KVPY Class-XII (SB/SX) - 2018

Let h(x) = g(f(x))
And h(x) is onto (given)
∴ Co-domain of h(x) = Range of h(x)
Range of h(x) = [0,2] and h(x) = g(f(x) ).
It means g is giving [0,2] which is also co-domain of g.
So, g must be onto.
Now, domain of g = [-1,1] which must be range of f.
But, co-domain of f = [- 1,1]
So, f must be onto.

Due to contrifugal force, electrons have a tendency to go towards the circumference.

For iso-electronic species, the radii are in the following order:
Cation < Neutral atom < Anion
Ionic radii increase with the increase in the –ve charge on anion and decrease with the increase in positive charge on the cation. Hence, the decreasing order of the radii is:
N^3- > O^2- > F^- > Na⁺

Sulphuric acids reacts with carbon, sulphur and phosphorous as follows:
C+ 2H₂SO₄ → CO₂ + 2SO₂ + 2H₂O
3S + 2H₂SO₄ → 3SO₂ + 2H₂O
P₄ + 6H₂SO₄ → 4H₃PO₃ + 6SO₂

The extent of back bonding in BCl₃ is the least because of the energy difference between the 3p orbital of the Cl atom (containing the lone pair) and the empty 2p orbital in Boron. The lone pair in Fluorine, Oxygen and Nitrogen are in the 2p orbitals, but the extent of back bonding depends on the compatibility in the size of the 2p orbitals in these atoms with that of the Boron atom.
Hence, the correct order for the extent of back bonding is:
BCl₃ < BF₃ < B(OMe)₃ < B(NMe₂)₃

The statement (iii) is factually incorrect.
Langumir's isotherm is based on the following assumptions:

• All sites are equivalent.
• Each site can hold at most one molecule of the adsorbate (mono-layer coverage only).
• There are no interactions between adsorbate molecules and the adjacent sites.

Hence, the initially adsorbed layer cannot act as a substrate for further adsorption.

Mixing equal volumes of NH₄OH (0.2 M) and HCl (0.1M) results in the formation of NH₄OH and NH₄Cl, which is a basic buffer mixture. This will form a perfect buffer because equal quantities of the weak base (NH₄OH) and salt of its conjugate acid ( NH₄Cl) is present.

The mammalian hemoglobin molecule can bind (carry) up to four oxygen molecules or 8 oxygen atoms. Hemoglobin is made up of four symmetrical sub-units and four heme groups. Iron associated with heme binds oxygen.

Bt toxin is produced by a soil bacterium called Bacillus thuringiensis. This toxin does not kill the bacteria because when it is present in the bacteria, it is in an inactive protoxin form. It becomes active and toxic when it is consumed by insects, such as lepidopterans, coleopterans and dipterans. The activated toxin (delta endotoxins) binds to the epithelial cells in the midgut of an insect and creates pores that cause swelling, eventually killing the insect.

The ploidy of endosperm generally is 3n in angiosperms.
The ploidy of the endosperm given in the question is 6n
This implies that the two polar nuclei in the central cell are of ploidy 2n each. Similarly, the ploidy of the pollen is 2n. The formation of 6n endosperm is possible only with the above given set of ploidy.
Hence, n in this case will be 2n.The ploidy of mature plant is double the ploidy of the pollen, i.e. 2 × 2n = 4n.

Virus is non-autonomous outside a living host body. As viruses are obligate intracellular pathogens they cannot replicate without the machinery and metabolism of a host cell. Hence, statement 4 is true.
The genetic material of a virus can either be DNA or RNA. Adenovirus, herpesvirus, and poxvirus are all examples of DNA viruses. Examples of RNA viruses are Ebola virus and polio virus.
During attachment and penetration into a host cell, the virus attaches itself to a host cell and injects its genetic material into it. Hence,viruses do not possess a protein coat around its genetic material at all stages of their life cycle.

Mitochondrial cristae are folds of the mitochondrial inner membrane that provide an increase in the surface area. This allows a greater space for processes like the electron transport chain and chemiosmosis which help to produce ATP in the final steps of cellular respiration.

