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A pair of equal and opposite parallel line charges (charge per unit length \(+\lambda,-\lambda\)) are placed very close together. The electric field \(E,\) due to these charges, varies with distance \(r\) (measured from them) as:

1. \(E\propto r\)
2. \(E\propto{\Large\frac{1}{r}}\)
3. \(E\propto{\Large\frac{1}{r^2}}\)
4. \(E\propto{\Large\frac{1}{r^3}}\)

Find the magnetic field at the origin \(O\) due the three quarter circular wires with centres at \(O\) but lying in the \(x\text-y,y\text-z\) & \(z\text-x\) planes, respectively. They carry a current \(i.\) The radius of the arcs is \(r.\)

1.	\(\dfrac{\mu_0 i}{8r}\times 3\)	2.	\(\dfrac{\mu_0 i}{8r}\times \dfrac{1}{3}\)
3.	\(\dfrac{\mu_0 i}{8r}\times\sqrt3\)	4.	\(\dfrac{\mu_0 i}{8r}\times\dfrac{1}{\sqrt3}\)

A parallel beam of light of wavelength \(\lambda=400~\text{nm}\) falls normally onto a single slit of width \(d=0.2~\text{mm},\) placed in front of a screen which is \(50~\text{cm}\) away. The first maximum, next to the central maximum, is formed on the screen at a distance of:

1.	\(0.5~\text{mm}\)	2.	\(1~\text{mm}\)
3.	\(1.5~\text{mm}\)	4.	\(2~\text{mm}\)

Unpolarised red light is incident on the surface of a lake at an angle \(\theta_R.\) An observer, viewing the reflected light through a polariser, notices that when rotating the polarizer, the intensity of the light drops to zero at a particular orientation. The red light is then replaced by unpolarized blue light, and the observer observes the same phenomenon with the reflected blue light at an incident angle \(\theta_B.\) The relationship between \(\theta_B\)​ and \(\theta_R\)​ is described by which of the following options?
1. \( \theta_{B}<\theta_{R}<45^{\circ} \)
2. \( \theta_{B}=\theta_{R}\)
3. \( \theta_{B}>\theta_{R}>45^{\circ} \)
4. \( \theta_{R}>\theta_{B}>45^{\circ} \)

If an AND-gate and an OR-gate are OR-ed together, the resulting gate is:
1. AND
2. OR
3. XOR
4. none of the above

7 grams of a solute (molar mass = 93g) dissolves in 42 grams of water. If solute gets dimerized in water and depression at a freezing point is 2°C, then find the percentage association of solute:
[Given: \(K_f(H_2O) = 1.86~{ K kg \over Mole}\)]
1. 76%
2. 80%
3. 82%
4. 85%

How many charges in Faraday is required in the conversion of 1 mole \(Cr_2O_7^{2-}\) into \(Cr^{3+} \)?
1. 3 
2. 6
3. 4 
4. 2

For a 1^st order reaction, following graph is obtained between lnk and \({1000 \over T}\). Then, the activation energy of the reaction in kcal is: 
         
1. 37 kcal
2. 40 kcal
3. 42 kcal
4. 34 kcal

The number of possible isomers for the complex \([Co (en)_ 2 Cl_ 2] 𝐶 𝑙  \) will be:
(en=ethylenediamine)

1.	Two (2)	2.	One (1)
3.	Three (3)	4.	Four (4)

Alkyl halides prepared by among the following reaction(s) is/are:

I.	\(CH_3CH_2OH+HCl\xrightarrow{\bf{anh. ZnCl_2}}\)
II.	\(CH_3CH_2OH+HCl→\)
III.	\((CH_3)_3COH+HCl→ \)
IV.	\((CH_3)_2CHOH+HCl\xrightarrow{\bf{anh.ZnCl_2}}\)

 

1.	I, III, and IV	2.	I and II
3.	Only IV	4.	III and IV

Given below are two statements regarding hormonal regulation of the menstrual cycle:

Statement I:	Estrogen secreted by the growing Graafian follicle during the follicular phase stimulates repair and proliferation of the endometrium, while simultaneously exerting negative feedback on the anterior pituitary to suppress FSH secretion.
Statement II:	The mid-cycle LH surge, which triggers ovulation, is paradoxically caused by a brief switch from negative to positive feedback, where sustained high estrogen levels (above threshold) stimulate rather than suppress GnRH and LH release.

