MPPEB Group 2 Subgroup 4 Labour Inspector Official Paper(Held On: 7th Jan 2017 Shift 1) (Previous Year Paper)

The correct answer is Kerosene oil.

Key Points

• Sodium & Potassium metal being very reactive are stored in Kerosene oil.
• Potassium (K) is a most reactive metal and reacts vigorously with air and water.
• A large amount of heat is produced in their reaction.
• To avoid such accidents this metal is kept immersed in kerosene oil.
• Potassium undergoes a reaction with water similar to that of sodium; the products of the reaction are potassium hydroxide and hydrogen gas.
• This reaction releases a great deal of heat energy, often igniting the hydrogen gas that is produced.
• Sodium (Na) and Lithium (Li) are also very reactive to air and water and need to be stored under oil to prevent them from reacting with gases in the air and water.
• Caesium (Cs) is the most reactive of all metals.

Additional Information 

• Metals react with water and oxygen present in the air.
• Metal with higher reactivity has vigorous reactions.
• For example, sodium catches fire in the air, hence it is kept in kerosene oil.
• Due to such reactivity of metals, most of the metals are not available in nature in a free state.
• They are present in form of their compounds (oxides, carbonates, sulphides etc,)
• Few metals which are least reactive are available in a free state.
• Such metals are gold, silver, Platinum

Concept:

Human circulatory system:

• The human circulatory system, also called the blood vascular system consists of a muscular chambered heart blood vessel and blood.

Heart:

• The heart is an organ that beats continuously to act as a pump for the transport of blood.
• The heart, the mesodermally derived organ, is situated in the thoracic cavity, in between the two lungs, slightly tilted to the left.
• It is protected by a double-walled membranous bag, pericardium, enclosing the pericardial fluid.

Explanation:

Arteries:

• Arteries carry oxygen-rich blood from the heart to all parts of the body.
• The arteries have thick elastic walls.
• Arteries do not have valves.
• The blood flows in one direction only.

Thus, The main function of Arteries is to carry Oxygenated blood from heart to different parts of the body.

Additional Information Veins:

• Veins are the vessels that carry carbon dioxide-rich blood from all parts of the body back to the heart.
• The veins have thin walls.
• There are valves present in veins that allow blood to flow only towards the heart.

The correct answer is Land breeze.

Key Points

• Land Breeze:
• It blows during the night from land to sea as the land cools faster than the sea. The air above the sea becomes less dense therefore it rises and the cooler air from the land moves in to take its place.

Additional Information

• Sea Breeze
• It  blows in the day, during day time sun heats the land and sea as land becomes hot quickly the air at the land rises quickly which creates low pressure at the land and the sea which is less hot than land, the cooler air from the sea quickly move toward the low-pressure region over the land, which blows sea breeze during the day.

The correct answer is Venus and Uranus.

Key Points

• Our Solar System consists of the Sun and 8 planets:
• Mercury (nearest to the sun)
• Venus (Evening star, hottest planet)
• Earth (Only living planet, blue planet)
• Mars (the red planet)
• Jupiter (the largest planet in the solar system)
• Saturn (a planet with rings)
• Uranus (coldest planet)
• Neptune (farthest to the sun)

Important Points 

• All Planets in our solar system rotate counterclockwise i.e. West to East except for Venus and Uranus.
• Two planets Venus and Uranus are rotating from east to west in our solar system.
• Venus and Uranus are rotating in the opposite direction (clockwise) to the Sun, this is also known as a retrograde rotation.

The correct answer is Filament.

Key Points 

• Bulbs turn electricity into light by sending the electric current through filament.
• Filament refers to a thin wire. Moreover, electric filaments comprise mostly of the metal tungsten.
• Most noteworthy, it is the resistance of the filament which actually heats the bulb up.
• Consequently, when the filament gets hot enough, it starts glowing and produces light.

Additional Information 

• Fuses are the protectors, these are the safety devices which are used to protect the home appliances like televisions, refrigerators, computers with damage by high voltage. 
• A relay is an electrically operated switch. It consists of a set of input terminals for a single or multiple control signals, and a set of operating contact terminals.
• Resistor is a passive two terminals electrical component used for limiting or regulating the flow of electricity in a circuit.

