Mathematics and Science PYQs

The correct answer is good conductor of heat but bad conductor of electricity.

• Mica is a group of hydrous potassium, aluminum silicate minerals.
• Micas are found in three major rock varieties—igneous, sedimentary, and metamorphic.
• Mica is silicate minerals, known as sheet silicates because it forms in distinct layers.
• Mica is one of the most important mineral ingredients in cosmetics, used widely to add shimmer and sparkle.

Important Points

• Mica is a good conductor of heat but an electrical insulator.
• Electricity needs charged particles (or quasi-particles) to conduct it.
• Heat can be conducted with almost any quasi-particle.

​

Key Points

• Diamond is one of the best conductors of heat.
• Koderma, in Jharkhand, is the leading producer of mica.

The correct answer is 90°.

• The angles of dip at the poles and the equator respectively are 90°, 0°.
• The magnetic poles are defined as the area where the dip is vertical.
• The magnetic equator is where the dip or inclination is zero.
• The Earth acts like a large spherical magnet.
• It is surrounded by a magnetic field that changes with time and location.

Important Points

• At the magnetic poles, a dip needle stands vertical (dip=90 degrees), the horizontal intensity is zero, and a compass does not show direction.
• At the north magnetic pole, the north end of the dip needle is down.
• At the south magnetic pole, the north end is up.
• At the magnetic equator, the dip or inclination is zero.

 

Key Points

• The axis of the dipole is offset from the axis of the Earth's rotation by approximately 11 degrees.
• The lines of forces due to the earth's horizontal component of the magnetic field are parallel straight lines.

The correct answer is 50 cm.

Important Points

• Here given compression = 20 and rarefaction = 20.
• So, it makes 20 waves and given length = 10 m = 1000 cm.
• v = f λ
• So, 20 × wavelength = 1000 cm.
• wavelength=1000cm/20
• Wavelength = 50 cm.

 

Key Points

• A sound is a form of energy that is produced by the vibration of objects.
• Vibrations are rapid to and fro motion of an object.
• Compressions and rarefactions are produced because of the disturbance in the medium caused by sound waves.
• Sound waves propagate because of compressions and rarefactions of the particles of the medium.
• One compression and one rarefaction make one wavelength.
• The length between the compression and rarefaction is called a wavelength.

The correct answer is \(9 \over 8\)

• Here given 4/3 and 3/2 is the absolute refractive index of water and glass respectively.
• The refractive index of glass with respect to water = V(water)/V(glass).
• V(vac.) / V(glass) = 3/2 -- (1)
• V(vac.) / V(water) = 4/3 -- (2)

​By dividing (1) by (2) we will get the ratio V(water)/V(glass)

 \( {{3 \over 2} \over {4 \over 3}} = \frac{3}{2} \times \frac{3}{4} = \frac{9}{8}\) = \(9 \over 8\)

So, the reflective index of glass to water is

The correct option is 9898

Important Points

• The refractive index of a medium is the ratio of the speed of light in a vacuum to the speed of light in the medium.
• It has no units.
• The Refractive index is also equal to the velocity of light c of a given wavelength in empty space divided by its velocity v in a substance, or n = c/v.

Key Points

• The refractive index of water is 1.33.
• Each pair of objects is identified by the refractive index
• The greater value of the reflective index of a medium, the bending of light will be greater.

The correct answer is Green.

• Green wire stands for grounding/ earthing in the electric circuit.
• Earthing is used to protect circuits or devices from an electric shock. It does this by providing a path (a protective conductor) for a fault current to flow to earth.
• Green wires are chiefly used for socket purposes. Example AC, geyser, TV, microwave, etc.
• Normally, switches have only 2 wires i.e. neutral and phase.

Important Points

• Red wire signifies the phase (live wire) in an electric circuit.
• Sometimes used in switch legs and interconnection between smoke detectors that are hard-wired into the power system.
• The black wire is used for power in all circuits.
• It carries electricity from the breaker into the source.
• White or Gray wire is neutral wire and takes unused electricity (current) which is sent back to the breakers or the main breaker panel.

The correct answer is charge.

Key Points

• Kirchhoff’s Current Law (KCL) is Kirchhoff’s first law that deals with the conservation of charge entering and leaving a junction.
• Σ I_IN = Σ I_OUT
• To determine the amount or magnitude of the electrical current flowing around an electrical or electronic circuit.
• KCL states that for a parallel path the total current entering a circuit's junction is exactly equal to the total current leaving the same junction.

