Mathematics and Science PYQs

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 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.

The correct answer is Ligament.

• A Ligament is a fibrous connective tissue, which connects bone to another bone.

Important Points

Key Points

• There are 3 types of bone tissue:
• Compact tissue: The harder, outer tissue of bones.
• Cancellous tissue: The sponge-like tissue inside bones.
• Subchondral tissue: The smooth tissue at the ends of bones, which is covered with another type of tissue called cartilage.

The correct answer is Rhizophora.

• Many mangrove species show some form of vivipary. Rhizophora is an example.
• The ovum is fertilized while still on the parent tree and grows by a combination of photosynthesis and acquisition of nutrients from the parent.

Important Points

• In viviparous germination, the seeds germinate while still attached to the parent plant.
• The growth of the embryo continues until it pierces the seed coat, while still attached to the mother plant, without cessation of activity.

Key Points

• Difference between germination and vivipary:

The correct answer is joule.

• The unit of heat in the SI system is Joule.
• A unit of energy equal to the work done when a force of one newton acts through a distance of one meter.

Important Points

• The other common units for heat are-
• BTU (Btu) - British Thermal Unit - also known as a "heat unit" in the United States.
• Calorie: The amount of heat required to raise the temperature of one gram of water 1^oC.
• Erg is a unit of energy.
• It equal to the force of one dyne over a distance of one centimeter.
• 1 erg = 10^-7 joule.
• Watt is a unit (SI) of power.
• It is equal to one joule of work performed per second.
• 1 horsepower = 746 watt

Key Points

• 1 joule = 0.14 calorie = 9.478 x 10^-4 Btu.
• 4.184 joule of heat energy (or one calorie) is required to raise the temperature of a unit weight (1 g) of water from 0^oC to 1oC, or from 32^oF to 33.8^oF.
• 1 dyne = 0.00001 newton.

The correct answer is ​ \(P = \dfrac{\vec{F}}{A}\)

• Pressure is defined as the force divided by the area perpendicular to the force over which the force is applied.
• The SI unit for pressure is the pascal, 1 Pa = 1N/m².

Key Points

• A force has both magnitude and direction, therefore: Force is a vector quantity
• Muscular force is being applied by a vendor when he is pushing the pushcart.
• Opening a door is an example of a Contact force.
• Magnet is an example of a Non-contact force.

Concept:

The correct answer is 3 units.

• Newton's 2^nd law of motion says the rate change of momentum is called force.
• The equation for the change in momentum is F ×  t = m ×  Δv
• If the momentum of a body increases from 10 units to 25 units in 5 seconds.
• Then the change in the momentum is 25 – 10 = 15 units in time 5 seconds.
• So the Force extract from this is 15/5 = 3 Newton.

Key Points

• Momentum is a vector quantity that is the product of the mass (weight) of a particle and its velocity (speed).
• SI unit: kilogram meter per second (kg⋅m/s).
• A spinning object has angular momentum.
• An object travelling with a velocity has linear momentum.
• A change in momentum may result from an acceleration or a force or an impulse.

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 water.

• Photosynthesis uses carbon dioxide and water to assemble carbohydrate molecules (usually glucose) and releases oxygen into the air.
• Carbon dioxide is the byproduct of respiration.
• In this process, water and carbon dioxide react in the presence of sunlight to give off oxygen and form glucose molecules.
• Photolysis of water is the source of oxygen liberated in photosynthesis.
• The process is explained through the following equation:
• 6 CO2 + 6 H2O + light → C6H12O6 + 6 O2

Where, CO2 is Carbon Dioxide

H2O is Water

C6H12O6 is Sugar 

O2 is Oxygen

Important Points

• With the help of chlorophyll, plants obtain their nutrients and water from the soil, and sunlight provides solar energy for photosynthesis.
• The proportion of carbon in their chemical makeup can rise on a particularly sunny day because more photosynthesis occurs.