The correct answer is One second.

Key Points

• Second -
• It is the international standard unit of time.
• Other units of time in the International Standard are derived from the Second.
• These units are in multiples of ten.​

Additional Information

• ​One Millisecond -
• ​A millisecond is one-thousandth of a second.
• A nanosecond is one billionth of a second.
• 60 seconds is equal to one minute.
• 60 hour is equal to 60 minutes.

The correct answer is Milk teeth.

Key Points

• They begin to come through the gums at around 6 months and usually, all teeth are visible by the time a child is 2 to 3 years old.
• This process is called a tooth extraction.
• The majority of mammals including human beings form two sets of teeth during their life, a set of temporary milk or deciduous teeth replaced by a set of permanent or adult teeth. This type of dentition is called diphyodont.
• There are 20 temporary teeth that erupt at about six months of age.
• The dental formula of milk teeth is 2102/2102 = 10. It means 4 incisors, 2 canines, 0 premolar, and 4 molars on each side of each jaw, therefore in both the jaws - 10 x 2 = 20 teeth
• These teeth are replaced by a set of permanent teeth, hence 20 teeth are born twice in the life of a man.

Important Points

• A normal adult mouth has 32 teeth.
• Incisors (8) help in biting into the food.
• Canines (4) help in tearing the food.
• Molars (12) help in grinding the food.
• Premolars (8) help in crushing the food.
• The dental formula of human is 2123/2123.

The correct answer is Plane mirror.

Key Points

Periscope:

• An optical instrument that is used for observing through an object which is prevented by a direct line of sight is called as a Periscope.

• There are two plane mirrors in the periscope which are placed at an angle of 45°.

• When the light falls on one of the mirrors then after reflection from first mirror it fall on the second mirror which further reflect it and fall on the eye of the observer.

• We use two plane mirrors placed at 45° to each other in a periscope.

The correct answer is cellulose.

Key Points 

• Cellulose is a type of carbohydrate that can be digested by ruminants and not by humans.
• Ruminants have a large sac-like structure called a rumen between the esophagus and the small intestine.
• The cellulose of the food is digested here by the action of certain bacteria that are not present in humans.

Additional Information 

• Carbohydrates are naturally occurring sugars, starches, and fiber in food.
• All carbohydrates are made up of sugar molecules.
• Sugar molecules linked together form starches and fiber.
• Whole grains are the best source of carbohydrates because they provide energy plus vitamins, minerals, and fiber.
• Carbohydrates are classified into three subtypes:
• Monosaccharides, (mono = ”one”, “alone”; saccharide = “sugar, sweet”)
• Disaccharides (di = “two”; saccharide = “sugar, sweet”)
• Polysaccharides(poly = “many"; saccharide = “sugar, sweet”).

Explanation:

Maximum - Minimum thermometer: 

• Maximum and minimum thermometer or Six's thermometer is a registering thermometer that can record the highest and lowest temperatures reached over a given time period, such as 24 hours.
• In the meteorology and the Weather department, for example, it is used to record temperature extremes at a site.
• It was created in 1780 by British scientist James Six, and the basic design is still in use today.
• It's also known as a maximum-minimum, minimum–maximum, maxima–minima, or minima–maxima thermometer, and it's the first practical design of its kind.
• Since the last reset, the thermometer displays the current temperature as well as the highest and lowest values.
• Hence, the correct answer to this question is the Weather department which helps them to record the temperature at a site or for a period of time for a region.

Important Points

• A clinical Thermometer is used to measure body temperature. It is having ranges from 35 °C to 42 ° C. It is having a kink.
• Laboratory Thermometer is used to find the boiling point or melting point of water. It is having ranges from - 10 °C to 110 °C. It does not have a kink.

