Please be patient as the PDF generation may take up to a minute.

An equilateral triangular prism of glass \((\mu=1.5)\) is placed in air. A ray of light is incident normally onto the surface \(AB.\) The ray will finally emerge:
           

1.	normally from the surface \(BC.\)
2.	normally from the surface \(AC.\)
3.	either from the surface \(BC\) or \(AC,\) normally.
4.	either from the surface \(BC\) or \(AC,\)         at an angle of emergence greater than \(60^{\circ}\) but less than \(90^{\circ}.\)

A convex lens of focal length \(60\) cm is placed in the path of a parallel beam, falling parallel to its principal axis. A plane mirror is placed on the principal axis, making an angle of \(45^{\circ}\) with it, at a distance of \(30\) cm behind the lens. The distance of the new focus from lens (optical centre) is:
1. \(60\) cm
2. \((60+30\sqrt2)\) cm
3. \(60\sqrt2\) cm
4. \(30\sqrt2\) cm

Assume that the corner of \(O\) of the room is the origin, and the axes \(x,y,z \) are along the edges. The three walls meeting orthogonally at \(O\) are perfect mirrors. A ray of light travelling parallel to the vector \(-(\hat i+2\hat j+\hat k) \) is incident on the \(y\text-z\) mirror (wall). The emerging ray, after all reflections, will be along:
                       
1. \(\hat i-2\hat j-\hat k\)
2. \(\hat i+\hat k-2\hat j\)
3. \(-\hat i+2\hat j+\hat k\)
4. \(\hat i+2\hat j+\hat k\)

Polarized light is incident on a polaroid. Let ${\mathrm{}}_{}$\(I_{0}\) be the intensity of light transmitted by this polaroid. Now, a very large number (say \(N\)) of polaroids are placed in a row with their axes displaced through a small angle \(\theta\) successively. If the last polaroid is crossed to the first one, the intensity of light transmitted by the last polaroid is about:
1. \(0\)
2. \(\dfrac{I_{0}}{2}\)
3. \(I_{0}\)
4. \(\dfrac{I_{0}}{N}\)

The number of fringes formed in a Young's double-slit experiment (on the screen): (here \(d\) = slit width, \(\lambda\) = wavelength of light)

1.	is \(\Large\frac{d}{\lambda}\)
2.	is \(\Large\frac{\lambda}{d}\)
3.	cannot be greater than \(\Large\frac{d}{\lambda}\)
4.	cannot be greater than \(\Large\frac{2d}{\lambda}\)

The major product of the following reaction is:
 
1. 6-Phenylhepta-2,4-diene
2. 2-Phenylhepta-2,5-diene
3. 6-Phenylhepta-3,5-diene
4. 2-Phenylhepta-2,4-diene

The correct pair(s) of the ambident nucleophiles is/are:

(A)	\(\mathrm{AgCN/KCN}\)
(B)	\(\mathrm{RCOOAg/RCOOK}\)
(C)	\(\mathrm{AgNO_2/KNO_2}\)
(D)	\(\mathrm{AgI/KI}\)

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

Consider the following reaction sequence:
 
The product (B) will be:

1.		2.
3.		4.

Which one of the following pairs of isomers is an example of metamerism?

1.
2.
3.
4.

Among the given species, the resonance stabilised carbocations are:

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

 

1.	(A), (B) and (C) only
2.	(A) and (B) only
3.	(C) and (D) only
4.	(A), (B) and (D) only

Consider the following statements:

Statement I:	Natural active immunity develops when a person suffers from an infection and recovers, producing their own antibodies.
Statement II:	Artificial passive immunity is provided when a person receives a vaccine containing weakened or killed pathogens.
Statement III:	Artificial active immunity is acquired through vaccination, where antigens stimulate the body to produce antibodies.
Statement IV:	Natural passive immunity occurs when antibodies are transferred from mother to fetus through placenta or to infant through colostrum.

Which statements are correct?
1. Statements I and IV only
2. Statements I and III only
3. Statements I, III, and IV only
4. All statements are correct

Compare the following microbial products:
Product X: Blood cholesterol lowering agent produced by Monascus purpureus
Product Y: Clot dissolving agent produced by Streptococcus
A patient with atherosclerosis (plaque buildup) causing both high cholesterol and risk of blood clots would potentially benefit from:

1.	Only Product X, as it addresses both cholesterol and clots
2.	Only Product Y, as clot dissolution automatically lowers cholesterol
3.	Both products, as they address different aspects of cardiovascular disease
4.	Neither product, as atherosclerosis cannot be treated with microbial products

Compare two water bodies:

Lake A:	Receives untreated sewage from nearby town; BOD = 20 mg/L; few fish observed
Lake B:	Protected lake with no sewage input; BOD = 3 mg/L; diverse aquatic life

Which explanation best accounts for the difference?

