Mathematics and Science PYQs

Explanation:

Ferromagnetic substances:

• Ferromagnetic substances are those which develop strong magnetization in the direction of the magnetizing field.
• They are strongly attracted by a magnet and tend to move from weaker to the stronger part of a magnetic field.
• Example: Iron, cobalt, nickel, gadolinium, and alloys like alnico.

Paramagnetic substances:

• Paramagnetic substances are those which develop feeble magnetization in the direction of the magnetizing field.
• Such substances are feebly attracted by magnets and tend to move from weaker to stronger parts of a magnetic field.
• Example: Manganese, aluminium, chromium, platinum, etc.

Diamagnetic Substance:

• Diamagnetic substances are those which develop feeble magnetization in the opposite direction of the magnetizing field.
• Such substances are feebly repelled by magnets and tend to move from stronger to weaker parts of a magnetic field.
• Examples: Bismuth, copper, lead, zinc, etc.

Hence, Nikel is only ferromagnetic material in the above options.

Concept:

• The velocity of sound in any gaseous medium is affected by a large number of factors like density, pressure, temperature, humidity, and wind velocity, etc.
• The velocity of sound  in a gaseous medium is given by

\(\Rightarrow v=\sqrt {\frac {γ P}{ρ}}\)

Where P = pressure, ρ = density, and γ = ratio of two principal specific heats of the gas.

Explanation:

• The above table shows the speed of sound in solids > speed of sound in liquids > speed of sound in gases — although the densities of solids and liquids are much higher than those of the gases.
• This is because liquids and solids are less compressible than gases i.e., liquids and solids have much greater bulk modulus than that of gases.
• Thus, the speed of sound decreases when we go from solid to a gaseous state.

Therefore the speed of sound is maximum in Steel than other options available.

Explanation:

There are two types of charges found in nature -

1. Positive charge
2. Negative charge

Properties of charges:

1. Like charges (same charges) repel each other.
2. Unlike charges (different charges) attract each other.

When two objects are rubbed against each other, they develop charges.

When a glass rod is individually rubbed with a silk cloth.

• The silk cloth develop negative charge on it.
• The glass rod having positive charge over it.

Hence, Glass rod have a positive charge on it.

Concept:

Reflection: The phenomena in which light ray is sent back into the same medium from which it is coming, on interaction with boundary, is called reflection.

Laws of reflection:

1. It states that, if a light ray is reflected from a plane flat polished surface its angle of the incident will always be equal the angle of reflection.

• i.e., The angle of incidence (θ i ) = Angle of reflection (θ r )

2. The ​incident ray, the reflected ray, and normal to the surface of incidence always lies in the same plane.​

Additional Information

The law of reflection is also valid for all curved and spherical surface.

Explanation:

According to laws of reflection:

The angle of incidence (θ_i) = Angle of reflection (θ_r)

Given,

The angle of incidence = 60°

⇒ The angle of reflection is also 60°

Hence the option 60° is correct.

A resource is a source or supply from which a benefit is produced and that has some utility. Resources can broadly be classified upon their availability. They are classified into renewable and non-renewable resources.

Renewable resources

• Resources that are used by humans since human life exists.
• These resources are used by our ancestors for their daily purposes like lighting, shelter, transportation, cooking, heating, protection from harm.
• These are also known as non-conventional sources of energy.
• For example Soil, water bodies, sun, wind, tidal energy, geothermal, forest, mountains, wildlife, atmospheric resources.
• These can be used unlimited.
• They are environment friendly.
• The cost is low.
• They are pollution-free.
• They require high maintenance costs.
• They are sustainable resources.
• They cause no harm to life to exist on earth.

Non-Renewable resources

• The sources that cannot be replaced or reused once they are destroyed are called the Non-renewable resources.
• These are limited resources. so these are used limitedly.
• These are not environmentally friendly because the amount of carbon emission is high.
• The cost of these resources is high.
• They are not pollution-free.
• They require low maintenance cost.
• Coal, oil, nuclear energy, petroleum, natural gas, batteries, shale gas, phosphate are some examples.