Additional Information 

Structure of Maximum - Minimum thermometer: 

• A U-shaped glass tube with two distinct temperature scales situated along each arm of the U makes up Six's Maximum and Minimum thermometer.
• One is for recording the highest temperature and the other is for recording the lowest temperature.
• The U-shaped tube's arms terminate in sealed glass bulbs.
• The top of the minimum reading scale arm has an alcohol-filled bulb, while the other has a vacuum (or low-pressure alcohol vapor)
• A portion of mercury, a metal that is liquid at normal temperatures, is embedded in the U's bend.
• The thermal expansion and contraction of the alcohol in the first bulb as it responds to the external temperature push this around.
• The vacuum in the other bulb allows the alcohol and mercury to circulate freely.
• The temperature is measured by the alcohol, while the mercury indicates the temperature measurement on both scales.
• This differs from a general clinical or laboratory thermometer, which uses the expansion and contraction of mercury to determine temperature.

The correct answer is Radiation.

Key Points

• The movement of energy from one place to other is called energy transfer. Heat transfer mainly takes place due to temperature differences.

There are three modes of Heat transfer.

1. Conduction: The mode of heat transfer in solids where heat transfer takes place without the movement of medium particles is called conduction.

For example:  By heating one end of a metal rod we can feel hotness at another end. 2. Convection: The mode of heat transfer in fluids where heat transfer takes place due to the movement of particles of the medium is called convection.

For example Heating of water in a pot 3. Radiation: The mode of heat transfer where heat is transferred from one place to another without affecting the medium particles is called radiation.

For example: When we place our hands nearby the burning gas stove then we can feel the heat. This is due to radiation.

Additional Information

• The heat from the sun reaches the earth by the process of radiation, covering millions of kilometers of empty space or vacuum.
• The heat from the sun cannot reach Earth by conduction or convection because space is almost completely empty, there is nothing to transfer the energy from the sun to the earth.
• The radiation will help to transmit the heat from one place to another in the form of waves or particles through space or through a material medium.
• Hence heat is received from the sun to the earth by the process is called radiation.

The correct answer is option 2.

Key Points

Plant Fibre:

• Plant fibre is composed of cellulose and sometimes lignin.
• These fibres are classified by their source in plants.
• Examples of fibre are cotton, wool, jute etc.

Wool:

• The wool comes from sheep, goats, yak and some other animals.
• These wool-yielding animals bear hair on their body.

Processing fibres into wool:

• Step I or shearing:
• The fleece of the sheep along with a thin layer of skin is removed from its body.
• This process is called shearing.
• Hair is removed during hot weather.
• The hair provides woollen fibres.
• Woollen fibres are then processed to obtain woollen yarn.​​

Additional Information 

• ​Step II or scouring:
• The sheared skin with hair is thoroughly washed in tanks to remove grease, dust and dirt.
• This is called scouring.

The correct answer is option 3.

Key Points

• Iron is coated with zinc to strengthen it.
• So that it can be saved from rust.

Additional Information

• Galvanization -
• This is a method that is used for coating metal
• It is a method of protecting metal from corrosion by coating it with a **thin layer of zinc.**​
• Zinc -
• It is galvanized by using iron rods to make them rust-free.
• In addition, zinc finds its greatest use in the pharmaceutical industry.
• It is the fourth most common metal in use after iron, aluminum, and copper.
• It is**, like lead**, can be recycled infinitely without loss of its physical or chemical properties.
• It is present in a wide variety of foods and is especially found in association with **protein foods.**​

The correct answer is Concave mirror.

• A concave mirror or converging mirror is a spherical mirror, which has a reflecting surface which bends inwards.

Key Points 

• They reflect and focus incoming light rays at a point which is called the focus point.
• A concave mirror is used as a reflector in torches, searchlights, headlights of motor vehicles, etc. to get a powerful parallel beam of light.
• This helps us to see things up to a considerable distance in the darkness of night.
• Some dental mirrors also use a concave surface to provide a magnified image.

The correct answer is Low ignition temperature.

Key Points

• Ignition Temperature -
• ​It is the lowest temperature of a substance at which combustion of the substance starts.

