IISER IAT 2021 question paper

1. A.
   Ciliated
2. B.
   Squamous
3. C.
   Cuboidal
4. D.
   Columnar

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1. A.
   Conidia of Penicillium
2. B.
   Isogametes of Cladophora
3. C.
   Zoospores of Chlamydomonas
4. D.
   Gemmules in a sponge

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1. A.
   5' GACCAG 3' 3' CTGGTC 5'
2. B.
   5' GAATTC 3' 3' CTTAAG 5'
3. C.
   5' GAAGTC 3' 3' CTTCAG 5'
4. D.
   5' GACTTC 3' 3' CTGAAG 5'

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1. A.
   IgG1
2. B.
   IgA
3. C.
   IgE
4. D.
   IgM

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1. A.
   Mutation
2. B.
   Gene flow
3. C.
   Genetic drift
4. D.
   Reduction in population size

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1. A.
   T1: live, T2: die, T3: die, T4: die, T5: live, T6: die
2. B.
   T1: live, T2: die, T3: die, T4: live, T5: die, T6: live
3. C.
   T1: live, T2: die, T3: live, T4: die, T5: die, T6: live
4. D.
   T1: live, T2: live, T3: die, T4: live, T5: live, T6: live

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1. A.
   Only NADPH
2. B.
   Only ATP
3. C.
   NADPH and $\mathrm{H^+}$
4. D.
   ATP, NADPH and $\mathrm{H^+}$

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1. A.
   540, 760, 1200 and 1500
2. B.
   220, 540, 900 and 2340
3. C.
   220, 540, 1200 and 2040
4. D.
   320, 540, 800 and 2340

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1. A.
   Plant P1 is a $\mathrm{C_3}$ plant having tropical adaptation whereas Plant P2 is a $\mathrm{C_4}$ plant with temperate adaptation
2. B.
   Plant P1 is a $\mathrm{C_4}$ plant having temperate adaptation whereas Plant P2 is a $\mathrm{C_3}$ plant with tropical adaptation
3. C.
   Plant P1 is a $\mathrm{C_3}$ plant having temperate adaptation whereas Plant P2 is a $\mathrm{C_4}$ plant with tropical adaptation
4. D.
   Plant P1 is a $\mathrm{C_4}$ plant having tropical adaptation whereas Plant P2 is a $\mathrm{C_3}$ plant with temperate adaptation

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1. A.
   Xa; Yb; Ya; Xb
2. B.
   Ya; Yb; Xa; Xb
3. C.
   Xb; Ya; Yb; Xa
4. D.
   Yb; Xb; Xa; Ya

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1. A.
   Lactate dehydrogenase
2. B.
   Glutamate dehydrogenase
3. C.
   Transacetylase
4. D.
   Nitrogenase

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1. A.
   Excretion of waste materials
2. B.
   Absorption of proteins
3. C.
   Excretion of water
4. D.
   Absorption of glucose

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1. A.
   i and b; ii and c; iii and d; iv and a
2. B.
   i and b; ii and a; iii and c; iv and d
3. C.
   i and c; ii and b; iii and d; iv and a
4. D.
   i and b; ii and d; iii and c; iv and a

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1. A.
   iv $\rightarrow$ i $\rightarrow$ iii $\rightarrow$ ii
2. B.
   iii $\rightarrow$ iv $\rightarrow$ ii $\rightarrow$ i
3. C.
   i $\rightarrow$ iii $\rightarrow$ iv $\rightarrow$ ii
4. D.
   iv $\rightarrow$ iii $\rightarrow$ i $\rightarrow$ ii

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1. A.
   % ⚥ $\mathrm{K_{(5)}\ C_{(5+5)}\ A_{(\infty)}\ G_{\underline{1}}}$
2. B.
   $\oplus$ ⚥ $\mathrm{K_{(5)}\ C_{(5+5)}\ A_{(\infty)}\ \underline{G}_1}$
3. C.
   % ⚥ $\mathrm{K_{(5)}\ C_{(5)}\ A_2\ G_{\underline{1}}}$
4. D.
   % ⚥ $\mathrm{K_{(5)}\ C_{1+2+(2)}\ A_{(9)+1}\ \underline{G}_1}$

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1. A.
   $90^\circ$ and $120^\circ$.
2. B.
   $90^\circ$ only.
3. C.
   $90^\circ$, $120^\circ$, and $180^\circ$.
4. D.
   $90^\circ$ and $180^\circ$.

