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A light ball is thrown with a horizontal velocity of \(50~\text{km/h}\) towards an approaching truck, which is moving at \(50~\text{km/h},\) as shown in the figure. The collision between the ball and the truck is perfectly elastic. The speed of the ball, just after it rebounds from the truck, is:
(assume that the ball rebounds off a vertical surface and that the effect of gravity is negligible)
                      
1. zero
2. \(50~\text{km/h}\)
3. \(100~\text{km/h}\)
4. \(150~\text{km/h}\)

The left end of a rod \(AB,\) of cross-section \(1~\text{cm}^2\) and length \(2~\text m,\) is inserted into an oven at \(200^\circ~\text C\) while its right end is kept in an ice-box. The sides of the rod are insulated to prevent any loss of heat, and the system is allowed to reach a steady state.
           
The thermal resistance of the rod \(AB\) is ratio of the temperature difference across it and the thermal current through it, in the steady state. For the rod \(AB,\) it is (nearly):
1. \(0.05~\text{K/W}\)
2. \(0.15~\text{K/W}\)
3. \(3~\text{K/W}\)
4. \(36~\text{K/W}\)

Given below are two statements: 

Assertion (A):	The speed of sound in air increases as the pressure is increased.
Reason (R):	The speed of sound in a gas is given by, \(v=\sqrt{\dfrac{\gamma P}{\rho}},\) where \(P\) is the pressure & \(\rho\) is the density.

 

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.	(A) is False but (R) is True.

Which of the following statements is correct for an electron having azimuthal quantum number l = 2?
1. The electron may be in the lowest energy shell.
2. The electron is in a spherical orbital.
3. The electron must have spin \(m_s=+\frac{1}{2}\)
4. The electron may have a magnetic quantum number = -1

Given below are two statements:
C(diamond) \(+\mathrm{O}_2 \longrightarrow \mathrm{CO}_2 ; \Delta H=-395 \mathrm{~kJ}\)
C(graphite) \(+\mathrm{O}_2 \longrightarrow \mathrm{CO}_2 ; \Delta H=-393 \mathrm{~kJ}\)
The enthalpy of formation of diamond from graphite is:
1. \(+2.0 \mathrm{~kJ}\)
2. \(-1.5 \mathrm{~kJ}\)
3. \(-788 \mathrm{~kJ}\)
4. \(+788 \mathrm{~kJ}\)

What is the minimum number of electrons needed to balance the following half-reaction with whole-number coefficients?
\(\text{IO}^-_3\rightarrow \text{I}_2\)
1. Six (6)
2. Four (4)
3. Ten (10)
4. Eight (8)

Which of the following is the major product (P) of the given reaction?

 

1.		2.
3.		4.

If the value of the solubility product in water is 1.08 × 10^–10 mol² L^–2 , calculate the solubility of BaSO₄ in water:
(Given: Molar mass of BaSO₄ = 233 gmol^–1)

1.	2.42 × 10-3g/ litre	2.	4.08 × 10–12 g/ litre
3.	2.42 × 103 g/ litre	4.	6.08 × 10–8 g/ litre

Emphysema results from alveolar wall destruction, reducing respiratory surface area and elastic recoil, causing air trapping during expiration and progressive breathlessness. The primary pathological mechanism involves:

1.	Protease-antiprotease imbalance causing enzymatic breakdown of alveolar elastin fibers
2.	Chronic bacterial infection leading to fibrotic thickening of alveolar-capillary membrane
3.	Excessive mucus secretion physically blocking terminal bronchioles and alveolar ducts
4.	Pulmonary hypertension causing capillary damage and interstitial fluid accumulation

Hyperthyroidism results from excessive thyroid hormone secretion causing elevated metabolic rate, heat intolerance, weight loss, and exophthalmos in Graves' disease. The pathophysiological mechanism includes:

1.	Impaired peripheral conversion of T4 to reverse T3 increasing metabolically active hormone
2.	Thyroid follicular hyperplasia from iodine deficiency attempting compensatory hormone synthesis
3.	Ectopic hormone production from thyroid tissue in ovarian teratomas secreting T3 and T4
4.	TSH receptor antibodies mimicking TSH action causing unregulated thyroid hormone overproduction

Consider the following statements regarding events of meiosis, as described in NCERT:

A.	Pairing of homologous chromosomes occurs during zygotene.
B.	Crossing over takes place during pachytene.
C.	Terminalisation of chiasmata begins during diplotene.
D.	Separation of homologous chromosomes occurs during anaphase II.
E.	Meiosis results in the formation of four haploid cells.

How many of the above statements are correct?

