑎}_3,\dots$ is an Arithmetic Progression.
3. ${𝑎}_1,2{𝑎}_2,3{𝑎}_3,\dots$ is a Geometric Progression.
4. ${𝑎}_1,{𝑎}_2,{𝑎}_3$, ...is a Geometric Progression.

1. $𝑔$ is increasing on $[0,𝜋]$.
2. $𝑔$ is decreasing on $[0,𝜋]$.
3. $𝑔$ is increasing on $(0,𝜋/2)$ and decreasing on $(𝜋/2,𝜋)$.
4. $𝑔$ is decreasing on $(0,𝜋/2)$ and increasing on $(𝜋/2,𝜋)$.

1. $𝑔\left(𝑥\right)=\left(𝑓\right(𝑥){)}^2$
2. $𝑔\left(𝑥\right)=\left|𝑓\right(𝑥\left)\right|$
3. $𝑔\left(𝑥\right)=\left(𝑓\right(𝑥){)}^3$
4. $𝑔\left(𝑥\right)=\sin \left(𝑓\right(𝑥\left)\right)$

1. $\frac{2}{3\sqrt{3}}$
2. $\frac{4}{3\sqrt{3}}$
3. $\frac{1}{3}$
4. $\frac{4}{3}$

1. $𝑅$ is reflexive and symmetric, but not transitive.
2. $𝑅$ is reflexive, but neither symmetric nor transitive.
3. $𝑅$ is an equivalence relation.
4. $𝑅$ is symmetric and transitive, but not reflexive.

1. $2^{23}$
2. $2^{22}-1$
3. $2^{23}+1$
4. $2^{22}$

1. $𝑓$ is neither injective nor surjective
2. $𝑓$ is injective but not surjective
3. $𝑓$ is surjective but not injective
4. $𝑓$ is bijective

1. 0
2. $\frac{𝜋{𝑒}^{\frac{𝜋}{2}}}{2}$
3. ${𝑒}^{𝜋/2}-{𝑒}^{-𝜋/2}$
4. ${𝑒}^{𝜋}-1$

1. $𝑆$ is a circle
2. $𝑆$ is a parabola.
3. $𝑆$ is an ellipse but not a circle
4. $𝑆$ is a hyperbola.

1. 3/4
2. $1/2$
3. $1/32$
4. $1/4$

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

In the given figure, the angles $\angle 𝐵𝐴𝑄=\angle 𝐶𝑃𝑄=\angle 𝐶𝐵𝑄=\frac{𝜋}{2}$; and the lengths $𝑄𝐴=3$ units, $𝐴𝐵=$ 4 units, and $𝐵𝐶=1$ unit. What is the length of $𝑃𝑄$ ?

1. 2 unit
2. 2.2 unit
3. $\sqrt{2}$ unit
4. $3-\sqrt{2}$ unit

1. Abhijit travelled the same distance travelled by Vani.
2. Abhijit travelled half the distance travelled by Vani.
3. Abhijit travelled double the distance travelled by Vani.
4. Abhijit travelled $4/3$ of the distance travelled by Vani.

1. $𝐴\propto {𝑇}^1$
2. $𝐴\propto {𝑇}^2$
3. $𝐴\propto {𝑇}^3$
4. $𝐴\propto {𝑇}^4$

An inextensible cord of negligible mass passes over the rim of a solid disc of mass $𝑀$ and radius $𝑅$. The disc is free to rotate about an axis passing through the centre perpendicular to the plane of the screen, as shown in the figure. Two blocks of masses $𝑀$ and $M/2$ are attached to the two free ends of the cord. Assume that there is no slipping of the cord on the disc. The acceleration due to gravity is $𝑔$. What is the value of the angular acceleration of the disc?

1. $𝑔/𝑅$
2. $𝑔/2𝑅$
3. $𝑔/3𝑅$
4. $𝑔/4𝑅$

Transcription note: Removed an accidental accent on M in the secondary transcription; masses are M and M/2.

1. $\frac{2𝜋}{𝜔}$
2. $\frac{2𝜋}{3𝜔}$
3. $\frac{2𝜋}{5𝜔}$
4. $\frac{2𝜋}{15𝜔}$

A solid bob of a material having density twice that of water is suspended with a massless and inextensible string of length $𝐿$. The whole set-up is placed inside a water-filled tank. The bob is imparted a horizontal velocity ${𝑉}_0$ at the lowest point A , while the other end of the string is fixed, such that the bob completes a semi-circular trajectory in the vertical plane. The string becomes slack only when the bob reaches the topmost point C. Assume that the effects of viscosity and water currents are negligible. The acceleration due to gravity is $𝑔$. What is the expression for ${𝑉}_0$ ?