Important Points

• Kirchhoff’s Voltage Law (KVL) is Kirchhoff’s second law that deals with the conservation of energy around a closed circuit path.
• KVL states that for a closed-loop series path the algebraic sum of all the voltages around any closed loop in a circuit is equal to zero.
• The algebraic sum of all the potential differences around the loop must be equal to zero as ΣV = 0.
• Momentum is a term used in physics to describe the quantity of motion of a moving body, measured as a product of its mass and velocity.
• Newton's 2^nd law of motion related to the momentum that is the rate of change of momentum in an object is directly proportional to the force applied, and the change in momentum will be in the direction of the applied force.
• The law of conservation of mass states that matter cannot be created or destroyed in a chemical reaction.
• For example, when wood burns, the mass of the soot, ashes, and gases, equals the original mass of the charcoal and the oxygen when it first reacted.

The correct answer is 13.

• Step by step solution:
• Step 1: Write down the binary number: 1101
• Step 2: Multiply each digit of the binary number by the corresponding power of two: 1x2³ + 1x2² + 0x2¹ + 1x2⁰
• Step 3: Solve the powers: 1x8 + 1x4 + 0x2 + 1x1 = 8 + 4 + 0 + 1
• Step 4: Add up the numbers written above: 8 + 4 + 0 + 1 = 13

So, (1101)₂ = (13)₁₀

Key Points

• (1101)₂ = (?)₈  (Binary to octal conversation)
• Step 1: Write down the binary number (001101)₂, Group all the digits in sets of three starting from the LSB (far right). Add zeros to the left of the last digit if there aren't enough digits to make a set of three. (001 101)
• Step 2: Use the table below to convert each set of three into an octal digit. In this case, 001=1, 101=5.

So, the number 1101 in binary is equivalent to 15 in octal.

• Table for binary to the octal conversation:

The correct answer is Coke.

Key Points

• Coke is prepared by heating coal in the absence of air (destructive distillation).
• It contains high carbon and few impurities.
• Coke is used as a fuel and a reducing agent in smelting iron ore in a blast furnace.
• Coke is one of the purest forms of carbon when impurities are removed.

 

Important Points

• Petrol (also known as gasoline), is a product of petroleum, produced by distilling and refining petroleum.
• Paraffin wax is a soft colorless solid derived from petroleum.
• Lubricating oil is derived from the refining of petroleum crude oil, processed by solvent extraction or hydrogenation.
• Petroleum is known as Liquid Gold or Black gold.

The correct answer is Cu.

• Copper (Cu) does not liberate H₂ when it reacts with acid.
• Cu is least reactive than Hydrogen. So it cannot displace hydrogen from acid.
• When Cu reacts with oxygen, it gives a black colour product, that is a Copper oxide.

2Cu + O₂ ⇒ 2CuO

Important Points

• Sodium (Na) metal dissolves readily in dilute sulphuric acid to form solutions containing the aquated Na⁺ ion with hydrogen gas.
• 2Na(s) + H₂SO₄(aq) → 2Na⁺(aq) + SO₄^2-(aq) + H₂(g)
• Magnesium (Mg) metal dissolves readily in dilute sulphuric acid to form solutions containing the aquated Mg²⁺ ion with hydrogen gas.
• Mg(s) + H₂SO₄(aq) → Mg²⁺(aq) + SO₄^2-(aq) + H₂(g)
• Calcium (Ca) metal dissolves readily in dilute or concentrated hydrochloric acid to form solutions containing the aquated Ca²⁺ ion with hydrogen gas.
• Ca(s) + 2HCl(aq) → Ca²⁺(aq) + 2Cl^-(aq) + H₂(g)

Key Points

• Sodium metal reacts rapidly with water to form a colorless solution of sodium hydroxide (NaOH) and hydrogen gas (H₂).
• 2Na(s) + 2H₂O → 2NaOH(aq) + H₂(g)

The correct answer is 16 g of CH₄

• Find the mole number of each:

N₂ = 16/28 = 0.5714

CO₂ = 16/44 = 0.3636

CH₄ = 16/16 = 1

O₂ = 16/36 = 0.5

So, mol number of CH₄ is maximum, so 16 g of CH₄ has maximum number of atoms.