Choose the most appropriate answer:

1.	Statement I is correct; Statement II is incorrect — LH surge is always under negative feedback control
2.	Statement I is incorrect; Statement II is correct — estrogen never suppresses FSH during follicular phase
3.	Both statements are correct — estrogen exerts context-dependent dual feedback based on concentration and duration
4.	Both statements are incorrect — progesterone, not estrogen, is responsible for endometrial proliferation and LH surge

Which of the following statements about linkage and recombination are correct?

(a)	Genes located on the same chromosome are said to be linked; they tend to be inherited together and deviate from the expected 9:3:3:1 ratio in dihybrid crosses, showing parental combinations at higher frequency than recombinant combinations.
(b)	The frequency of recombination between two linked genes is directly proportional to the physical distance between them; recombination frequencies above 50% are never observed because independent assortment becomes indistinguishable from free recombination at that threshold.
(c)	Morgan's experiments with Drosophila demonstrated incomplete linkage — recombinant phenotypes appeared at lower frequency than parentals, providing the conceptual basis for constructing chromosomal linkage maps using recombination frequency as map distance.
(d)	Complete linkage, as theoretically observed in male Drosophila, occurs because crossing over is entirely absent in males; recombinant classes are therefore never produced, and parental combinations are transmitted intact to all offspring.
(e)	A recombination frequency of 1% between two genes is defined as 1 centimorgan (cM) or 1 map unit; since recombination frequencies are additive for short distances, three-point crosses can construct more accurate linear gene maps than two-point crosses.

Choose the most appropriate answer:

1.	(a), (b), (c) and (e) only
2.	(a), (c), (d) and (e) only
3.	(b), (c), (d) and (e) only
4.	(a), (b), (c), (d) and (e)

In a family, a phenotypically normal woman has a colour-blind father (X-linked recessive) and a normal mother whose own father was colour-blind. This woman marries a man with normal colour vision. What is the probability that their first child will be a colour-blind son?

1.	1/8 — mother has 50% probability of being a carrier; probability of colour-blind son among all children is therefore 1/8
2.	1/4 — mother is an obligatory carrier since her father is colour-blind; probability of a colour-blind son among all children is 1/4
3.	1/2 — mother is an obligatory carrier; among her sons specifically, 1/2 will be colour-blind, making overall probability 1/2
4.	1/16 — both maternal grandfather and maternal great-grandfather were affected, doubling the recombination risk across two generations

Given below are two statements regarding regulation of the lac operon in E. coli:

Statement I:	In negative regulation of the lac operon, the repressor protein (encoded by the i gene) binds to the operator region in the absence of lactose, physically blocking RNA polymerase movement and preventing transcription; lactose acts as an inducer by binding the repressor, causing conformational change that releases it from the operator.
Statement II:	In positive regulation of the lac operon, the CAP–cAMP complex binds to the CAP binding site upstream of the promoter and enhances RNA polymerase binding affinity; this system ensures that even when lactose is present, the operon is maximally transcribed only when glucose is simultaneously absent, reflecting the cell's preference hierarchy for carbon sources.

Choose the most appropriate answer:

1.	Statement I is correct; Statement II is incorrect — CAP–cAMP actually represses transcription by blocking the promoter
2.	Statement I is incorrect; Statement II is correct — the repressor in negative regulation enhances, not blocks, RNA polymerase
3.	Both statements are correct — negative and positive regulation operate independently to achieve exquisite metabolic control
4.	Both statements are incorrect — lac operon is regulated exclusively by negative control; positive regulation does not exist in prokaryotes

Consider the given two statements:

Assertion (A):	The promoter sequence is a structural component of the transcription unit that is not itself transcribed; it serves as the binding site for RNA polymerase and determines both the strand that will serve as template and the direction of transcription.
Reason (R):	RNA polymerase binds the promoter in a specific orientation because promoter sequences (such as Pribnow box/–10 and –35 elements in prokaryotes) are asymmetric, nonpalindromic sequences that confer directionality; without the promoter, RNA polymerase cannot initiate transcription even in the presence of structural genes.

Choose the most appropriate answer:

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 — promoter sequences are palindromic and do not confer directionality
4.	(A) is false but (R) is true — promoter is transcribed as part of the 5'-UTR of the mRNA

In certain Sub-Saharan African populations, the frequency of the sickle cell allele (HbS) remains far higher than would be predicted given that homozygous individuals (HbS HbS) suffer severe haemolytic anaemia and early mortality. Which explanation most accurately accounts for this evolutionary anomaly?