Additional Information

• Inflammable Material -
• The substances whose ignition temperature is very low and which easily catch fire with the flame are called inflammable substances.
• Examples of inflammable substances are petrol, alcohol, Liquefied Petroleum Gas (LPG), etc.
• Calorific Value -
• The amount of heat energy produced on the complete combustion of 1 kg of a fuel is called its calorific value.
• The calorific value of a fuel is expressed in units called kilojoules per kg (kJ/kg).
• The most important property of a fuel is its calorific value.
• Different amounts of heat are produced by burning equal amounts of different fuels.
• The fuel which produces more heat has more calorific value.

The correct answer is Sandy soil.

Key Points

• Sandy soil -
• The proportion of large particles is more in this soil.
• This soil has the highest rate of water percolation and the sand particles are very large.​

Additional Information

• ​loamy soil -
• It is a type of soil which is very fertile for crops.
• It contains about 40% silt, 20% clay and the remaining 40% sand.
• Due to it being more porous, the fertility of crops is more.
• Such soil has the capacity to hold water 50% of its total weight.
• Humus -
• It is the top most thin layer of soil which is rich in organic matter.
• Ready compost manure or natural compost obtained from forests is also called humus.
• Clayey soil -
• ​It is a soil that is composed of very fine mineral particles and does not contain much organic matter.

The correct answer is Waste water treatment plant.

Key Points

• The wastewater treatment plant is a combination of various physical, chemical & biological processes to remove pollutants from the water.
• There are two types of wastewater, used for treatment, which are-

1. Sewage water - It is all wastewater used in domestic dwellings (e.g. originating from toilets, showers or sinks).
2. Industrial wastewater - It originates from production, industrial and commercial activities, and has a different chemical composition to sewage water.

• Basically, there are three stages in the process of wastewater treatment, which are-
• Primary Treatment
• Secondary Treatment
• Deep Inspection

The correct answer is Ohm.

Key Points 

• The unit of the electrical resistance, measured with direct current, is the ohm (Ω), named after the German physicist and mathematician Georg Simon Ohm.
• According to ohm’s law, the resistance R is the ratio of the voltage U across a conductor and the current I flowing through it:  R = U / I.
• Hence it follows: 1 Ω = 1 V/A.
• The ohm is defined as an electrical resistance between two points of a conductor when a constant potential difference of one volt, applied to these points, produces in the conductor a current of one ampere, the conductor not being the seat of any electromotive force.

Additional Information 

• Coulomb:
• The coulomb (C) is the standard unit of electric charge in the International System of Units (SI).
• It is a dimensionless quantity, sharing this aspect with the mole.
• A quantity of 1 C is equal to approximately 6.24 x 1018, or 6.24 quintillion.
• Seimens:
• The siemens (S) is the SI-derived unit of electric conductance and admittance, also known as the mho (ohm spelled backward, ℧); it is the reciprocal of resistance in ohms (Ω).
• The related property, electrical conductivity, is measured in units of siemens per metre (S/m).

The correct answer is Traditional methods of irrigation

Key Points

• Traditional methods of irrigation consist of chain pump, dhekli, Moat, Rahat.
• Dhekli method
• In the Dhekli method, the ropes and containers were used to gain water from the well. It is a commonly used method.
• There is a bucket and a rock is connected to a wooden beam at either ends.
• When the farmer sink an empty bucket into the water, the bucket is fetched up due to the weight of the rock attached to the other end of a wooden beam.
• Chain pump:
• It has been used since ancient times, in various parts of Europe, China, and the middle-east.
• Two sizable wheels are joined by an unending chain to form this traditional chain pump.
• Half of the bottom wheel is submerged in the water.
• The attached buckets drop into the pool when the wheel is rotated, collecting water.
• The water from the buckets is then moved from the higher wheel to the pool as the chain then hoists them there.
• Moat Method
• It is a pully system of Irrigation.
• Rahat method.
• In the Rahat method, animals move and rotate the wheel, which results in drawing the water from the well.
• IThe Cattle is attached to a wheel.
• When the cattle does the movement, it rotates the wheel that has buckets connected to it.
• This results in drawing water from the well.

