Answer is (a) 27

 1. Balmer: Visible 

2. psubshell: dumb-bell 

3. de Broglie relation: λ = \(\frac{h}{mv}\)

The order of esterification of alcohol is 1° > 2° > 3°.

 Zymase enzyme is converting glucose into alcohol .

(a) (1) Aufbau principle 

(2) Pauli’s exclusion principle 

(3) Hund’s rule of maximum multiplicity 

(b) Hund’s rule of maximum multiplicity – electron pairing in orbitals of same energy will not take place until each degenerate orbital of a given subshell is singly occupied.

Answer is (4) 2

Effective Atomic Number - The resultant number of electrons of the central metal atom/ion after gaining electrons from the donor atoms of the ligands in co-ordination entity is known as effective atomic number of central metal atom/ion.

EAN = Atomic number of central metal (Z) – ON + 2CN

The correct answer is (a) 6.022 × 10²³

_{I can't get this answer} 

Let \(z = x + iy\)

Then

\(|z - 2 - 2i|\le 1\)

⇒ \(|(x - 2) + i (y - 2)| \le 1\)

⇒ \(|(x - 2) + i(y - 2)|^2 \le 1\)

⇒ \((x - 2)^2 + (y - 2)^2 \le 1\)    .....(1)

which represent the interior of a circle whose radius is 1 unit and centre is (2, 2).

Now,

\(|3iz + 6|^2 = |3i (x + iy) + 6|^2\)

\(=|3xi - 3y + 6|\)

\(= 9x^2 + (6 - 3y) ^2\)

\(= 9x^2 + 9(y - 2)^2\)

\(= 9x^2 + 9(1 - (x -2)^2)\)    (From (1))

\(= 9x^2 + 9 - 9 (x^2 - 4x + 4)\)

\(= -27 + 36 x \) but \(-1\le x -2\le 1 \) or \(1 \le x \le 3\)

\(|3iz + 6|\) is maximum if x = 3

Then \((y - 2)^2 = 1 - (3 -2)^2 = 1 - 1=0\) 

⇒ \(y = 2\)

Hence, maximum value of \(|3iz + 6|\) is 81 attained at \(3 +2i\).

\(\therefore a + b = 3 + 2 = 5\).

It is presumed that mitochondria were primitive aerobic prokaryotes that were engulfed in mutualism by primitive anaerobic eukaryotes, receiving protection from these beings and offering energy to them. This hypothesis is called the endosymbiotic hypothesis on the origin of mitochondria.

The hypothesis is strengthened by some molecular evidence such as the fact that mitochondria have their own independent DNA and protein synthesis machinery, with their own RNA and ribosomes, and that they can self-replicate.

The endosymbiotic theory can be applied to chloroplasts too. It is supposed that these organelles were primitive photosynthetic prokaryotes because they have their own DNA, RNA and ribosomes and they can self-replicate too.

Charles Darwin in 1859 explained the mechanism of organic evolution based on the principle of natural selection. Darwin encountered with a wide range of variation among organisms in the Galopagos islands during his voyage. On returning, Darwin authored his famous book ‘Origin of species’ by means of Natural selection to describe the process of evolution. 

The Darwinian view of evolution is based on following observations and their deductions– 

(1) Enormous fertility among organisms causes struggle for existence. Organisms possess enormous potentiality of reproduction and this results in struggle among them for limited natural resources (food and space). 

(2) Members of a population differ from each other and most variations are hereditary. The organisms, that possess variations which make them best adapted to existing environmental conditions, can make better use of resources. Organisms with such variations are, therefore, more likely to survive and leave descendants. 

(3) This differential reproductive success of organisms is the consequence of a process called natural selection. Herbert Spencer used the term “survival of the fittest” to describe this weeding out of less perfect ones. 

(4) After a certain period of time, continuous changes in specificities due to changing environmental conditions lead to emergence of new phenotypes and ultimately cause origin of a new species. 