1.	Two	2.	Three
3.	Four	4.	Five

In a controlled laboratory experiment, a healthy C₃ plant is exposed to normal light intensity and adequate water supply. Atmospheric CO₂ concentration is increased from 0.03% to 0.10% while O₂ remains constant at 21%. Subsequently, the temperature is raised from 25°C to 40°C. Based on the limiting factor principle and temperature sensitivity of Calvin cycle enzymes, what is the most likely effect on the rate of photosynthesis?

1.	Photosynthesis will increase with elevated CO₂ but decline at 40°C as temperature exceeds the optimum range for key enzymes of carbon fixation.
2.	Photosynthesis will continue increasing proportionally because high CO₂ fully offsets temperature effects on RuBisCO activity.
3.	Photosynthesis will immediately decrease at 40°C because photorespiration overrides the effect of elevated CO₂.
4.	Photosynthesis will remain unchanged since CO₂ is no longer limiting and temperature has minimal influence under enriched CO₂ conditions.

Match List I (Cell-Cycle Stage) with List II (Feature)

	List A		List B
A	G₁ phase	1	DNA replication and histone synthesis
B	S phase	2	Cell growth and metabolic activity
C	G₂ phase	3	Non-dividing quiescent state
D	G₀ phase	4	Preparation for mitosis

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

A botanist studying respiratory pathways in germinating seeds conducts an experiment where seeds are allowed to germinate under two conditions: Condition A with adequate oxygen supply, and Condition B under strictly anaerobic conditions. After 48 hours, ethanol is detected in seeds from Condition B but not from Condition A, while both conditions show consumption of stored glucose. The respiratory quotient (RQ) in Condition A is measured as 1.0. Which conclusion can be logically deduced about the metabolic pathway and energy yield in Condition B compared to Condition A?

1.	Condition B produces equal ATP per glucose molecule as Condition A because glycolysis occurs in both, but pathway diverges only after pyruvate formation
2.	Condition B produces significantly less ATP per glucose molecule because fermentation pathway yields only 2 ATP from glycolysis while aerobic respiration in Condition A yields approximately 36-38 ATP
3.	Condition B produces more ATP per glucose molecule because fermentation is more efficient than aerobic respiration when oxygen availability becomes the limiting factor
4.	Condition B produces the same intermediate metabolites as Condition A up to the citric acid cycle, differing only in the final electron acceptor used

Consider the given two statements:

Assertion(A):	Plastids are found in both prokaryotic and eukaryotic cells.
Reason(R):	Plastids contain their own DNA and ribosomes.

Choose the correct option:

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.	(A) is False, but (R) is True.

In humans, the ascending limb of the Loop of Henle actively transports sodium and chloride ions into the medullary interstitium but remains impermeable to water. A student concludes that this segment directly concentrates urine by causing osmotic removal of water from the filtrate. Which incorrect physiological assumption is this conclusion primarily based upon?

1.	The assumption that solute transport necessarily results in osmotic water movement from the same tubular segment, despite the absence of water permeability
2.	The assumption that the ascending limb functions independently of the descending limb within the countercurrent system
3.	The assumption that the medullary interstitium becomes hypertonic during countercurrent multiplication
4.	The assumption that active transport of sodium and chloride requires metabolic energy

Consider the given two statements:

Statement A:	In the fluid mosaic model, integral membrane proteins are amphipathic molecules that can move laterally within the membrane bilayer, but cannot flip from one side of the membrane to the other due to the energy barrier created by the hydrophobic core.
Statement B:	Peripheral membrane proteins are always located on the cytoplasmic side of the membrane and are attached through covalent bonds with membrane lipids, making them permanently associated with specific membrane domains.

 

1.	Statement A is correct; Statement B is incorrect
2.	Statement A is incorrect; Statement B is correct
3.	Both Statement A and Statement B are correct
4.	Both Statement A and Statement B are incorrect

During intense muscular exercise, the oxygen-haemoglobin dissociation curve for an athlete's blood shifts to the right compared to resting conditions. This rightward shift occurs because the actively metabolising muscle tissues produce increased amounts of carbon dioxide and lactic acid, lowering the local pH. Based on the Bohr effect and cooperative binding properties of haemoglobin, which physiological consequence does this rightward shift primarily accomplish to meet the metabolic demands of exercising tissues?

1.	It increases haemoglobin's oxygen-carrying capacity in the lungs by enhancing the cooperative binding of oxygen molecules to all four heme groups in the haemoglobin molecule
2.	It increases the affinity of haemoglobin for oxygen in the tissue capillaries, ensuring more efficient oxygen uptake from surrounding interstitial fluid into red blood cells
3.	It decreases the affinity of haemoglobin for carbon dioxide in muscle tissues, allowing more efficient removal of metabolic waste products through the Haldane effect
4.	It decreases haemoglobin's oxygen affinity at tissue level, promoting greater oxygen release from haemoglobin to supply the increased oxygen demand of actively respiring muscle cells