Key Points

• The fungus receives sugar from the plant—made by photosynthesis in the leaves and transported to the roots via the plant’s sap.
• In places where there is no sunlight, organisms producing their food are called chemotrophs.
• Those in the deep ocean, organisms get the energy from chemicals released by hydrothermal vents.
• Bacteria can do photosynthesis.

The correct answer is heparin.

• Heparin is an anticoagulant (blood thinner) that prevents the formation of blood clots.
• It is also used before surgery to reduce the risk of blood clots.

Important Points

The correct answer is pancreas.

• Islets of Langerhans are islands of endocrine cells scattered throughout the pancreas.
• The islets of Langerhans are a cluster of cells within the pancreas that are responsible for the production and release of hormones that regulate glucose levels.
• These cells discovered by Dr. Paul Langerhans.
• Pancreatic islets house three major cell types:
• Alpha cells (A cells) secrete the hormone glucagon.
• Beta cells (B cells) produce insulin.
• Delta cells (D cells) secrete the hormone somatostatin, which is also produced by a number of other endocrine cells in the body.

Important Points

• The stomach is the widest part of the digestive system. It not only digests food, it also stores it.
• The stomach is a bean-shaped sack located behind the lower ribs.
• The stomach secretes hydrochloric acids and enzymes that break down the food so that it can continue on its journey through the digestive system.
• This process called peristalsis (mix the food with the acid and enzymes).
• The human liver is the largest glandular organ of the human body and the second largest organ besides our skin.
• Some of these important functions include supplying glucose to the brain, combating infections, and storing nutrients.
• the liver detoxifies the harmful things we take in like alcohol and drugs.
• The liver creates the blood that circulates in bodies. The liver starts producing blood before born.
• The liver has the amazing ability to regenerate itself, making liver transplant possible.
• Heart is a part of circulatory system and responsible for pumping oxygen-rich blood throughout our body.
• An electrical system controls the rhythm of your heart. It’s called the cardiac conduction system.
• Cardiac muscle is a special type of muscle tissue that's only found in your heart.
• Coordinated contractions of cardiac muscle, which are controlled by special cells called pacemaker cells, allow for your heart to pump blood as a single functional unit.

Key Points

• The first open-heart surgery occurred in 1893. It was performed by Daniel Hale Williams, who was one of the few black cardiologists in the United States at the time.
• The first implantable pacemaker was used in 1958. Arne Larsson, who received the pacemaker, lived longer than the surgeon who implanted it.

The correct answer is protein.

• Enzymes are proteins.
• They are high molecular weight compounds made up principally of chains of amino acids linked together by peptide bonds.
• Enzymes can be denatured and precipitated with salts, solvents, and other reagents.
• Enzymes function as organic catalysts. A catalyst is a chemical involved in, but not changed by a chemical reaction.
• The enzyme speeds up the reaction by lowering the activation energy needed for the reaction to start.

Important Points

The correct answer is Ascorbic acid.

• Vitamin C, also known as ascorbic acid or L-ascorbic acid.
• The richest sources of ascorbic acid including Indian gooseberry, citrus fruits such as limes, oranges, and lemons, tomatoes, potatoes, papaya, green and red peppers, kiwifruit, strawberries, etc.
• Deficiency of Vitamin C and iron often occur in anemia.

Important Points

• Formic acid is also known as methanoic acid (HCOOH).
• It is naturally found in ants.
• It is made by the action of sulphuric acid upon sodium formate, which is produced from carbon monoxide and sodium hydroxide.
• Maleic acid is a butanediol acid in which the double bond has a cis- (Z)-configuration.
• It found in many fruits, including apricots, blackberries, blueberries, cherries, grapes, mirabelles, peaches, pears, plums, and quince
• Maleic acid is present in the apple.
• Palmitic Acid is a saturated long-chain fatty acid with a 16-carbon backbone.
• It found naturally in palm oil and palm kernel oil, as well as in butter, cheese, milk, and meat.
• The palmitic acid is attached to the alcohol form of vitamin A, called retinol, to make vitamin A stable in milk.