Additional Information 

• Irrigation
• The agricultural practise of applying regulated amounts of water to land to help in crop production, as well as to develop landscape plants and lawns, where it may be known as watering, is known as irrigation.
• Modern methods of irrigations includes Drip system and Sprinkler system.
• Sprinkler system:
• Pipes are used to spray water onto the fields in the form of rain-like water droplets.
• The sprinkler system prevents any water loss.
• This system does not have the waterlogging issue.
• Drip system: 
• ​The fields are covered in small pipes with tiny perforations.
• Water drips at the plant roots when it passes through pipes and is used for irrigation.
• The plants are supplied with water by the roots, which also absorb it.

The correct answer is 2 to 7 days.

Key Points Menstruation:

• In this phase menstrual fluid consisting of blood, mucus, and the cells of the uterine lining is eliminated through the vaginal opening.
• It can last anywhere between 2 to 7 days.

Additional Information

• The Follicular Phase:
• The follicular phase of the menstrual cycle begins from the first day of the period and lasts up until ovulation.
• In the course of this phase, estrogen levels rise, and the ovaries prepare for the release of an egg for possible fertilization.
• The follicular phase also stimulates the phase where the uterine lining begins to build again.
• Ovulation:
• In this phase, the ovaries release the egg. It travels through the fallopian tubes and implants itself into the lining along the walls of your uterus.
• This phase usually occurs around two weeks prior to your period.
• During this process, the estrogen level peaks and drops just shortly after.
• The typical life span of this egg is about 24 hours. Unless it is fertilized by a sperm cell during this window, it dies and is shed along with the uterine lining.

The correct answer is Antibiotics.

Key Points

• Medicines manufactured by growing specific microorganism & used to cure a variety of diseases is Antibiotics.
• Antibiotics are the medicines which fight against the bacteria in our body.
• Antibiotics either kill the bacteria or inhibit their multiplication or reproduction.
• Some antibiotics are effective against protozoa also, but they are ineffective to viral infections.
• Antibiotics are naturally obtained from bacteria or fungi (moulds are a type of fungi) or can be synthesized in labs.
• Penicillin was the first antibiotic discovered by Alexnder Fleming in 1928, obtained from Penicillium Notatum (a type of fungus).
• But the use of antibiotics is subject to medical prescriptions, unnecessary, excess or incomplete dosage of antibiotics can cause complications.
• Careless intake of antibiotics can make the body or bacteria antibiotic-resistant, and the antibiotics are no longer able to cure the infection.
• Development of Multidrug-resistant Tuberculosis (MDR TB) and Extensively drug-resistant TB (XDR TB) are an example of antibiotic resistance

The correct answer is Infiltration.

Key Points

• In the world, a portion of the water that falls as rain and snow infiltrates into the subsurface soil and rock.
• Infiltration divides water resources into surface and subsurface water, it is a key process in the hydrological cycle.
• The infiltration depends on the availability of water at the soil surface and on soil characteristics which influence the water retention capacity and hydraulic conductivity.
• Soil texture, or the percentage of sand, silt, and clay in the soil, is the major inherent factor affecting infiltration.
• Water moves more quickly through the large pores in sandy soil than it does through the small pores in clayey soil.

Additional Information 

Concept:

• Symbiotic denotes “living together” of two or more organisms. Symbiosis is the biological interaction between two different biological organisms

Explanation:

• Lichens are symbiotic associations i.e. mutually useful associations, between algae and fungi.
• The algal partner is known as phycobiont, which is autotrophic and fungal partner is know as mycobiont, which is heterotrophic.
• Algae prepare food for fungi and fungi provide shelter and absorb mineral nutrients and water for its partner.
• The symbiotic association between fungi and roots of higher plants is called as Mycorrhizae.

Additional Information

The symbiotic association may be mutualistic, commensalism or parasitism.

• Mutualisms are a form of association in which both partners benefit from the interaction with each other.
• Commensalism is a form of association in which one organism benefits from others. One partner is completely dependent on the other for food, shelter and locomotion, but there is no harmful effect on the other partner.
• Parasitism is the non-mutualistic form of the symbiotic association. In this type of association when one of the organisms benefits and the other organism get harmed.