Important Points

• One mole of a substance is equal to 6.022 × 10²³ units of that substance (such as atoms, molecules, or ions).
• The number 6.022 × 10²³ is known as Avogadro's number or Avogadro's constant.
• The concept of the mole can be used to convert between mass and number of particles.

The correct answer is Tollens reagent.

• In the laboratory, ethylene and acetylene can be distinguished by Tollens reagent.
• Tollens' reagent is a chemical reagent used to determine the presence of aldehyde, aromatic aldehyde, and alpha-hydroxy ketone functional groups.
• The reagent consists of a solution of silver nitrate and ammonia.

Important Points

• Fehling's solution is a deep blue alkaline solution that is used to identify the presence of aldehydes, groups that contain an aldehyde functional group or a ketone.
• Fehling’s A containing blue color copper(II) sulfate.
• Fehling’s B is a clear liquid containing potassium sodium tartrate (Rochelle salt) and a strong alkali (sodium hydroxide).

Ammonical silver nitrate solution(Tollen's reagent) is used to distinguish between ethene and ethyne.

Ethyne + tollens reagent --------> silver acetylide (white ppt) + NH₃

Ethene + tollens reagent ---------> no reaction

• Br₂/H₂O or Bromine water, also called Bromide bromate solution.
• It is used to identify the alkene or alkane functional groups present in the compound.
• Alkene groups react with bromine water in the dark condition and undergo an addition reaction, to give a decolourized solution.
• Alkane doesn’t react with bromine water and the colour of the bromine water remains the same.
• KMnO₄/OH⊖/H₂O or Potassium permanganate (purple color compound) is a strong oxidizing agent.
• It is used for medication for dermatitis, for cleaning wounds, and general disinfection.

Key Points

• The main difference between ethylene (H₂C=CH₂) and acetylene (C₂H₂) is that ethylene is an alkene whereas acetylene is an alkyne.

The correct answer is OF₂.

Key Points

• Oxygen shows +ve oxidation states only in compounds with fluorine because fluorine is the only element more electronegative than oxygen.
• In OF₂, the oxidation state of O is +2.
• OF₂ pulls the bonded electrons towards itself and **leaving oxygen with a positive charge.**​

Important Points

• The oxidation number is also called the oxidation state, the total number of electrons that an atom either gains or loses to form a chemical bond with another atom.
• In Na₂O oxidation state of Na is +1.
• The oxidation number of a free element is always 0.
• The oxidation number of a monatomic ion equals the charge of the ion.

Additional Information

• The oxidation number of H is +1, but it is -1 when combined with less electronegative elements.
• The oxidation number of O in compounds is usually -2, but it is -1 in peroxides.
• The oxidation number of a Group 17 element in a binary compound is -1.
• The sum of the oxidation numbers in a polyatomic ion is equal to the charge of the ion.

The correct answer is Isoprene.

Key Points

• The monomer (“one-part”) of natural rubber is isoprene.
• The chemical name for natural rubber is polyisoprene.
• Its IUPAC name of isoprene is 2-methyl but-1,3-diene.

Important Points

 

Additional Information

• An addition polymerization joins thousands of isoprene units together to form poly(isoprene) or natural rubber.
• Vulcanization is a manufacturing process discovered by Charles Goodyear in 1839 to convert raw rubber into a tough useful product.
• In this process, about 1 – 3% by weight of sulphur is added to raw rubber and the mixture is heated carefully.

The correct answer is n-Pentane.

Key Points

• The n-pentane melts higher than others because it can assume a rodlike shape in which adjacent molecules can pack closely together.
• The long n-pentane molecules fit rather nearly together, they present the greatest intermolecular attraction.
• The boiling point of n-pentane is 36°C.

Important Points

• The surface area of the simple long chain compound will be more as compared to the branched-chain compound.
• So, less temperature will be required for branched-chain compounds as compared to a simple long chain compound.
• The boiling point of iso-pentane is 28°C, and the boiling point of neo-pentane is 10°C.
• The boiling point of isobutane is -11.7°C.
• **Iso-pentane, neo-pentane and Isobutane are branched-chain compounds.**​

Additional Information

• Hydrocarbons with the same numbers of atoms but different shapes form different compounds called isomers.

The correct answer is 4π + 2.

Key Points

• The pi-electron count is defined by the series of numbers generated from 4n+2 where n = zero or any positive integer (i.e, n = 0, 1, 2, etc.).
• The most common case in six pi electrons (n = 1) is found for example in benzene, pyrrole, furan, and pyridine.
• For a compound to be considered aromatic, it must be flat, cyclic, and conjugated and it must obey Huckel's rule.