1. $\sqrt{5𝑔𝐿}$
2. $\sqrt{(5/2)𝑔𝐿}$
3. $\sqrt{2𝑔𝐿}$
4. $\sqrt{(3/2)𝑔𝐿}$

1. $2𝜋\sqrt{\frac{2𝑅}{𝑔}}$
2. $2𝜋\sqrt{\frac{𝑅}{𝑔}}$
3. $2𝜋\sqrt{\frac{3𝑅}{2𝑔}}$
4. $2𝜋\sqrt{\frac{2𝑅}{3𝑔}}$

1. $\frac{𝑅𝑇}{𝑉}$
2. $\frac{𝑅𝑇}{2𝑉}$
3. $\frac{2𝑅𝑇}{𝑉}$
4. $\frac{𝑅𝑇}{4𝑉}$

1. $𝜆=\frac{{𝜆}_1{𝜆}_2}{{𝜆}_1+{𝜆}_2},𝑇=\frac{{𝑛}_1{𝑇}_1+{𝑛}_2{𝑇}_2}{{𝑛}_1+{𝑛}_2}$
2. $𝜆=\frac{{𝑛}_1{𝜆}_1+{𝑛}_2{𝜆}_2}{{𝑛}_1+{𝑛}_2},𝑇=\frac{{𝑛}_1{𝑇}_1+{𝑛}_2{𝑇}_2}{{𝑛}_1+{𝑛}_2}$
3. $𝜆=\frac{{𝑛}_1{𝜆}_1+{𝑛}_2{𝜆}_2}{{𝑛}_1+{𝑛}_2},𝑇=\sqrt{{𝑇}_1{𝑇}_2}$
4. $𝜆=\frac{{𝜆}_1{𝜆}_2}{{𝜆}_1+{𝜆}_2},𝑇=\sqrt{{𝑇}_1{𝑇}_2}$

Transcription note: Corrected a typographical transcription error against the 2024 paper; physical data are unchanged.

Consider two point charges $+𝑞$ and $+2𝑞$ fixed on the $𝑥-𝑦$ plane at $(-\ell /2,0)$ and $(+\ell /2,0)$ respectively. Another point charge $-𝑞$ having mass $𝑚$ is released from rest at $(0,(\sqrt{3}/2\left)\ell \right)$ on the $𝑥𝑦$ plane, as shown in the figure The permittivity of free space is ${𝜖}_0$. What is the acceleration of the charge $-𝑞$ at the time of release?

1. $\frac{{𝑞}^2}{8𝜋{𝜖}_0𝑚{𝑙}^2}(3\hat{ı}-\sqrt{3}\hat{ȷ})$
2. $\frac{{𝑞}^2}{8𝜋{𝜖}_0𝑚{𝑙}^2}(\hat{ı}-\sqrt{3}\hat{ȷ})$
3. $\frac{{𝑞}^2}{8𝜋{𝜖}_0𝑚{𝑙}^2}(\hat{ı}-3\sqrt{3}\hat{ȷ})$
4. $\frac{{𝑞}^2}{8𝜋{𝜖}_0𝑚{𝑙}^2}(3\sqrt{3}\hat{ı}-\hat{ȷ})$

1. $\frac{1}{\sqrt{𝐿𝐶}}$
2. $\frac{1}{\sqrt{2𝐿𝐶}}$
3. $\frac{1}{2\sqrt{𝐿𝐶}}$
4. $\frac{1}{\sqrt{3𝐿𝐶}}$

A conducting wire carrying a steady current $𝐼$ is shaped as shown in the figure below. All connected straight segments meet at right angles. What is the magnetic moment of the current loop?

1. $\mathrm{Iab}(\hat{ȷ}-\widehat{𝑘})$
2. $\mathrm{Iab}(\hat{ȷ}+\widehat{𝑘})$
3. $\sqrt{2}I𝑎𝑏(\hat{ȷ}+\widehat{𝑘})$
4. $\mathrm{Iab}(\hat{k}-\hat{ȷ})$

Transcription note: Corrected a typographical transcription error against the 2024 paper; physical data are unchanged.

Consider the shown circuit. The capacitors ${𝐶}_1$ and ${𝐶}_2$ have capacitances $2𝜇F$ and $8𝜇F$, respectively. The switch can connect point $𝑋$ to either $𝑌$ or $𝑍$. Initially $𝑋𝑌$ is connected until the capacitor is fully charged by the battery. Then the switch connects $𝑋$ and $𝑍$, and the final charges on C₁ and C₂ are ${𝑄}_1$ and ${𝑄}_2$, respectively. What is the value of the ratio $\frac{{𝑄}_2}{{𝑄}_1+{𝑄}_2}$ ?

1. $1/2$
2. $1/4$
3. $1/5$
4. $4/5$

Transcription note: Corrected a typographical transcription error against the 2024 paper; physical data are unchanged.

1. 0.01307
2. 2.00425
3. 0.99559
4. 3.01291

Transcription note: Restored the missing word and numerical typography from the 2024 paper.

The refractive indices $\left(𝑛\right)$ of two transparent slabs are 2 and $2/\sqrt{3}$. They are attached together and placed in a third transparent medium of refractive index $\sqrt{2}$, as shown in the figure. The thickness of the upper slab is $1\mathrm{cm}$. A monochromatic light ray is incident on the upper slab at ${45}^{\circ }$. What would be the thickness in cm of the lower slab such that the lateral shift of the ray after passing through both the slabs is zero?

1. $1/2$
2. $1/\sqrt{2}$
3. $1/\sqrt{3}$
4. $\sqrt{3}/2$

Transcription note: Corrected a typographical transcription error against the 2024 paper; physical data are unchanged.

1. 1 eV
2. 1.25 eV
3. 1.5 eV
4. 2 eV