The correct answer is Photosynthesis**.**

Key Points

• The dissolution of salt in water is a physical change.
• Because salt can be obtained again by making water vapor.
• As a result, no new substance is formed, called physical changes.
• Photosynthesis is the process by which green plants transform solar energy into chemical energy. During photosynthesis in green plants, light energy is captured and used to convert water, carbon dioxide, and minerals into oxygen and energy.
• In Photosynthesis, Solar energy is converted into chemical energy.
• Photosynthesis is not a physical process.

Additional Information

• ​Physical change -
• Under this, there is no change in the chemical nature or chemical identity of the substance.
• For example, after pouring water on a utensil and heating it from below, the water turns into vapor, if you keep a lid on that utensil, then that vapor again converts into the water, this is a kind of physical change.
• Chemical changes -
• Under this, the structure of matter changes.
• One or more substances combine or break down to form new substances.
• Its properties and characteristics change

The correct answer is Carbon dioxide and alcohol.

Key Points 

• Yeast breaks down glucose, forming ethanol(alcohol), carbon dioxide and energy.
• Yeast respires anaerobically.

Additional Information 

• Anaerobic respiration
• It takes place in the absence of oxygen.
• Equation of anaerobic respiration- C6H12O6+2ADP+2PHOSPHATE→2C2H5OH+2CO2+2ATP
• Some prokaryotes i.e. bacteria and archaea, that live in low-oxygen environments rely on anaerobic respiration to break down fuels
• Aerobic respiration
• It's a process of respiration that takes place in the presence of oxygen gas to produce energy from food.
• Example- most of the plants and animals, birds, humans.
• Water and carbon dioxide are produced as end products.
• Equation- Glucose (C6H12O6)  + Oxygen 6(O2) → Carbon-dioxide 6(CO2)  +  Water 6 (H2O) + Energy (ATP)

दिए गए विकल्पों में से "फातिमा" शब्द  “इमा” प्रत्यय रहित शब्द है। 

Key Points

• फातिमा शब्द में कोई सार्थक अर्थ नही होने के कारण गलत है।

अन्य विकल्पों में “इमा” प्रत्यय  है - 

• कालिमा - काल + इमा
• लालिमा- लाल + इमा
• हरीतिमा- हरीत + इमा
• इमा प्रत्यय के अन्य शब्द -  महिमा, गरिमा ,लघिमा।

Additional Information प्रत्यय - जो शब्दांश शब्दों के अंत में विशेषता या परिवर्तन ला देते हैं, वे प्रत्यय कहलाते हैं।

प्रत्यय के प्रकार- 

• कृत् प्रत्यय - वे प्रत्यय जो धातु में जोड़े जाते हैं, कृत प्रत्यय कहलाते हैं।
• कृत् प्रत्यय से बने शब्द कृदंत (कृत्+अंत) शब्द कहलाते हैं।

कृत् प्रत्यय के उदाहरण-  

• तद्धित प्रत्यय - वे प्रत्यय जो धातु को छोड़कर अन्य शब्दों- संज्ञा, सर्वनाम व विशेषण में जुड़ते हैं,
• तद्धित प्रत्यय कहलाते हैं। तद्धित प्रत्यय से बने शब्द तद्धितांत शब्द कहलाते हैं।

तद्धित प्रत्यय के उदाहरण - 

निम्नलिखित मुहावरों में से "आँख में पानी न होना" मुहावरे का अर्थ 'लज्जित न होना' है।

Key Points

• आँख में पानी न होना मुहावरे का अर्थ - लज्जित न होना/ शर्म का नहीं होना।
• वाक्य प्रयोग - तुम्हारी आँख में पानी नही है, जो तुम अपनी माता को बुरा- भला कह रहे हो।

Additional Informationआँख' पर मुहावरे-

दिए गए विकल्पों में से "रोगी - आरोगी" सही विलोम युग्म नहीं है। 

Key Points

• अतः सही विलोम युग्म होगा - "रोगी - निरोगी"
• शेष विकल्पों में सही विलोम युग्म है।

Additional Information

• विलोम शब्द - जो शब्द किसी दूसरे शब्द का उल्टा अर्थ बताते हैं,
• उन्हें विलोम शब्द या विपरीतार्थक शब्द या विरुद्धार्थी शब्द कहते है।