​Conclusion

• Petroleum, natural gas, coal: All three are non-renewable resources.
• Groundwater is a renewable resource of energy.

CONCEPT:

• Momentum: Momentum of the body is equivalent to the product of mass and velocity.
• Its SI unit is kg m/s.
• Its dimensional formula is [M L T^-1].

P = m × v

where P is momentum, m is mass of the body; v is the velocity of the body.

• Velocity: The velocity of an object is the rate of change of its position with respect to time.
• Its SI unit is m/s.
• Its dimensional formula is [L T^-1].

EXPLANATION:

The ratio of momentum and velocity = \(\frac{{\rm{P}}}{{\rm{v}}}\)

⇒ \(\frac{{\rm{P}}}{{\rm{v}}} = \frac{{{\rm{m}} \times {\rm{v}}}}{{\rm{v}}} = {\rm{m}}\)

• Mass: Mass is a measure of the amount of matter in an object.
• Its SI unit is kilogram (kg).
• Its dimensional formula is [M].

​where P is momentum, m is mass of the body; v is the velocity of the body.

Explanation:

1 nano = 10^-9 m

⇒ 10-9 × 10² cm

⇒ 10^-7 cm = 10-7 × 10 mm = 10^-6 mm

Additional Information

The conversion of the units is shown below in the table.

Decimal multiples and parts of units

Please read the question with the options carefully.

• In 1895, during his study of the discharge through gases at very low pressure, German professor W.K. Roentgen accidentally discovered X-rays.​
• He observed that there was some radiation coming from the discharge tube that had the ability to penetrate through objects which were opaque to ordinary light. These rays were called X-rays or Roentgen rays.
• These rays are produced when a fast-moving electron strikes a target of high atomic weight.
• Ernest Rutherford is credited with discovering the concept of radioactive half-life.​
• Albert Einstein discovered the law of the photoelectric effect.​
• J. J. Thomson discovered electron in 1897.​

Concept:

Fibre can be obtained from various sources.

Natural Fibre: Natural fibres are the fibres that are obtained from plants, animals or mineral sources.

Some examples are cotton, silk, wool etc.

Synthetic fibres: Synthetic fibres are man-made polymers designed to make a fabric.

Polymers are obtained when many small units are joined together chemically.

Some examples are silk, acrylic, rayon, dacron etc.

Conclusion:

• Silk, cotton and jute are natural fibres.
• Acrylic is not a natural fibre, it is a man-made synthetic fibre.

CONCEPT:

• Plant reproduction: All organisms multiply or reproduce their own kind.
• In plants, there are two modes of reproduction, asexual and sexual.
• There are several methods of asexual reproduction such as fragmentation, budding, spore formation and vegetative propagation.
• Sexual reproduction involves the fusion of male and female gametes.

EXPLANATION:

• The reproducing part of ginger is the stem.
• The rootstocks (plant stem) has "eyes," small round irregularities where new shoots form and grow, producing leaves and stalks. Example: Potato, Ginger, Turmeric.

Concept:

Fruit Formation process in plants:

• Pollination: Pollen is transferred from a stamen to a stigma. The stamen is the male organ in a flowering plant and the stigma is the female part.
• Growth of Pollen Tube: A pollen tube develops to carry the pollen downward. Pollen travels from the stigma, down the style, and into the ovule of the plant.
• Fertilization: The male gamete (pollen) unites with a female gamete (ovule) to form a seed. The seeds are the embryo of the plant.
• Fruit Formation: The ovary ripens and forms a fruit. The fruit may contain a single seed or multiple seeds.

Explanation:

• True Fruits- True fruits are those that are formed solely from the ovary with ovules inside it. No other flower parts form a part of this type of fruit. For example Cherries, plums, and peaches, mangoes etc.
• False Fruits-False fruits are formed from the ripened ovary along with some other flower parts like the base or receptacle, the perianth etc. For example apples, strawberries etc.