Nitrogenases are enzymes that are produced by certain bacteria, such as cyanobacteria. These enzymes are responsible for the reduction of nitrogen to ammonia. Nitrogenases are the only family of enzymes known to catalyze this reaction, which is a key step in the process of nitrogen fixation.

Contact inhibition is a process of arresting cell growth when cells come in contact with each other. As a result, normal cells stop proliferating when they form a monolayer. If a cell has plenty of available substrate space, it replicates rapidly and moves freely. Contact inhibition is a powerful anticancer mechanism that is lost in cancer cells.

Anaerobic respiration (fermentation) involves the breakdown of carbohydrates in the absence of oxygen. In yeasts, fermentation results in the production of ethanol and carbon dioxide – which can be used in food processing.

Serine proteases (or serine endopeptidases) are enzymes that cleave peptide bonds in proteins, in which serine serves as the nucleophilic amino acid at the enzyme's active site. They are found ubiquitously in both eukaryotes and prokaryotes.Serine proteases fall into two broad categories based on their structure: chymotrypsin-like and subtilisin-like.

The number of gametes formed is decided by the number of heterozygous alleles present in the given genotype.
Genotype of the given plant is : TtRrYY
In the above genotype Rr and Tt are the 2 heterozygous alleles, so here n = 2. (n = number of heterozygous alleles)
Total number of gamete formed will be: 2ⁿ, here n = 2
Hence, 2² = 4

Estrogen is a steroid hormone that is responsible for the growth and regulation of the female reproductive system and secondary sex characteristics. Estrogen is produced by the granulosa cells of the developing follicle. Progesterone is a steroid hormone that is responsible for preparing the endometrium for uterine implantation of the fertilized egg. If a fertilized egg implants, the corpus luteum secretes progesterone in early pregnancy until the placenta develops and takes over progesterone production for the remaining period of the pregnancy.

Antibodies are synthesised by 'B' cells. Every B cell is specific to a single antigen, but each cell can produce several thousand matching antibodies per second. This prolific production of antibodies is an integral part of the humoral immune response.

0.9% NaCl solution is isotonic for human blood cell. When blood cells come in contact with such a medium, the intracellular and extracellular fluids are in osmotic equilibrium across the cell membrane, and there is no net influx or efflux of water.

Golgi apparatus is found in animals. Plant cells usually contain smaller arrays of golgi-type vesicles, called dictyosomes. Golgi is responsible for glycosylation of proteins and lipids. Proteins arrive in vesicles, following their assembly in the endoplasmic reticulum. After processing in the golgi apparatus, they are sorted into golgi vesicles, for secretion, storage, or transport to lysosomes.

Creutzfeldt-Jakob Disease (CJD) is caused by an abnormal misfolded protein in the brain, called a prion. Creutzfeldt-Jakob Disease (CJD) gradually destroys brain cells, and causes tiny holes in the brain. People with CJD have ataxia, or difficulty controlling body movements, abnormal gait, speech, and dementia.

Dinosaurs went extinct about 65 million years ago (at the end of the Cretaceous Period), after living on Earth for about 165 million years. The estimated origin of the bamboo is 30 mya in the mid oligocene age.

All amino acids, except glycine have at least one chiral centre at the α C. Threonine and isoleucine have an additional chiral centre at C. The β carbon of isoleucine is optically active, just as the β carbon of threonine. These two amino acids, isoleucine and threonine, have the fact that they have two chiral centres, in common.

Ribulose 1,5 bisphosphate is the 1^st CO₂ acceptor in C₃ cycle. In the carbon fixation stage, carbon dioxide is attached to RuBP by the enzyme rubisco. The resulting 6-carbon product quickly splits into two molecules of a three-carbon compound (3-phosphoglycerate).

