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The two ends of a rod with a non-uniform cross-sectional area are maintained at temperatures \(T_1 ~ \text {and}~T_2~ (T_1 >T_2),\) as shown in the figure.
       
If \(I\) represents the heat current through the cross-section of the conductor at a distance \(x\) from its left end, then the variation of \(I\) with \(x\) is best represented by: 

1.		2.
3.		4.

                                                                                           

An ideal monoatomic gas at a temperature of \(300\text{ K}\) and a pressure of \(10\text{ atm}\) is suddenly allowed to expand into vacuum so that its volume is doubled. No exchange of heat is allowed to take place between the gas and its surroundings during the process. After equilibrium is reached, the final temperature is:

1.	\(300\text{ K}\)	2.	\(\dfrac{300}{2^{5/3}}\text{ K}\)
3.	\(\dfrac{300}{2^{2/3}}\text{ K}\)	4.	\(600\text{ K}\)

A solid \(A\) has a lower coefficient of thermal expansion than a liquid \(B.\) A sphere made of \(A\) floats in liquid \(B\text:\) fully submerged, but does not sink, at a fixed temperature. If the temperature of the system is raised, the sphere will:

1.	move slightly upward, but remain submerged
2.	move slightly down, but remain submerged
3.	rise up to the surface
4.	sink within the liquid

In the arrangement shown in the figure, three very large plates are placed parallel to each other at close distances. Treating them as ideal black bodies, with the first plate maintained at temperature \(3T\) and the second plate at temperature \(2T,\) what will be the temperature of the middle plate under steady-state conditions?

1.	\(\left(\dfrac{97}{2}\right)^{\dfrac{1}{4}}T\)	2.	\(\left(\dfrac{90}{2}\right)^{\dfrac{1}{4}}T\)
3.	\(\left(\dfrac{65}{13}\right)^{\dfrac{1}{4}}T\)	4.	\(\left(\dfrac{81}{4}\right)^{\dfrac{1}{4}}T\)

If the temperature (in \(^\circ\text C\)) of a blackbody is increased \(2\)-fold, then the rate of radiation from the body will become:

1.	\(16\)-fold	2.	\(4\)-fold
3.	less than  \(16\)-fold	4.	more than  \(16\)-fold

Which compound is formed when an organic substance containing nitrogen (\(\text{N}\)) and sulfur (\(\text{S}\)) reacts with sodium (\(\text{Na} \)) during the preparation of a Lassaigne's extract, and this compound is subsequently used to confirm the presence of both elements?
(A) \(\mathrm{Fe}_{4}\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]_{3}\)
(B) \(\left[\mathrm{Fe}(\mathrm{CN})_{5} \mathrm{NOS}\right]^{4-}\)
(C) \(\left[\mathrm{Fe}(\mathrm{SCN})_{3}\right]^{2-}\)
Choose the correct option:
1. (B) & (A)
2. (C) 
3. (A)
4. (B) & (C)

On complete combustion, \(0.3 \mathrm{~g}\) of an organic compound gave \(0.2 \mathrm{~g}\) of \(\mathrm{CO}_2~ \mathrm{and}~ 0.1 \mathrm{~g}\) of \(\mathrm{H}_2 \mathrm{O}\). The percentage composition of carbon and hydrogen in the compound, respectively is:
1. \(4.07 \% ~\mathrm{and}~ 15.02 \%\)
2. \(18.18 \% ~\mathrm{and}~ 3.70 \%\)
3. \(15.02 \% ~\mathrm{and}~ 4.07 \%\)
4. \(3.70 \% ~\mathrm{and}~ 18.18 \%\)

Total number of isomers (including stereoisomers) obtained on monochlorination of methylcyclohexane is :
1. 12
2. 8
3. 14
4. 10
 

A molecule ("P") on treatment with acid undergoes rearrangement and gives ("Q") on ozonolysis, followed by reflux under alkaline conditions, yields ("R"). The structure of ("R") is shown below :

The structure of ("P" and "Q") can be:

(A)		(B)
(C)		(D)

1. (B) & (C)
2. (A) & (B)
3. (B) & (A)
4. (C) only

Determine the relationships between w₁ and P, as well as w₂ and P, for D-Erythrose as depicted below.