CONCEPT:

• Reproduction by spores: Spores are the asexual reproductive bodies. Spores are not seeds.
• In the spore formation method of reproduction, the parent plant produces hundreds of tiny spores in spore cases.
• When the spore case of the plant bursts, then the spores spread into the air. As the spores are very light, they keep floating in the air and carried over large distances by air.
• Each spore is covered by a hard, protective coat to withstand unfavourable conditions şuch as high temperature and low humidity.
• Due to this, spores can survive for a long time. When the airborne spores land on food (or soil) under favourable conditions (like damp and warm conditions), they germinate and produce new plants.

​

EXPLANATION:

• Coriander can be either grown for its leaves or for its seeds.
• A fern is a member of a group of vascular plants that reproduce via spores and have neither seeds nor flowers.
• The life cycle of the fern has two different stages; sporophyte, which releases spores, and gametophyte, which releases gametes. Gametophyte plants are haploid, sporophyte plants diploid. This type of life cycle is called alternation of generations.
• Mustard can grow from its seeds.
• Petunia reproduces itself through sexual reproduction. The seeds are the offspring of the reproductive process.

CONCEPT:

• Nitrogen gas makes up 78% of our atmosphere and nitrogen is also a part of many molecules essential to life like proteins, nucleic acids (DNA and RNA) and some vitamins.
• Nitrogen is thus an essential nutrient for all life-forms, but it can not be utilized directly in the form of atmospheric nitrogen. To use nitrogen by any organism it must be converted in the form of nitrates and nitrites.

Nitrogen Cycle:

1. ​The atmosphere contains nitrogen gas. The nitrogen-fixing bacteria (present in the soil and in the root nodules of leguminous plants), blue-green algae and lightning in the sky convert it into compounds of nitrogen which go into the soil.
2. The plant absorbs compounds of nitrogen from the soil for their growth. The plants convert the compounds of nitrogen into plant proteins and other organic compounds which make up the body of plants.
3. The plants are eaten up by animal as food. Animals convert plant protein into animal protein and other organic compounds which make up their body. Some animals also eat other animals to obtain nitrogen compounds.
4. When plants and animals die, the complex nitrogen compounds present in their dead bodies are decomposed and converted into simple compounds of nitrogen by certain bacteria and fungi. These nitrogen compounds are again absorbed by the new plants for their growth and this part of the nitrogen cycle is repeated endlessly.
5. Some of the compounds of nitrogen are decomposed by denitrifying bacteria to form nitrogen gas. The nitrogen gas goes back into the atmosphere.

EXPLANATION:

• Proteins are composed of major elements like carbon, nitrogen, hydrogen and oxygen.
• Among them, the nitrogen is the main component obtained by plants with the help of nitrogen-fixing bacteria like Rhizobium.
• Plants and animals are not capable to use atmospheric nitrogen directly for proteins synthesis.
• So, Nitrogen is essential for protein synthesis in plants.

Concept:

• Illness/Diseases: It is a state of experience by the body when one or more of the control systems of the body are not functioning normally.  
• Communicable disease: The diseases which are infectious or transmissible from a body to body through biological agents in humans and animals. Ex- Influenza, Ebola, Covid-19, etc.
• Non-communicable disease: The disease that is not transmissible directly from one person to another through biological agents, Ex- Astana, Diabetes, Hypertension, arthritis, etc.

Explanation:

Some common communicable diseases are:

So, Cholera is not a non-communicable disease.

Explanation:

• Antibiotics are the medicines used to kill or weaken the bacteria and also protozoa to some extent.
• Antibiotics can be natural, semi-synthetic, or synthetic.
• Penicillin in 1928 by Alexander Fleming was obtained from Penicillium Notatum.
• These are a group of antibacterial drugs obtained from Penicillium fungi.
• Penicillin fights the bacteria by attacking the cell wall forming substances (peptidoglycans).
• Anne Miller was the first patient who got treated using penicillin in 1942.