उदाहरण - 

दिए गए विकल्पों में से आशा से बहुत अधिक "आशातीत" कहलाता है। 

Key Pointsअन्य विकल्प - 

Additional Informationवाक्यांश के लिए एक शब्द के उदाहरण- 

वह व्यक्ति जो दिन में केवल एक बार भोजन करता है, "एकाहारी" कहलाता है। 

Key Points

• अल्पाहारी - कम भोजन करने वाला।
• सन्यासी - संन्यास का व्रत धारण करने वाला।
• भिक्षु - जो भिक्षा माँग कर खाता है।

Additional Information

वाक्यांश के लिए एक शब्द के उदाहरण-

• जिस पुस्तक में आठ अध्याय हो  - अष्टाध्यायी
• देखने योग्य**- दर्शनीय**
• जो अशिष्ट व्यवहार करता हो - गँवार
• जो जल से उत्पन्न होता हो - जलज
• जहां सिक्कों की ढलाई होती है - टकसाल
• आकाश में विचरण करने वाले जंतु - नभचर
• दूसरे के मन की बात जानने वाला**- अन्तर्यामी**
• देश के लिए अपने प्राण देने वाला**- शहीद**
• किसी काम में दखल देना**- हस्तक्षेप**
• किसी को भय से बचाने का वचन देना**- अभयदान**
• किसी पद का उम्मीदवार**- प्रत्याशी**

दिए गए विकल्पों में से ‘कुमार’ का एक अर्थ है- "तोता"

Key Points

• ‘कुमार’ के अन्य  अनेकार्थी शब्द - पुत्र, बालक, युवा, पाँच वर्ष से कम आयु का बालक।
• राजकुमार, युवराज, कार्तिकेय, अग्नि, सिन्धु नदी, आदि ।
• गौतम का अनेकार्थी शब्द-  गौतम बुद्ध, द्रोणाचार्य का साला, भारद्वाज।
• प्रभाव का अनेकार्थी शब्द - सामर्थ्य, असर, महिमा, दबाव।

Additional Information

• ऐसे शब्द, जिनके अनेक अर्थ होते है, अनेकार्थी शब्द कहलाते है।

अनेकार्थी शब्द के उदाहरण - 

• अधर - होंठ, आकाश, अनाधार, नीच, बुरा, चंचल।
• घन - हथौड़ा, बादल, बड़ा, मेघ, समूह, विस्तार, अभ्रक।
• चाप - धनुष, दबाव, परिधि का एक भाग, धनु राशि।
• जीव - जन्तु, जीविका, बृहस्पति, जीवात्मा।
• नाग - सर्प, हाथी, बादल, नागवल्ली, एक पर्वत।
• मधु - शहद, वसन्त, पराग, चैत्रमास, ऋतु, शराब।
• वर्ण - रंग, अक्षर, चतुर्वर्ण्य, भेद, रूप।
• क्षेत्र - शरीर, तीर्थ, गृह, प्रकृति, खेल, स्त्री।
• हेम - सोना, तुषार, इज़्ज़त, पीला रंग।
• सूर - वीर, अन्धा, एक कवि, सूर्य, अर्क, मदार, आचार्य, पण्डित।

दिए गए विकल्पों में से 'बहुत धन लाभ होना' अर्थ का मुहावरा "कंचन बरसना" है।  

• वाक्य प्रयोग - मोबाईल कारोबार में आजकल कंचन बरस रहे हैं।

Key Points

अन्य विकल्प - 

Additional Informationकुछ मुहावरे - 

दिए गए विकल्पों में से "संयम" शब्द 'संभ्रम' का विलोम है।

Key Points

• संभ्रम का अर्थ- बेचैनी, जल्दबाज़ी।
• संयम का अर्थ- धैर्य, नियंत्रण।
• अत: संभ्रम का विलोम संयम है।

अन्य विकल्प -

Additional Information

• विलोम शब्द - जो शब्द किसी दूसरे शब्द का उल्टा अर्थ बताते हैं,
• उन्हें विलोम शब्द या विपरीतार्थक शब्द या विरुद्धार्थी शब्द कहते है।