Various advancements that have occurred in the field of biology have helped us gain a better understanding to fight against various infectious diseases. Biology has helped us study the life cycle of various parasites, pathogens, and vectors along with the modes of transmission of various diseases and the measures for controlling them. Vaccination programmes against several infectious diseases such as small pox, chicken pox, tuberculosis, etc. have helped eradicate these diseases. Biotechnology has helped in the preparation of newer and safer drugs and vaccines. Antibiotics have also played an important role in treating infectious diseases.

When any foreign organism enters into the body it produces certain protein compounds which are called antigens. The other type of protein produced in the body against the antigens are called antibody. 

Public health measures are preventive measures which are taken to check the spread of various infectious diseases. These measures should be taken to reduce the contact with infectious agents.
Some of these methods are:

•  Maintenance of personal and public hygiene: It is one of the most important methods of preventing infectious diseases. This measure includes maintaining a clean body, consumption of healthy and nutritious food, drinking clean water, etc. Public hygienic includes proper disposal of waste material, excreta, periodic cleaning, and disinfection of water reservoirs.
• Isolation: To prevent the spread of air-borne diseases such as pneumonia, chicken pox, tuberculosis, etc., it is essential to keep the infected person in isolation to reduce the chances of spreading these diseases.
•  Vaccination: Vaccination is the protection of the body from communicable diseases by administering some agent that mimics the microbe inside the body. It helps in providing passive immunizationto the body. Several vaccines are available against many diseases such as tetanus, polio, measles, mumps, etc.
• Vector Eradication: Various diseases such as malaria, filariasis, dengue, and chikungunya spread through vectors. Thus, these diseases can be prevented by providing a clean environment and by preventing the breeding of mosquitoes. This can be achieved by not allowing water to stagnate around residential areas. Also, measures like regular cleaning of coolers, use of mosquito nets and insecticides such as malathion in drains, ponds, etc. can be undertaken to ensure a healthy environment. Introducing fish such as Gambusia in ponds also controls the breeding of mosquito larvae in stagnant water.

Increase in the level of green house gases has led to considerable heating of Earth leading to global warming. Carbon dioxide and methane are commonly known as greenhouse gases because they are responsible for the greenhouse effect. The greenhouse effect is a naturally occurring phenomenon that is responsible for heating of Earth’s surface and atmosphere. 

During the past century, the temperature of earth has increased by 0.6°C, most of it during the last three decades. Scientists believe that this rise in temperature is leading to deleterious changes in the environment and resulting in odd climatic changes, thus leading to increased melting of polar ice caps as well as of other places like the Himalayan snow caps. Over many years, this will result in a rise in sea level that can submerge many coastal areas. 

Global warming can be controlled by– 

(g) Cutting down use of fossil fuel. 

(h) Improving efficiency of energy usage. 

(i) Reducing deforestation. 

(j) Planting trees. 

(k) Slowing down the growth of human population. 

Plant diseases are caused by pathogenic bacteria, viruses, fungi, etc. which are called pathogens. Control of plant diseases are possible by controlling pathogens and pests. When it is controlled by micro-organisms then it is called biological control and these microbes are called biological control agents. The controlling measures are- 

(i) Control by Viruses – In this categories the viruses are used to control plant disease caused by pest. This is achieved by killing targeting pests. eg. Baculoviruses are pathogens that attack insects. 

(ii) Control by Bacteria – In this categories the Bacillus thuringiensis is used to control caterpillars of butterfly. 

(iii) Control by Fungi – In this category the freeliving fungi Tricoderma viridi is used in treatment of wound of fruit trees.

A biological process in which an organism gives rise to young ones (offspring) similar to itself is called reproduction. Reproduction is special characteristics of living organisms, but each organism has evolved its own mechanism to multiply and produce offspring. The organism’s habitat, its internal physiology and several other factors are collectively responsible for how it reproduces.

Reproduction is of two types – (1) Asexual reproduction and ((2) Sexual reproduction. 