So penicillin is obtained from fungi.

Concept:

• Macronutrients:  Macronutrients are those nutrients required in large amounts that provide the energy needed to maintain body functions and carry out the activities of daily life.
• There are three types of macronutrients: carbohydrates, proteins, fats and water.
• Micronutrients: A chemical element or substance required in trace amounts for the normal growth and development of living organisms.
• There are two micronutrients vitamins and minerals.

Explanation:

• The food you eat supplies many types of macronutrients — carbohydrates, fats and proteins — which deliver the energy (or calories) your body needs to function.
• The food also supplies micronutrients, such as vitamins and minerals, which don't provide calories but help the body with chemical reactions.

EXPLANATION:

• DNA was first recognized and identified by the Swiss biologist, Johannes Friedrich Miescher in 1869 during his research on white blood cells.
• DNA: DNA is a double helical long polymer of deoxyribonucleotides. The length of DNA is usually defined as a number of nucleotides (or a pair of nucleotide referred to as base pairs) present in it. This also is the characteristic of an organism.
• DNA contains a sugar-phosphate backbone, and the nucleotide bases (guanine, cytosine, adenine and thymine).

​

• The coding segment of DNA is called exon. A segment of DNA within a gene that encodes a sequence ultimately translated into a protein product.
• During gene expression, DNA gets translated to mRNA, which contains coding and non-coding nucleotide triplets.
• Non-coding sequences (intron) are removed from RNA by splicing.
• A codon is a sequence of three DNA or RNA nucleotides that corresponds with a specific amino acid or stop signal during protein synthesis.
• Muton is that length of DNA which is capable of undergoing mutation.

Key Points

• Micronutrient: A chemical element or substance required in lesser amounts for the normal growth and development of living organisms.
• Important micronutrients are iron, manganese, copper, molybdenum, zinc, boron, chlorine, and nickel.
• Macronutrients: Macronutrients are generally present in plant tissues in large amounts (in excess of 10 mmole Kg ^–1 of dry matter).
• The macronutrients include carbon, hydrogen, oxygen, nitrogen, phosphorous, sulphur, potassium, calcium and magnesium.

So, Calcium comes under the category of macronutrients, not micronutrients. 

Additional Information

• In addition to the micro-elements & macro-elements, there are some beneficial elements such as sodium, silicon, cobalt and selenium.

Given:

Each edge of a cube is doubled

Formula used:

Surface area of cube = 6a²

Calculation:

Let a be the length of the edge

⇒ Surface area = 6a²

When the edge is doubled

⇒ Length = 2a

⇒ Surface area = 6(2a)² = 24a²

Increase = 24a² - 6a² = 18a² 

Percentage increase = (18x²/6x²) × 100 = 3 × 100 = 300%

∴ Percentage increase is 300%

Given:

a/3 = b/2 = c/1

So, the ratio of a, b and c will be

⇒ a : b : c = 3 : 2 : 1

Let the values of a, b and c be 3x, 2x and x respectively.

Calculations:

Expression is \(\frac {a+b+2c}{b}\)

Putting values of a, b and c in the expression, we get

⇒ \(\frac {a+b+2c}{b}\) = [3x + 2x + (2 × x)]/(2x)

⇒ \(\frac {a+b+2c}{b}\) = 7x/2x

⇒ \(\frac {a+b+2c}{b}\) = 7/2

⇒ \(\frac {a+b+2c}{b}\) = 3.5

a/3 = b/2 = c/1

Multiplying and dividing by 6

2a = 3b = 6c

a = 3b/2

c = b/2

now,

\(\frac {a+b+2c}{b}\) = [(3b/2) + b + b]/b

\(\frac {a+b+2c}{b}\) = 3.5b/b = 3.5