1.	The HbS allele is maintained by genetic drift alone, since African populations historically had severe bottleneck events that randomly fixed the allele at high frequency
2.	Heterozygous individuals (HbA HbS) exhibit balanced polymorphism — they are protected against severe Plasmodium falciparum malaria while avoiding full sickle cell disease, conferring higher fitness than either homozygote in malaria-endemic regions
3.	The HbS allele has a high spontaneous mutation rate from HbA, constantly replenishing its frequency faster than natural selection can eliminate it through homozygous mortality
4.	HbS homozygotes in African populations have developed compensatory haemoglobin variants that reduce anaemia severity, allowing sufficient reproductive success to maintain the allele at observed frequencies

A research consortium attempting to develop an effective HIV vaccine has repeatedly failed despite decades of effort. Which combination of viral properties most comprehensively explains why conventional vaccine strategies that succeeded against polio and smallpox fail against HIV?

1.	HIV infects B-lymphocytes directly, destroying the very cells needed to generate vaccineinduced antibody responses, making immunological memory impossible to establish
2.	HIV's reverse transcriptase lacks proofreading activity causing extremely high mutation rates; its envelope glycoprotein (gp120) shows hypervariable regions that escape neutralizing antibodies; and the virus establishes latent proviral reservoirs in CD4⁺ T-cells that are immunologically invisible
3.	HIV is a DNA virus that integrates permanently into the host genome, and current adjuvant technologies cannot stimulate sufficient cytotoxic T-lymphocyte responses against DNA viral antigens
4.	HIV destroys macrophages before they can present antigens to T-cells, preventing the priming step of adaptive immunity that vaccination depends upon entirely

A plant biotechnologist wishes to develop transgenic crop varieties using Agrobacterium tumefaciens-mediated transformation. Her advisor cautions that this system has significant practical limitations for certain important crops. Which statement most accurately identifies the fundamental biological limitation of Agrobacterium-mediated transformation in modern crop biotechnology?

1.	Agrobacterium can only transfer DNA to plant cells during the G2 phase of the cell cycle, making transformation of non-dividing meristematic tissue practically impossible
2.	Agrobacterium-mediated transformation is largely restricted to dicotyledonous plants; most important cereal crops (rice, wheat, maize) are monocots and are either recalcitrant or inefficiently transformed because Agrobacterium has poor host-range compatibility with monocots
3.	The Ti-plasmid of Agrobacterium integrates transgenes exclusively into chloroplast DNA, making nuclear expression of transgenes and Mendelian inheritance across generations impossible
4.	Agrobacterium requires the transgene to contain a T-DNA border sequence of minimum 2,000 bp, severely limiting the size and complexity of useful genes that can be introduced into crop plants

Evolutionary biologists studying long-term species interactions have documented that certain symbioses drive reciprocal evolutionary change — where each species exerts selection pressure on the other across generations. Which of the following population interactions most classically exemplifies co-evolution, and for what reason?

1.	Commensalism between cattle egrets and grazing cattle — cattle evolve larger body size to disturb more insects, while egrets evolve sharper vision to exploit the foraging opportunity more efficiently
2.	Mutualism between figs and fig wasps (Ficus and Agaonidae) — the fig has evolved enclosed inflorescences accessible only to specific wasps, while the wasp has evolved morphology and behavior exclusively for fig pollination, creating obligate mutual dependence
3.	Predator-prey interaction between lions and zebras — zebras evolve speed while lions evolve strength, representing co-evolution between two species that are locked in a permanent evolutionary arms race
4.	Amensalism between Penicillium and bacteria — bacteria evolve antibiotic resistance while Penicillium simultaneously evolves more potent penicillin variants, representing chemical co-evolution

An ecologist studying a grassland ecosystem measured the following: the gross primary productivity (GPP) was 8,000 kcal/m²/year; plants used 3,000 kcal for their own respiration; herbivores consumed 1,500 kcal of the available plant biomass and lost 750 kcal through respiration and excretion; carnivores then assimilated 100 kcal from herbivores. Which set of conclusions about this ecosystem is most accurate?

1.	Net Primary Productivity = 8,000 kcal; ecological efficiency from producer to herbivore = 18.75%; energy available to carnivores represents 1.25% of GPP
2.	Net Primary Productivity = 5,000 kcal; ecological efficiency from producer to herbivore = 30%; the 10% law is violated at the herbivore-carnivore level since efficiency exceeds 10%
3.	Net Primary Productivity = 5,000 kcal; ecological efficiency from producer to herbivore = 30%; herbivore-to-carnivore efficiency ≈ 13.3%, showing ecological efficiencies vary and the 10% law is an approximation
4.	Net Primary Productivity = 3,000 kcal; ecological efficiency from producer to herbivore = 18.75%; only the 10% Lindeman efficiency applies strictly at each trophic level without exception