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1. A.
   $\angle \mathrm{Cl}_t\mathrm{{-}Al{-}Cl}_t > \angle \mathrm{Cl}_b\mathrm{{-}Al{-}Cl}_b$ and $\mathrm{Al{-}Cl}_b > \mathrm{Al{-}Cl}_t$.
2. B.
   $\angle \mathrm{Cl}_t\mathrm{{-}Al{-}Cl}_t > \angle \mathrm{Cl}_b\mathrm{{-}Al{-}Cl}_b$ and $\mathrm{Al{-}Cl}_t > \mathrm{Al{-}Cl}_b$.
3. C.
   $\angle \mathrm{Cl}_b\mathrm{{-}Al{-}Cl}_b > \angle \mathrm{Cl}_t\mathrm{{-}Al{-}Cl}_t$ and $\mathrm{Al{-}Cl}_b > \mathrm{Al{-}Cl}_t$.
4. D.
   $\angle \mathrm{Cl}_t\mathrm{{-}Al{-}Cl}_t = \angle \mathrm{Cl}_b\mathrm{{-}Al{-}Cl}_b$ and $\mathrm{Al{-}Cl}_t > \mathrm{Al{-}Cl}_b$.

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1. A.
   $\mathrm{(CH_3)_2SiCl_2}$ and $\mathrm{(CH_3)_3SiCl}$
2. B.
   $\mathrm{(CH_3)_3SiCl}$ and $\mathrm{(CH_3)_2SiCl_2}$
3. C.
   $\mathrm{(CH_3)_2SiCl_2}$ and $\mathrm{(CH_3)SiCl_3}$
4. D.
   $\mathrm{(CH_3)SiCl_3}$ and $\mathrm{(CH_3)_2SiCl_2}$

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1. A.
   Complex with weak field ligands in tetrahedral geometry has a magnetic moment of 5.92 BM.
2. B.
   Complex with weak field ligands in octahedral geometry has a magnetic moment of 5.92 BM.
3. C.
   Complex with strong field ligands in octahedral geometry has a magnetic moment of 1.73 BM.
4. D.
   Complex with weak field ligands in tetrahedral geometry has a magnetic moment of 1.73 BM.

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1. A.
   it is a square planar complex.
2. B.
   it has synergic bonding.
3. C.
   CO is a strong field ligand.
4. D.
   Ni has completely filled 3d orbitals.

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1. A.
   $\mathbf{II} \approx \mathbf{III} > \mathbf{IV} > \mathbf{I}$.
2. B.
   $\mathbf{I} > \mathbf{II} = \mathbf{III} > \mathbf{IV}$.
3. C.
   $\mathbf{IV} > \mathbf{III} = \mathbf{II} > \mathbf{I}$.
4. D.
   $\mathbf{IV} > \mathbf{III} > \mathbf{II} > \mathbf{I}$.

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1. A.
   $\mathbf{IV} > \mathbf{I} \approx \mathbf{III} > \mathbf{II}$.
2. B.
   $\mathbf{II} > \mathbf{III} \approx \mathbf{I} > \mathbf{IV}$.
3. C.
   $\mathbf{I} > \mathbf{IV} > \mathbf{III} > \mathbf{II}$.
4. D.
   $\mathbf{II} > \mathbf{III} > \mathbf{IV} > \mathbf{I}$.

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1. A.
   (ii) and (iii)
2. B.
   (i) and (ii)
3. C.
   (i) and (iv)
4. D.
   (iii) and (iv)

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1. A.
   $\mathbf{I}$.
2. B.
   $\mathbf{II}$.
3. C.
   $\mathbf{IV}$.
4. D.
   $\mathbf{III}$.

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1. A.
   4 .
2. B.
   6 .
3. C.
   2 .
4. D.
   8 .