1.	Lake A has more oxygen available, supporting fewer fish due to over-oxygenation
2.	Lake B has higher BOD indicating better water quality and supporting diverse life
3.	Lake A has high BOD due to organic pollution leading to oxygen depletion and fish mortality; Lake B has low BOD indicating clean water
4.	Both lakes have similar water quality; fish distribution is due to other factors

Compare normal cells and cancer cells grown in culture:
Normal Cells: Form a single layer (monolayer) and stop dividing when the surface is covered
Cancer Cells: Continue dividing and pile up forming multiple layers even after covering the surface
The fundamental difference responsible for this behaviour is:

1.	Normal cells have limited nutrients; cancer cells have unlimited nutrient supply
2.	Normal cells retain contact inhibition; cancer cells have lost contact inhibition
3.	Normal cells undergo apoptosis upon contact; cancer cells are resistant to death signals
4.	Normal cells divide slowly; cancer cells divide rapidly due to more growth factors

Consider two patients:

Patient X:	Infected with a bacterial pathogen circulating in the bloodstream
Patient Y:	Infected with a virus that has entered and replicated inside host cells

Which statement correctly describes the primary immune response?

1.	Patient X relies primarily on cell-mediated immunity (T-cells against infected cells); Patient Y relies primarily on humoral immunity (antibodies against extracellular bacteria)
2.	Patient X relies on innate immunity only; Patient Y relies on humoral immunity
3.	Both patients rely primarily on cell-mediated immunity as T-cells are the main defense against all infections
4.	Patient X relies primarily on humoral immunity (antibodies against extracellular bacteria); Patient Y relies primarily on cell-mediated immunity (T-cells against infected cells)

Consider the given two statements:

Statement I:	HIV is a retrovirus that enters helper T-lymphocytes and replicates, producing progeny viruses that attack more TH cells, leading to progressive immunodeficiency.
Statement II:	AIDS patients die from HIV directly destroying vital organs like the heart, liver, and brain.

Evaluate the statements:

1.	Both Statement I and Statement II are correct
2.	Statement I is correct; Statement II is incorrect
3.	Statement I is incorrect; Statement II is correct
4.	Both Statement I and Statement II are incorrect

In gene therapy for ADA-SCID (Adenosine Deaminase deficiency), lymphocytes are isolated from the patient, transfected with functional ADA gene using retroviral vector, and returned to the patient. Why must this treatment be repeated periodically?

1.	The retroviral vector gets degraded by the immune system
2.	Lymphocytes have limited lifespan and the introduced gene doesn't integrate into germ cells
3.	The ADA gene undergoes mutation within few months
4.	The body develops immunity against the modified lymphocytes

A bioreactor is being operated for penicillin production. The graph shows that product formation is maximum during the stationary phase rather than log phase. This indicates that penicillin is a: 

1.	Primary metabolite, produced during active growth
2.	Growth-associated product requiring rapid cell division
3.	Constitutive enzyme, always being produced
4.	Secondary metabolite, produced when growth slows down

A molecular diagnostic lab receives samples from two patients:

Patient A:	Suspected HIV infection, tested 2 weeks after potential exposure, ELISA antibody test negative.
Patient B:	Family history of sickle cell anemia, currently asymptomatic, wants to know carrier status.

The lab uses PCR for both cases. Which statement best explains the advantage of PCR in these scenarios?

Statement I:	PCR enables early diagnosis in Patient A because it can detect viral DNA/RNA even before antibodies develop, unlike ELISA which depends on immune response that takes weeks.
Statement II:	PCR enables diagnosis in Patient B because it amplifies the specific β-globin gene region to detect the point mutation, which cannot be identified by observing blood cell morphology in an asymptomatic carrier.

 

1.	Only Statement I correctly explains PCR's advantage; Statement II is incorrect as carriers always show some abnormal RBCs
2.	Only Statement II correctly explains PCR's advantage; Statement I is incorrect as PCR cannot detect HIV earlier than antibody tests
3.	Both statements correctly explain the advantage of PCR in early/presymptomatic diagnosis
4.	Neither statement is correct; PCR is used only for confirmation after other tests are positive

Consider the following statements about Ti plasmid of Agrobacterium tumefaciens:

(i)	The T-DNA region integrates into the plant nuclear genom
(ii)	Vir genes are present on T-DNA and get transferred to plant cells
(iii)	Disarmed Ti plasmids lack tumor-inducing genes but retain T-DNA transfer machinery
(iv)	The opines synthesized by transformed plant cells are used by Agrobacterium

Which combination is CORRECT? 
1. i, ii and iii only 
2. i, iii and iv only 
3. ii, iii and iv only 
4. i, ii and iv only