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A wire of cross-section \(A_{1}\) and length \(l_1\) breaks when it is under tension \(T_{1};\) a second wire made of the same material but of cross-section \(A_{2}\) and length \(l_2\) breaks under tension \(T_{2}.\) A third wire of the same material having cross-section \(A,\) length \(l\) breaks under tension \(\dfrac{T_1+T_2}{2}.\) Then:

1.	\(A=\dfrac{A_1+A_2}{2},~l=\dfrac{l_1+l_2}{2}\)
2.	\(l=\dfrac{l_1+l_2}{2}\)
3.	\(A=\dfrac{A_1+A_2}{2}\)
4.	\(A=\dfrac{A_1T_1+A_2T_2}{2(T_1+T_2)},~l=\dfrac{l_1T_1+l_2T_2}{2(T_1+T_2)}\)

Two wires of identical dimensions but of different materials having Young's moduli \(Y_1, Y_2\) are joined end to end. When the first wire is under a tension \(T,\) it elongates by \(x_1\) while the second wire elongates by \(x_2\) under the same tension \(T.\) The elongation of the composite wire when it is under tension \(T\) is:

1.	\(x_1+x_2\)	2.	\(\dfrac{Y_1x_1+Y_2x_2}{Y_1+Y_2}\)
3.	\(\dfrac{x_1+x_2}{2}\)	4.	\(\dfrac{Y_1x_2+Y_2x_1}{Y_1+Y_2}\)

A thin spherical shell of radius \(R,\) thickness \(t,\) made of a metal of density \(\large{\rho}_{\small{S}},\) floats half submerged in a vessel containing a liquid of density \(\large{\rho}_{\small{L}}.\) The ratio \(\dfrac{\large{\rho}_{\small{S}}}{\large{\rho}_{\small{L}}}\) is equal to:

1.	\(\dfrac{R}{6t}\)	2.	\(\dfrac{R}{3t}\)
3.	\(\dfrac{6t}{R}\)	4.	\(\dfrac{3t}{R}\)

Given below are two statements: 

Assertion (A):	The average velocity of the molecules of an ideal gas increases when the temperature rises.
Reason (R):	The internal energy of an ideal gas increases with temperature, and this internal energy is the random kinetic energy of molecular motion.

 

1.	(A) is True but (R) is False.
2.	(A) is False but (R) is True.
3.	Both (A) and (R) are True and (R) is the correct explanation of (A).
4.	Both (A) and (R) are True but (R) is not the correct explanation of (A).

Two waveforms given by;
\(y=A~\text{sin}2\pi(300~\text{s}^{-1})\bigg({\large t-{\frac{x}{120~\text{m/s}}}}\bigg)\) and 
\(y=A~\text{sin}2\pi(300~\text{s}^{-1})\bigg({\large t+{\frac{x}{120~\text{m/s}}}}\bigg)\)
are superposed on the \(x\)-axis.
Which, of the following, is true?

1.	Node is formed at \(x=0.\)
2.	Antinode is formed at \(x=30~\text{cm}.\)
3.	There is no vibration at \(x=10~\text{cm}.\)
4.	None of the above are true.

If 1 mM solution of ethylamine produces pH = 9, then the ionization constant (K_b) of ethylamine is 10^–x.
The value of x is: (nearest integer)
[Note: The degree of ionization of ethylamine can be neglected with respect to unity]
1. 5
2. 7
3. 9
4. 11

Determine the sum of the number of atoms in each of the following molecules—Br₃O₈, Cl₂O, H₂S₄O₆, H₂S₅O₆, and C₃O₂ that exist in a zero oxidation state:

1. Five (5)
2. Six (6)
3. Seven (7)
4. Two (2)

Find the IUPAC name of the given compound:

1. Hept-2-ene-6-yne-4-ol
2. Hept-6-ene-2-yne-4-ol
3. Hept-1-ene-6-yne-4-ol
4. Hept-6-ene-1-yne-4-ol

During "S" estimation, 160 mg of an organic compound gives 466 mg of barium sulphate. What is the percentage of sulphur in the given compound ?
(Given molar masses in g mol^–1 : Ba=137, S=32 and O=16)
1. 20
2. 40
3. 60
4. 80
 

Excess of isobutane on reaction with \(Br_2\) in presence of light at \(125^\circ C\) gives which one of the following, as the major product?
 

1.
2.
3.
4.

Consider the following three statements regarding Photosystem II (PSII) and choose the correct option:

I:	The reaction centre of PSII is P680 because the wavelength of light it absorbs best is 680 nm.
II:	PSII is predominantly located in the stroma lamellae of the chloroplast.
III:	Cyclic photophosphorylation does not involve the electrons from PSII.

1. I and II are correct
2. II and III are correct
3. I and III are correct
4. All are correct

Consider the following two statements:

Statement I:	The "fight or flight" hormone adrenaline is solely responsible for the long-term physiological adaptation of the body to stress.
Statement II:	Cortisol, released from the adrenal cortex, promotes the breakdown of proteins and fats and stimulates gluconeogenesis to provide a steady supply of glucose during prolonged stress.