Tuberculosis (TB) can be acquired after inhalation of aerosol droplets containing the bacilli from the cough of infected individuals.
Dysentery is an inflammatory disease of the intestine, especially of the colon, which always results in severe diarrhea and abdominal pains. It is caused by consuming contaminated food and water.
Filariasis is a parasitic disease caused by an infection with roundworms of the Filarioidea type. These are spread by blood-feeding diptera, such as black flies and mosquitoes.
Syphilis is a bacterial infection usually spread by sexual contact. The disease starts as a painless sore — typically on the genitals, rectum or mouth. Syphilis spreads from person to person via skin or mucous membrane contact with these sores.

Rouche's theorem: This theorem states that for any two complex-valued functions f and g are analytic inside some region K with closed contour ∂K, if |g(z)| < |f(z)| on ∂K, then f and f + g have the same number of zeros inside K, where each zero is counted as many times as its multiplicity.
Using above theorem we conclude that if 11z⁸ + 20 iz⁷ + 10iz - 22 = 0, then 1 < |z| < 2
Since, S = |z|² + |z| + 1
The maximum value of S = 2² + 2 + 1 = 7 and
The minimum value of S = 1² + 1 + 1 = 3
Hence, 3 < S < 7.

Eu (4f⁷6s²) will have the highest value of the third ionization energy as loss of the 3^rd electron would disturb the stable electronic configuration of half filled 4f orbital.
Ce (4f¹ 5d¹ 6s²) will have the lowest value of the third ionization energy as the 3^rd electron would be removed form the 5d orbital.

Note: Glycine is achiral. Therefore, the possible combinations are:
(A) Valine serine glycine alanine
(B) Serine valine glycine alanine
(C) Valine glycine serine alanine
(D) Serine glycine valine alanine

Humans have 46 chromosome in diploid cells, while haploid cells have 23 chromosomes. Every human being receives 1/2 of 46 chromosomes from each parent. Since there is a 50% chance of getting the grandfather's chromosome for each of the 23 in the cell, the probability of getting every one of the 23 from one grandparent is (0.5)²³ or (1/2)²³.

5' → 3' is the direction of initiation of replication with the help of primers in PCR. Both forward and reverse primers are used. The sequence of the primer (5'-CTAGTCGTCGAT-3' ) is used to initiate replication in the lower strand and the sequence (5'-CAGCTCAGCTCAGTC-3') is used to initiate replication in the upper strand.

In ABCO blood group system, except for 'O', all alleles are co-dominant. Hence, seven blood groups can be formed. The possible possible blood groups can be A, B, C, O, AB, AC and BC.

Equation of exponential growth in plants, W_t = W₀ × e^rt
W₀ = 10 mm²
r = 0.015 mm²/hour
t = 4 days → 4 × 24 = 96 hours
w_t = 10 × e^{0.015 × 96} = 42.2 mm²

Globular proteins are folded such that their tertiary structure consists of the polar, or hydrophilic, amino acids arranged on the outside and the nonpolar, or hydrophobic, amino acids on the inside of the three-dimensional shape. This arrangement is responsible for the solubility of globular proteins in water. Hence, red and green will be on the surface and blue will be at the core.

Vitamin B complex is necessary for vital functions and essential for formation of co-enzymes, necessary for enzymatic reactions.
Thiamine pyrophosphate is the coenzyme of vitamin B₁ or thiamine.
Flavin adenine dinucleotide is a redox-active coenzyme associated with various proteins, which is involved with several important enzymatic reactions in metabolism.
Vitamin B₂, also called riboflavin, is required for FMN/FAD formation.
Pyridoxal phosphate (PLP, pyridoxal 5'-phosphate), the active form of vitamin B₆, is a coenzyme in a variety of enzymatic reactions.
Methylcobalamin is a cobalamin, a form of vitamin B₁₂. Methylcobalamin has been used as a supplement in patients with vitamin B12 deficiency and in those with diabetes and other neuropathies.

By the use of O¹⁸ radioisotope it was confirmed that O₂ comes from H₂O and not from CO₂ during light reaction.
By the use of C¹⁴ radioisotope it was confirmed that C in C₆H₁₂O₆ comes from CO₂. 3-PGA is the first labelled product formed in the C3 photosynthetic cycle.