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An electromagnetic waveform whose electric field is given by:
\(\vec E=(2\times10^{-4}\text{ V/m})\hat j\sin\bigg({\large\frac{2\pi}{0.2~\text m}}\bigg)(x-2\times10^8~\text{m/s }t)\)
is travelling in a region.
When this wave travels into vacuum, its wavelength will be:

1.	\(0.2~\text{m}\)	2.	\(0.3~\text{m}\)
3.	\(0.1~\text{m}\)	4.	\(0.15~\text{m}\)

The magnetic field in a plane electromagnetic wave is given by; 
    \(B=2\times10^{-7} \sin\left(0.5\times10^3x+10^{11}t\right)~\text{T}.\)
The electromagnetic wave is:

1.	visible light	2.	infrared
3.	microwave	4.	radio wave

The equivalent resistance between \(A\) and \(B\) is:
       

1.	\(20~\Omega\)	2.	\(4.8~\Omega\)
3.	\(10~\Omega\)	4.	\(5~\Omega\)

A ferromagnetic material consists of domains in which the magnetic moments of the atoms are in the same direction within each domain. However, the domains are randomly oriented. A ferromagnetic material is placed in an external magnetic field. Then, 

1.	all the domains grow in size.
2.	all the domains shrink in size.
3.	some domains grow in size, others shrink.
4.	domains rotate in the magnetic field.

The two long, parallel wires shown in the diagram carry equal and opposite currents \(i\). The currents change linearly with time: \(\dfrac{di} {dt}\) = a constant = \(K\). The small circuit is situated midway between the wires and has an area \(A\). The emf induced in the small circuit is: 

1.	zero	2.	\(\dfrac{\mu_{0} A K}{2 \pi l}\)
3.	\(\dfrac{\mu_{0} A K}{ \pi l}\)	4.	\(\dfrac{2 \mu_{0} A K}{\pi l}\)

The number of unpaired electrons and the hybridization of \(\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-}, \) respectively are:
1. \(4\) and \(\mathrm{d^2 sp^3}\)
2. \(4\) and \(\mathrm{sp ^3 d^2} \)
3. \(2\) and \(\mathrm{d^2 sp^3}\)
4. \(2\) and \(\mathrm{sp ^3 d^2}\)

Consider the following statements:

Statement I:	\(\mathrm{N-N} \) bond has less bond strength than \(\mathrm{P-P} \) bond
Statement II:	All group \(15\) elements in \(+3\) oxidation state undergoes disproportionation.

In the light of above statements, choose the correct option.

1.	Statement I and Statement II both are correct.
2.	Statement I and Statement II both are incorrect.
3.	Statement I is correct but Statement II is incorrect.
4.	Statement I is incorrect but Statement II is correct.

Electrolysis of dilute aqueous \(NaCl\) solution was carried out by passing \(10\) milli ampere current. What is the time required to liberate \(0.01~mol\) of \(H_2\) gas at the cathode?
(\(1\) Faraday \(= 96500~C~ mol^{−1}\) )
1. \(9.65\times 10^4~sec\)
2. \(19.3\times 10^4~sec\)
3. \(28.95\times 10^4~sec\)
4. \(38.6\times 10^4~sec\)

A reaction has an activation energy of 209 kJ mol^-1 The rate increases 10-fold when the temperature in increased from \(27^{\circ} \mathrm{C}\) to \(\mathrm{X}^{\circ} \mathrm{C}\). The temperature X is closest to [G constant, R=8.314 J mol^-1 K^-1]
1. 35
2. 40
3. 30
4. 45

Naphthalene and 2-methyl naphthalene forms an ideal solution at \(298~K.\) For the process, true statement(s) is/are:
A. \(\Delta S_{\text {system }}>0 \)
B. \(\Delta S_{\text {surrounding }}=0 \)
C. \(\Delta H=0 \)
D. \(\Delta G_{\text {system }}=\text { +ve } \)
1. A, B, and C 
2, A, C, and D  
3, B, C, and D 
4, A, B, and D 

The 'RNA World' hypothesis proposes the first life was self-replicating RNA, solving the nucleic-acid/protein "chicken-and-egg" problem.
What is a major implicit assumption in this hypothesis about early Earth conditions?

1.	That a reducing atmosphere existed to allow the abiotic formation of simple organic molecules.
2.	That RNA molecules could form abiotically and persist long enough to replicate and evolve.
3.	That lipid membranes formed spontaneously to encapsulate and protect these early RNA molecules.
4.	That DNA-based systems must have evolved almost immediately due to RNA's instability.

A researcher observes that in a particular cleistogamous flower species, seed set is consistently high even without pollinators. He assumes this reproductive strategy has evolved primarily to ensure genetic uniformity and preserve a superior genotype in a stable environment, as outcrossing is eliminated.

Which critical ecological-evolutionary trade-off of cleistogamy, well-known in plant breeding systems, is the researcher's assumption most likely overlooking?

1.	It guarantees seed set but reduces genetic variation, which could limit adaptive potential in a changing environment.
2.	It still depends on external pollen vectors like wind, making it less reliable than true self-pollination.
3.	It prevents the more efficient geitonogamy, which is the preferred mode of pollination in most angiosperms.
4.	It primarily conserves pollinator energy, which can then be directed towards other plant species in the ecosystem.