 

1.	Both Statement I and Statement II are true, and Statement II is the correct explanation for Statement I.
2.	Both Statement I and Statement II are true, but Statement II is not the correct explanation for Statement I.
3.	Statement I is true, but Statement II is false.
4.	Statement I is false, but Statement II is true.

Consider the following three statements regarding oxygen transport by haemoglobin:

I:	The binding of oxygen to haemoglobin is cooperative, meaning the binding of the first oxygen molecule increases the affinity for the next.
II:	The Bohr effect states that an increase in carbon dioxide concentration or a decrease in pH decreases the affinity of haemoglobin for oxygen.
III:	Foetal haemoglobin has a lower affinity for oxygen compared to adult haemoglobin to facilitate oxygen transfer from mother to foetus.

Which of the above statements is/are correct?
1. I and II only
2. II and III only
3. I and III only
4. I, II, and III

In an experiment, a C₃ plant was subjected to the following two conditions separately:
Condition A: High light intensity, 30°C, normal atmospheric O₂ (21%)
      
Condition B: High light intensity, 30°C, low O₂ (2%)
It was observed that the rate of CO₂ fixation dropped significantly in Condition A compared to Condition B, and glycolate accumulated in the leaves in Condition A.
Based on this: Which of the following conclusions is best supported by the experiment?

1.	High oxygen concentration inhibits the enzyme RuBisCO's carboxylase activity and promotes its oxygenase function, leading to glycolate production.
2.	Low oxygen concentration prevents the formation of glycolate because photorespiration is completely absent in C₃ plants.
3.	Glycolate accumulation indicates enhanced efficiency of the Calvin cycle under high O₂.
4.	The drop in CO₂ fixation in Condition A is primarily due to the destruction of chloroplast membranes at high O₂ levels.

Consider the following two statements about the effect of gibberellins on sugarcane crop yield:

Statement 1:	Gibberellins increase sugarcane yield primarily by promoting internode elongation, leading to longer stalks and higher total biomass.
Statement 2:	Gibberellins increase sugarcane yield by significantly raising the sucrose concentration in the juice of the cane stalks.

Which of the following is correct?

1.	Only Statement 1 is true.
2.	Only Statement 2 is true.
3.	Both Statement 1 and Statement 2 are true.
4.	Neither Statement 1 nor Statement 2 is true.

Which of the following statements about the Krebs cycle is NOT true?

1.	It serves a major amphibolic role, providing precursors for biosynthesis.
2.	Three molecules of NADH and one molecule of FADH₂ are produced per acetyl-CoA oxidised.
3.	The GTP produced in the cycle is a result of oxidative phosphorylation.
4.	The first committed step is the condensation of acetyl-CoA with oxaloacetate.

Consider the given two statements:

Assertion (A):	Abscisic Acid (ABA) is often referred to as a 'stress hormone' in plants.
Reason (R):	Its rapid accumulation under conditions of water stress leads to stomatal closure, reducing transpirational water loss.

 

1.	Both (A) and (R) are true and (R) is the correct explanation of (A).
2.	Both (A) and (R) are true but (R) is not the correct explanation of (A).
3.	(A) is true but (R) is false.
4.	Both (A) and (R) are false.

Consider the following statements regarding glycolysis and select the correct option:

I:	Glycolysis is a common pathway in both aerobic and anaerobic respiration.
II:	The net gain of ATP during glycolysis is 4 molecules of ATP per glucose molecule.
III:	Phosphofructokinase is a key regulatory enzyme of glycolysis and is inhibited by ATP.

1. I and II are correct
2. I and III are correct
3. II and III are correct
4. All are correct

Consider the following three statements regarding the electron transport chain (ETC) in the inner mitochondrial membrane:

I:	Complex I (NADH dehydrogenase) directly pumps 2 protons from the matrix to the inter-membrane space for every pair of electrons it transfers.
II:	Complex II (Succinate dehydrogenase) is a part of both the Krebs cycle and the ETC, but does not pump protons.
III:	Cytochrome *c* oxidase (Complex IV) transfers electrons to molecular oxygen, producing water, and pumps protons across the membrane.

Which of the above statements is/are correct?
1. I and II only
2. II and III only
3. I and III only
4. I, II, and III

Mrs. K, a 62-year-old retired teacher, presents with her daughter who reports  progressive "clumsiness" over several months.
Clinical Features:

• Gait: Stumbles and sways with a wide-based stance; veers to one side
• Fine motor: Drops objects; handwriting has become shaky and irregular
• Speech: Slurred with uneven loudness and rhythm (scanning quality)
• Muscle strength is normal in all limbs

If an MRI scan is ordered, which brain region is most likely to show abnormality?
1. Hippocampus
2. Olfactory lobe
3. Brainstem
4. Cerebellum