 

Important Points

• Huckel's Rule (4n+2 rule): To be aromatic, a molecule must have a certain number of pi electrons (electrons with pi bonds, or lone pairs within p orbitals) within a closed loop of parallel, adjacent p orbitals.
• π bonds are simply the second bond made in a double bond. Any pure double bond is one sigma/σ and one pi/π bond.

The correct answer is the nucleus in the atom.

CONCEPT:

Rutherford Experiment: 

• Rutherford with his co-workers initiated a series of groundbreaking experiments that completely changed the accepted model of the atom.
• The very thin sheets of gold foil were bombarded with fast-moving alpha particles.
• Bombardment of alpha particles on the gold foil showed that a very small percentage of alpha particles were deflected.
• This experiment showed that 'The nuclear model of the atom consists of a small and dense positively charged interior surrounded by a cloud of electrons.'

Figure (A) The experimental setup for Rutherford's gold foil

Figure (B) The plum pudding model (top) says that all of the alpha particles should have been passed through the gold foil with no deflection or very little deflection. Rutherford found that a small percentage of alpha particles were deflected at large angles, which could be explained by an atom with a very small, dense, positively-charged nucleus at its center (bottom).

EXPLANATION:

• Rutherford’s atomic model accounts for the positively charged central core of an atom.
• So that positive charge is termed as the nucleus.

Important Points

• Electron was discovered by J. J. Thomson in 1897 when he was studying the properties of cathode rays.
• Proton was discovered by Ernest Rutherford.
• By his experiment, nitrogen under alpha-particle bombardment ejects what appear to be hydrogen nuclei.
• He had accepted the hydrogen nucleus as an elementary particle, naming its proton.

The correct answer is Air.

• Air is a homogeneous mixture of gaseous substances like nitrogen, oxygen, and smaller amounts of other substances
• Each layer of the Earth's atmosphere has a different density, each layer of air is its own homogeneous mixture.

Important Points

• Whole milk is actually a heterogeneous mixture composed of globules of fat and protein dispersed in water.
• Smoke is a heterogeneous mixture as smoke does not have uniform composition throughout.
• Jelly is a mixture of fruit juice and sugar and it is a heterogeneous mixture.

Key Points

• Mixing two solids, without melting them together, typically results in a heterogeneous mixture.
• Heterogeneous mixtures are not uniform.
• If two samples from different parts of the mixture, they will not have an identical composition.
• Use a mechanical method to separate components of a heterogeneous mixture.
• Examples include sand and sugar, salt and gravel, ice cubes in a drink, a mixture of oil and water.
• Homogeneous mixtures appear uniform to the eye. They consist of a single phase.
• Example: brass, bronze, steel, sterling silver, vodka, vinegar, and dishwashing liquid.

The correct answer is Sericulture.

Key Points

• The process of raising silkworms to produce silk is called sericulture or silk farming.
• Sericulture is the production of raw silk by means of raising caterpillars (larvae), those of the domesticated silkworm.
• Silk is a continuous filament within each cocoon.

 

Additional Information

The correct answer is unicellular and eukaryotic.

• Protista is green, golden, red, and brown unicellular algae large, single eukaryotic cell.
• The nucleus is enclosed by a membrane.
• It is composed of a single cell or a colony of similar cells.
• Protists live in water, in moist terrestrial habitats, and as parasites and other symbionts in the bodies of multicellular eukaryotes.

Important Points

• Whittaker proposed an elaborate five-kingdom classification – Monera, Protista, Fungi, Plantae, and Animalia.
• Carl Woese proposed six-kingdom classification - Animalia, Plantae, Fungi, Protista, Archaea/Archaebacteria, and Bacteria/Eubacteria.
• In the six-kingdom classification, Monera was divided into two parts Archaea and Eubacteria.

 

Additional Information

The correct answer is Phytochrome.

• Phytochrome is a blue-green plant pigment which regulates plant development, including seed germination, stem growth, leaf expansion, pigment synthesis, and flowering.

Important Points

Key Points

• Phytochrome is responsible for the absorption of red and far-red light and it is involved in red-far red light interconversion.
• Photoperiodism is the effect of duration of light and darkness on the growth, development and behaviour of organisms.
• Compound florigen is synthesized in photoperiodism which is responsible for flowering of plants.