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1. A.
   $-13.41\ \mathrm{kJmol^{-1}}$.
2. B.
   $-20.89\ \mathrm{kJmol^{-1}}$.
3. C.
   $-23.39\ \mathrm{kJmol^{-1}}$.
4. D.
   $-15.91\ \mathrm{kJmol^{-1}}$.

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1. A.
   at the Bohr radius.
2. B.
   at infinite distance.
3. C.
   at the nucleus.
4. D.
   at twice the Bohr radius.

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1. A.
   Half-life of a first order reaction is inversely proportional to the rate constant.
2. B.
   Half-life of a zero order reaction is proportional to the initial concentration of reactant.
3. C.
   Half-life of a zero order reaction is proportional to the rate constant.
4. D.
   Half-life of a first order reaction is independent of the initial concentration of reactant.

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1. A.
   53.6 hours.
2. B.
   10.7 hours.
3. C.
   12.9 microeconds.
4. D.
   64.8 microseconds.

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1. A.
   Free energy against reaction coordinate: X in a well, a first barrier, Y in a well slightly above X, a second barrier higher than the first, Z in a well below X
2. B.
   Free energy against reaction coordinate: X on a shoulder, a high first barrier, Y in a shallow well below X, a small second barrier, Z lowest
3. C.
   Free energy against reaction coordinate: X in a well, a first barrier, Y in a well slightly below X, a second barrier higher than the first, Z lowest
4. D.
   Free energy against reaction coordinate: X in a well, a first barrier higher than the second, Y lowest, a second barrier, Z in a well between X and Y

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1. A.
   $2\sqrt{2}$
2. B.
   $2$
3. C.
   $\sqrt{2}$
4. D.
   $1$

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1. A.
   $\frac{1}{5}$
2. B.
   $\frac{1}{4}$
3. C.
   $\frac{1}{3}$
4. D.
   $\frac{1}{2}$

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1. A.
   infinitely many values.
2. B.
   exactly two values.
3. C.
   exactly three values.
4. D.
   exactly one value.

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1. A.
   $5$.
2. B.
   $10$.
3. C.
   $55$.
4. D.
   $60$.

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1. A.
   $e^2$.
2. B.
   $1$.
3. C.
   $0$.
4. D.
   $e$.

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1. A.
   $4 < f(\sqrt{2}) < 5$
2. B.
   $2 < f(\sqrt{2}) < 3$
3. C.
   $3 < f(\sqrt{2}) < 4$
4. D.
   $5 < f(\sqrt{2}) < 6$

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1. A.
   $p_a$ has a real root if and only if $a \ge 1$.
2. B.
   $p_a$ has a real root if and only if $a \le -1$.
3. C.
   $p_a$ has only non-real complex roots for all $a \in \mathbf{R}$.
4. D.
   $p_a$ has a real root for all $a \in \mathbf{R}$.

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1. A.
   $120$.
2. B.
   $31$.
3. C.
   $41$.
4. D.
   $25$.

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1. A.
   $x + 2y + z = 6$
2. B.
   $y - z = 1$
3. C.
   $x + y + 2z = 5$
4. D.
   $x + z = 2$

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1. A.
   $\frac{\pi}{4}$.
2. B.
   $\frac{\pi}{6}$.
3. C.
   $\frac{\pi}{2}$.
4. D.
   $\frac{\pi}{3}$.

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1. A.
   $8 + 2\pi$.
2. B.
   $8 + 4\pi$.
3. C.
   $8 + 8\pi$.
4. D.
   $8 + 6\pi$.

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1. A.
   $f$ is differentiable but $f'$ is not differentiable.
2. B.
   $f$ is continuous but not differentiable.
3. C.
   $f'$ is differentiable but $f''$ is not differentiable.
4. D.
   $f''$ is differentiable.

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1. A.
   Both $A$ and $A + I$ are invertible.
2. B.
   $A$ is invertible but $A + I$ may not be invertible.
3. C.
   Neither $A + I$ nor $A$ may be invertible.
4. D.
   $A + I$ is invertible but $A$ may not be invertible.