1. Enantiomer, Diastereomer
2. Identical, Diastereomer
3. Enantiomer, Identical
4. Identical, Enantiomer

In C₃ plants, photorespiration rate increases under high temperature conditions because:

A.	RuBisCO's affinity for O₂ increases relative to CO₂ at higher temperatures
B.	The solubility of CO₂ in water decreases more than that of O₂ as temperature rises
C.	Stomata close partially to reduce water loss, decreasing the CO₂/O₂ ratio in the leaf

 
1. Only A and  B are correct
2. Only A and C are correct
3. Only B and C are correct
4. A, B and C are correct

Consider the given fact to be true:
In plant tissues, oxygen consumption increases when switching from anaerobic to aerobic conditions. 
What might be the plausible explanations?

A.	Aerobic respiration produces more ATP per glucose, reducing the need to consume more glucose
B.	Fermentation products (ethanol/lactate) accumulate and inhibit glycolysis in anaerobic conditions
C.	The electron transport chain generates a proton gradient that increases the efficiency of ATP production

    
1. Only A and  B are correct
2. Only A and C are correct
3. Only B and C are correct
4. A, B and C are correct

The climacteric rise in respiration during fruit ripening is characterized by:

A.	Increased ethylene production that triggers autocatalytic ethylene synthesis
B.	A shift from aerobic to anaerobic respiration as oxygen becomes limiting
C.	Breakdown of stored starch and organic acids providing substrates for increased respiration

   
1. Only A and  B are correct
2. Only A and C are correct
3. Only B and C are correct
4. A, B and C are correct

During the propagation of an action potential in a myelinated axon, if a toxin selectively disables the sodium channels at the nodes of Ranvier without affecting potassium channels or the myelin sheath, what would be observed?

1.	Action potentials propagate normally because myelin allows salutatory conduction.
2.	Action potentials fail to propagate because depolarisation cannot jump between nodes.
3.	Action potentials become faster due to reduced sodium influx at each node.
4.	The axon enters a permanent refractory period and cannot fire again.

Which event directly exposes the myosin-binding sites on actin filaments?
1. Binding of Ca²⁺ to tropomyosin
2. Binding of Ca²⁺ to troponin
3. ATP binding to myosin head
4. Hydrolysis of ATP to ADP + Pi

In aerobic respiration of one glucose molecule, how many of the following are correct?

1	A net of two molecules of ATP are formed by substrate-level phosphorylation in glycolysis.
2	Pyruvate dehydrogenase complex releases CO₂ during formation of acetyl CoA.
3	The Krebs cycle yields 3 NADH and 1 FADH₂ per acetyl CoA oxidised.
4	The total ATP yield from one glucose molecule is universally 38 in all organisms.
5	Oxidative phosphorylation requires intact inner mitochondrial membrane.

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

Consider the given facts to be true:
In myasthenia gravis, autoantibodies target acetylcholine receptors at the neuromuscular junction.
A patient is given an acetylcholinesterase [an enzyme that breaks down acetylcholine] inhibitor. 
Which physiological change would BEST explain the temporary improvement in muscle strength?

1.	Prolonged presence of acetylcholine in the synaptic cleft, allowing more receptor binding
2.	Increased synthesis of acetylcholine in motor neuron terminals
3.	Upregulation of alternative neurotransmitter receptors on the muscle membrane
4.	Direct agonistic action of the chemical on acetylcholine receptors

Erythropoietin is a hormone secreted mainly by the kidneys. What is its primary function?
1. Regulates calcium levels
2. Stimulates red blood cell formation in bone marrow
3. Controls blood pressure

4. Promotes sodium reabsorption

How many statements regarding transmission of nerve impulse are correct?

1	The resting membrane potential is maintained by Na⁺/K⁺ ATPase.
2	Depolarisation occurs when Na⁺ ions enter the neuron.
3	Repolarisation involves the efflux of K⁺ ions
4	The refractory period ensures unidirectional propagation of the impulse.
5	Myelin sheath decreases the speed of impulse conduction.

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

How many of the following statements about endocrine glands are correct?

1	Thyroid hormones increase the basal metabolic rate.
2	Parathyroid hormone raises blood calcium level.
3	Aldosterone regulates sodium reabsorption in kidneys.
4	Glucagon increases blood glucose level by gluconeogenesis and glycogenolysis.
5	Cortisol helps the body cope with stress by stimulating gluconeogenesis.

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