(1) Asexual reproduction – When offspring is produced by a single parent with or without the involvement of gamete formation, it is called asexual reproduction. 

(2) Sexual reproduction – When two parents of opposite sex participate in the reproductive process and also involve fusion of male and female gametes, it is called sexual reproduction. 

Advantages of reproduction : 

1. Reproduction enables the continuity of the species, generation after generation. 

2. After birth of offspring, it grows, matures and in turn produces new offsprings. 

3. It involves the cycle of birth, growth and death. 

4. It is a means for the survival of the population of species on this earth. 

5. It fulfills the statement “life comes from life”.

Intentional or voluntary termination of pregnancy before full term is called medical termination of pregnancy (MTP) or induced abortion. MTP is generally to get rid of unwanted pregnancy due to rapes, casual relationship etc. as also in cases when the continuation of pregnancy could be harmful or even fatal to either the mother or the foetus or both. Medical termination of pregnancy is legalized in our country. 

(i) Sexual –contact with the person infected with HIV. 

(ii) Through contaminated HIV blood-transfusion.

(iii) By using contaminated needles of injection with HIV. 

Hardy-Weinberg principle says that allele frequencies in a population are stable and is constant from generation to generation. 

The gene pool remains constant. This is called genetic equilibrium. Sum total of all the allelic frequencies is 1. Individual frequencies for example can be named p.q. etc. In a diploid p and q represents the frequency of allele A and allele a. 

The frequency of AA individual in a population is  → p² , in another ways i.e. the probability that an allele A with a frequency of p appear on both the chromosomes of a diploid individual is simply the product of probabilities i.e. p². Similarly of aa is q², of Aa 2pq. 

Hence p² + 2pq + q = 1. 

This is a binomial expansion of (p + q)². When frequency measured, differs from expected values, the difference (direction) indicates the extent evolutionary change. Disturbance in genetic equilibrium or Hardly-Weinberg equilibrium i.e. change of frequency of allele in a population would be interpreted as resulting in evolution.

Malaria – This disease is transmitted through bite of female Anopheles mosquito by an infective person to healthy person. 

Ascariasis- This disease is transmitted by a worm Ascaris egg through contaminated water, vegetables and fruits taken by a healthy person.

Pneumonia- Transmitted through droplet and Aerosol of causative bacteria through breathing. 

Water-borne diseases such as cholera, typhoid, hepatitis B, etc. spread by drinking contaminated water. These water-borne diseases can be prevented by ensuring proper disposal of sewage, excreta, periodic cleaning. Also, measures such as disinfecting community water reservoirs, boiling drinking water, etc. should be observed.

Wastes generated at home include plastic bags, paper napkin, toiletries, kitchen wastes (such as peelings of vegetables and fruits, tea leaves), domestic sewage, glass, etc.
Wastes generated at schools include waste paper, plastics, vegetable and fruit peels, food wrappings, sewage etc.
Wastes generated at trips or picnics include plastic, paper, vegetable and fruit peels, disposable cups, plates, spoons etc.
Yes, wastes can be easily reduced by the judicious use of the above materials. Wastage of paper can be minimized by writing on both sides of the paper and by using recycled paper. Plastic and glass waste can also be reduced by recycling and re-using. Also, substituting plastics bags with biodegradable jute bags can reduce wastes generated at home, school, or during trips. Domestic sewage can be reduced by optimizing the use of water while bathing, cooking, and other household activities.
Non- biodegradable wastes such as plastic, metal, broken glass, etc. are difficult to decompose because micro-organisms do not have the ability to decompose them.

A ‘suitable gene’ refers to a specific DNA segment which can be injected into the cells of the host body to produce specific proteins. This protein kills the specific disease causing organism in the host body and provides immunity.

Here, ½ kA² = (9 – 5) J = 4 J

So, k = 8/A² = 8/(0.01)² = 8 x10⁴ N/m

T = 2π√m/k = 2π√[2/(8 x 10⁴)] = (π/100) s