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1. A.
   $x^2 + 2b$.
2. B.
   $0$.
3. C.
   $a + c - b$.
4. D.
   $2a$.

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1. A.
   $m_2 = m_1 + 50,\ v_2 < v_1$.
2. B.
   $m_2 = m_1 + 50,\ v_2 = v_1$.
3. C.
   $m_2 = m_1 + 50,\ v_2 = v_1 + 50$.
4. D.
   $m_2 = m_1,\ v_2 = v_1$.

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1. A.
   Graph of $\omega$ against $x$: a curve rising from the origin, steep at first and flattening out (concave down), up to $x = L$, then dropping vertically to zero and staying at zero beyond $L$.
2. B.
   Graph of $\omega$ against $x$: a curve rising from the origin, slowly at first and steepening (concave up), up to $x = L$, then dropping vertically to zero and staying at zero beyond $L$.
3. C.
   Graph of $\omega$ against $x$: a straight line rising from the origin to its highest value at $x = L$, then dropping vertically to zero and staying at zero beyond $L$.
4. D.
   Graph of $\omega$ against $x$: zero from the origin up to $x = \frac{L}{3}$, then a curve rising steeply and flattening out (concave down) up to $x = L$, then dropping vertically to zero and staying at zero beyond $L$.

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1. A.
   $\frac{\sqrt{2}}{T}\sqrt{\frac{E}{m}}$
2. B.
   $\frac{2\sqrt{2}\pi}{T}\sqrt{\frac{E}{m}}$
3. C.
   $\frac{\pi}{T}\sqrt{\frac{E}{m}}$
4. D.
   $\frac{2\pi}{T}\sqrt{\frac{E}{m}}$

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1. A.
   $90\ \mathrm{m}$
2. B.
   $72\ \mathrm{m}$
3. C.
   $108\ \mathrm{m}$
4. D.
   $81\ \mathrm{m}$

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1. A.
   $-\alpha \Delta T C$
2. B.
   $2\alpha \Delta T C$
3. C.
   $\alpha \Delta T C$
4. D.
   $-2\alpha \Delta T C$

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1. A.
   $18\,\mu\mathrm{C}$ and $18\,\mu\mathrm{C}$ respectively
2. B.
   $\frac{8}{3}\,\mu\mathrm{C}$ and $\frac{16}{3}\,\mu\mathrm{C}$ respectively
3. C.
   $8\,\mu\mathrm{C}$ and $8\,\mu\mathrm{C}$ respectively
4. D.
   $\frac{16}{3}\,\mu\mathrm{C}$ and $\frac{8}{3}\,\mu\mathrm{C}$ respectively

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1. A.
   $E_x = v B_x, E_y = v B_y$
2. B.
   $E_x = -v B_y, E_y = v B_x$
3. C.
   $E_x = -v B_x, E_y = -v B_y$
4. D.
   $E_x = v B_y, E_y = -v B_x$

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1. A.
   $-\frac{15q^2}{4\pi\varepsilon_0 L}$
2. B.
   $\frac{30q^2}{4\pi\varepsilon_0 L}$
3. C.
   $-\frac{30q^2}{4\pi\varepsilon_0 L}$
4. D.
   $\frac{15q^2}{4\pi\varepsilon_0 L}$

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1. A.
   1170 hours
2. B.
   2830 hours
3. C.
   3000 hours
4. D.
   3170 hours

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1. A.
   $P = 1,\ Q = 1$
2. B.
   $P = 0,\ Q = 1$
3. C.
   $P = 1,\ Q = 0$
4. D.
   $P = 0,\ Q = 0$

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1. A.
   $\frac{h^2}{4m_e\lambda_B^2}$
2. B.
   $\frac{h^2}{8m_e\lambda_B^2}$
3. C.
   $\frac{h^2}{10m_e\lambda_B^2}$
4. D.
   $\frac{h^2}{12m_e\lambda_B^2}$

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1. A.
   $72.00\ \mathrm{Hz}$
2. B.
   $135.5\ \mathrm{Hz}$
3. C.
   $127.5\ \mathrm{Hz}$
4. D.
   $128.8\ \mathrm{Hz}$

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