 

It is a proven fact that in E. coli, transcription and translation are coupled processes—ribosomes begin translating an mRNA while it is still being synthesised.
If this fact is true, what else must logically also be true about genes and their expression in E. coli?

1.	Introns must be absent from bacterial genes, as splicing machinery would interfere with simultaneous translation.
2.	The genetic code must be universal, allowing bacterial ribosomes to translate any mRNA sequence accurately.
3.	mRNA in bacteria must be long-lived and highly stable to allow multiple rounds of translation over time.
4.	Transcription termination in bacteria must occur via a mechanism that does not depend on the nuclear envelope or compartmentalisation.

How many of the following statements regarding Mendelian genetics and chromosomal theory are correct?

I.	Mendel proposed that factors (genes) occur in pairs in diploid organisms and segregate during gamete formation so each gamete receives only one factor.
II.	In a test cross, the organism with dominant phenotype is crossed with a recessive parent to reveal its genotype based on progeny ratios.
III.	Sutton and Boveri independently proposed the chromosomal theory in 1902, correlating chromosomal segregation with Mendelian factor segregation.
IV.	Morgan's Drosophila experiments showed that genes on different chromosomes produce more parental combinations than non-parental types, disproving independent assortment.
V.	Genetic map distance is measured in centiMorgans (cM), where 1 cM equals 1% recombination frequency, and crossover probability is proportional to gene distance.

1. Two
2. Three
3. Four
4. Five
 

A rare genetic disorder shows the following pattern: An affected man has all daughters affected but no sons affected. His affected daughters, when married to normal men, have approximately 50% of their sons and 50% of their daughters affected.

What is the most likely mode of inheritance for this disorder?

1.	Autosomal dominant, as it appears in every generation and affects both sexes.
2.	Autosomal recessive, as it can skip generations through unaffected carriers.
3.	Y-linked inheritance, since it is passed from an affected father to his sons.
4.	X-linked dominant, as affected fathers pass it to all daughters but no sons.

How many of the following statements are correct?

I.	Darwin's finches with varied beak shapes adapted to different food sources represent an example of convergent evolution.
II.	Analogous organs like wings of butterflies and birds are results of divergent evolution.
III.	Australian marsupials such as marsupial mole, marsupial mouse, and Tasmanian wolf represent adaptive radiation.
IV.	Genetic drift operates in large populations and its effect is maximum when population size is in millions.
V.	Hugo de Vries proposed that evolution occurs through gradual accumulation of small continuous variations.

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

How many of the following statements about human male reproductive system are correct?

I.	The testis is situated outside the abdominal cavity within the scrotum because the scrotum helps in maintaining the low temperature of the testes (2–2.5°C lower than the normal body temperature) necessary for spermatogenesis.
II.	The male sex accessory ducts include rete testis, vasa efferentia, epididymis and vas deferens, and the accessory glands include seminal vesicles, prostate and bulbourethral glands.
III.	The seminal plasma is rich in fructose, calcium and certain enzymes, while the prostatic secretions are rich in citric acid and acid phosphatase.
IV.	The process of spermiogenesis involves the transformation of spermatids into spermatozoa, where the spermatids are transformed into spermatozoa (sperms) by the process called spermiation.
V.	The acrosome of sperm is filled with enzymes that help in fertilisation of the ovum, and the middle piece possesses numerous mitochondria which produce energy for the movement of tail that facilitates sperm motility essential for fertilisation.

1. One
2. Two
3. Three
4. Four
 

Consider the given two statements:

Assertion (A):	According to the Hardy-Weinberg principle, allele frequencies in a population remain constant from generation to generation in the absence of evolutionary forces, and this explains why dominant traits always increase in frequency over time.
Reason (R):	In a Hardy-Weinberg equilibrium population, the genotypic frequencies can be calculated as p² + 2pq + q² = 1, where p and q represent the frequencies of dominant and recessive alleles respectively.

 

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

Consider the given two statements:

Assertion (A):	The founder effect and genetic bottleneck both result in reduced genetic variation, but the founder effect produces random changes in allele frequencies while bottleneck effect always eliminates deleterious alleles preferentially.
Reason (R):	Both founder effect and bottleneck effect are examples of genetic drift where chance events rather than natural selection determine which alleles are passed to the next generation.

Options:

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

How many of the following statements are correct?

I.	Spermatogenesis begins at puberty, and each primary spermatocyte undergoes meiosis I to produce two equal haploid secondary spermatocytes.
II.	The acrosome of sperm is formed from Golgi complex and contains enzymes like hyaluronidase that help in penetrating the ovum during fertilization.
III.	Oogenesis begins during embryonic development, and primary oocytes remain arrested in prophase II of meiosis I until puberty.
IV.	The secondary oocyte completes meiosis II after fertilization by sperm, forming the ovum and second polar body.
V.	Capacitation of sperm occurs in the male reproductive tract and involves removal of cholesterol from the sperm membrane to prepare it for fertilization.

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