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A uniform rod \(AB\) of mass \(M\) is pivoted at its end \(A\) so that it can rotate about \(A\) in a vertical plane. The other end \(B\) is connected to a fixed vertical spring of spring constant \(k.\) If the rod were to perform small rotational oscillations about its horizontal mean position, the angular frequency \((\omega)\) would be:

1.	\(\sqrt{\Large\frac{k}{M}}\)	2.	\(\sqrt{\Large\frac{12k}{M}}\)
3.	\(\sqrt{\Large\frac{3k}{M}}\)	4.	\(\sqrt{\Large\frac{3k}{2M}}\)

The figure shows a pendulum at the bottom of its swing.

What is the direction of the acceleration vector for the bob?

1.		2.
3.		4.	There is no acceleration at this point.

A general graph showing variation in the potential energy \((PE)\) of a particle with time while executing simple harmonic motion is:

1.		2.
3.		4.

The ratio of the speed of sound in nitrogen gas to that in helium gas, at \(300\) K is:

1.	\(\sqrt{\dfrac{2}{7}}\)	2.	\(\sqrt{\dfrac{1}{7}}\)
3.	\(\dfrac{\sqrt{3 }}{5}\)	4.	\(\dfrac{\sqrt{6 }}{5}\)

Consider the depicted hydrogen (H) in the hydrocarbons given below. The most acidic hydrogen (H) is:

1.		2.
3.		4.

Which one of the following molecules does not show stereoisomerism?
1. 3,4-Dimethylhex-3-ene
2. 3-Ethylhex-3-ene
3. 3-Methylhex-1-ene
4. 4-Methylhex-1-ene

Arrange the following compounds in increasing order of electrophilic aromatic substitution:

1. (iv) < (i) < (ii) < (iii)
2. (iii) < (ii) < (i) < (iv)
3. (i) < (iv) < (iii) < (ii)
4. (ii) < (iii) < (i) < (iv)
 

Which one of the following compounds does not exhibit resonance?

1.	\(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{CONH}_2\)
2.	\(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{OCH}=\mathrm{CH}_2\)
3.
4.	\(\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}=\mathrm{CHCH}_2 \mathrm{NH}_2\)

Why do most human enzymes exhibit optimal activity at 37°C and become rapidly inactivated at temperatures above 45°C, while thermophilic bacterial enzymes from deep-sea hydrothermal vents remain active at temperatures exceeding 100°C?

1.	Human enzymes have more flexible protein structures optimised for body temperature, while thermophilic enzymes have rigid structures with extensive disulfide bonds, additional salt bridges, and modified amino acid compositions that maintain structural integrity at high temperatures
2.	Human enzymes rely on weak hydrogen bonds for structure, while thermophilic enzymes use primarily covalent bonds throughout their structure, making them temperature-resistant but less catalytically efficient
3.	Human enzymes contain heat-sensitive cofactors that decompose above 45°C, while thermophilic enzymes use inorganic metal cofactors that remain stable at extreme temperatures
4.	Human enzymes are designed for rapid turnover and are intentionally thermolabile, while thermophilic enzymes have evolved slow but steady catalytic rates to function in extreme environments

Consider the given statements:

A.	Cellulose is a polymer of β-D-glucose.
B.	Glycogen contains α-1,4 and α-1,6 linkages.
C.	Sucrose is a reducing sugar.
D.	Enzymes generally do not alter ΔG of reactions.
E.	Phospholipids contain two fatty acids esterified to glycerol.

How many are correct?
1. 1
2. 2
3. 3
4. 4

Consider the given statements:

A.	Mitochondria and chloroplasts possess 70S ribosomes.
B.	Both show circular DNA.
C.	Both are semiautonomous.
D.	Both divide by fission-like process.
E.	Both participate in key metabolic pathways (respiration/photosynthesis).

How many are correct?
1. 1
2. 2
3. 3
4. 5

Which check point in regulation of cell cycle is called the 'restriction point'?
1. G1/S
2. Intra S
3. G2 M
4. Spindle check point

Consider the given statements:

A.	The middle lamella is primarily composed of pectins.
B.	The secondary cell wall is deposited before the primary cell wall.
C.	Plasmodesmata allow symplastic transport between adjacent plant cells.
D.	Mesosomes are functional membrane bound organelles found in living bacterial cells.
E.	80S ribosomes occur in mitochondria of eukaryotes.

How many of the above statements are correct?
1. 1
2. 2
3. 3
4. 5

Tonoplast refers to

1.	membrane of the vacuole regulating transport of ions and metabolites
2.	inner membrane of the mitochondria housing ATP synthase
3.	outer membrane of chloroplast
4.	membrane covering the nucleolus

Match List-I (Protein Level) with List-II (Description)

	List-I		List-II
A.	Primary structure	1.	Multiple polypeptides association
B.	Secondary structure	2.	Hydrogen bonds forming α-helix/β-sheet
C.	Tertiary structure	3.	Unique sequence of amino acids
D.	Quaternary structure	4.	3D folding due to interactions among R groups

Codes:
1. A–3, B–2, C–4, D–1
2. A–4, B–1, C–3, D–2
3. A–3, B–2, C–1, D–4
4. A–2, B–3, C–1, D–4

Why is interkinesis between meiosis I and meiosis II much shorter than typical interphase, and what critical difference in DNA replication explains why cells can proceed directly from meiosis I to meiosis II without an intervening S phase?

1.	Interkinesis is shorter because cells are smaller after meiosis I; no S phase occurs because reduced cell size requires less DNA for proper function
2.	Interkinesis lacks S phase because chromosomes remain condensed from meiosis I; DNA replication is unnecessary since sister chromatids are still joined by centromeres
3.	Interkinesis is brief because meiotic cells have higher metabolic rates; S phase is skipped due to accumulated DNA damage requiring immediate division
4.	Interkinesis omits S phase because DNA was already replicated before meiosis I; the purpose is to separate existing sister chromatids, not create new ones

Compare the structural organisation and functional significance of rough endoplasmic reticulum (RER) versus smooth endoplasmic reticulum (SER) in terms of ribosome association and metabolic specialisation:

1.	RER has bound ribosomes for protein synthesis and lipid metabolism; SER lacks ribosomes but specialises in carbohydrate synthesis and storage
2.	RER synthesises all cellular proteins; SER synthesises only membrane lipids and has no other metabolic functions
3.	Both RER and SER have ribosomes but RER specialises in enzyme production while SER focuses on structural protein synthesis
4.	RER has bound ribosomes for synthesis of secretory and membrane proteins; SER lacks ribosomes and specialises in lipid synthesis, steroid production, and detoxification

Plant cells undergo cytokinesis by cell plate formation. The cell plate originates from

1.	dissolution of middle lamella
2.	contraction of actin ring
3.	separation of plasma membranes
4.	fusion of Golgi vesicles