उदाहरण -

भूत अथवा वर्तमान की विशेष घटना, प्रसंग या विषय के प्रमुख कार्यों के क्रमबद्ध और संक्षिप्त विवरण "प्रतिवेदन" कहते हैं।

• वह लिखित सामग्री, जो किसी घटना, कार्य-योजना, समारोह आदि के बारे में प्रत्यक्ष देखकर या छानबीन करके तैयार की गई हो,
• प्रतिवेदन या रिपोर्ट कहलाती है।

Key Pointsप्रतिवेदन के तीन प्रकार हैं-

Additional Information

दिए गए विकल्पों में से निषेधात्मक वाक्य है - "मैं आज बाजार नहीं जाऊँगा।"

Key Pointsअन्य विकल्प - 

Additional Informationअर्थ की दृष्टि से 8 प्रकार के होते हैं-

दिए गए विकल्पों में से हिंदी भाषा में "तीन" प्रकार के उपसर्ग हैं।

Key Points

• हिंदी भाषा में तीन प्रकार के उपसर्गों का प्रयोग किया जाता है।

Additional Information

• किसी शब्द के प्रारंभ में जुड़ने वाले शब्दांश या अव्यय को उपसर्ग कहते हैं,
• इसके जुड़ने से शब्द के अर्थ बदल जाते हैं।
• जैसे - भर+सक = भरसक , सु +बोध= सुबोध , अति + आचार = अत्याचार आदि।

हिंदी भाषा में तीन प्रकार के उपसर्ग- 

दिए गए विकल्पों में से अर्थ के आधार पर "इच्छावाचक" वाक्य है। 

Key Points

• वाक्य - ईश्वर करे। आपकी यात्रा शुभ हो।
• इस वाक्य में इच्छा/ शुभकामना के  भाव को प्रकट किया है, इसलिए  इच्छावाचक वाक्य है।

Additional Informationअर्थ के आधार पर वाक्य आठ प्रकार के होते है - 

दिए गए विकल्पों में से ‘तंत्र' का एक अर्थ है**- "सेना"**

Key Points

• तंत्र के अन्य अनेकार्थी शब्द- उपासना, दवा, पद्धति, कपड़ा, सूत।
• हेम का एक अर्थ "पाला" है।
• हेम अन्य अनेकार्थी शब्द -  स्वर्ण, जल, तुषार, केशर का फूल।
• तारा के अनेकार्थी शब्द - आँख की पुतली, सितारा, महाराजा हरिश्चंद्र की पत्नी।
• तम  के अनेकार्थी शब्द -  अँधेरा, कालिख, अज्ञान, क्रोध, राहु, पाप।

Additional Information

• जिन शब्दों के एक से अधिक अर्थ होते हैं, उन्हें 'अनेकार्थी शब्द' कहते है।

उदाहरण - 

दिए गए विकल्पों में से लिपि से क्या अभिप्राय है - "भाषा को लिखने के चिन्ह"

Key Points

• किसी भाषा को लिखने के लिए जिन चिन्हों की जरूरत होती है, उन चिन्हों को लिपि कहते है।
• लिपि भाषा का लिखित रूप होता है।
• इसके माध्यम से मौखिक रूप की ध्वनियों को लिखकर प्रकट किया जाता है।
• सारी भाषाओँ के लिखने की लिपि अलग होती है।

Additional Information

• हिंदी व संस्कृत भाषा की लिपि देवनागरी है।

देवनागरी लिपि की विशेषताएं –

• इसे बायें से दायें लिखा जाता है।
• हर वर्ण का आकार समान होता है।
• ये उच्चारण के अनुरूप लिखी जाती हैं।
• शिरोरेखा के प्रयोग से यह विश्व की सुन्दरतम लिपि है।

जब कोई कागज़ पत्र मूल रूप से प्रेषक को लौटाना होता है, तो "पृष्ठांकन" की आवश्यकता पड़ती है।

Key Points

• पृष्ठांकन से तात्पर्य उस कार्य विधि से है, जब कोई कागज अपने मूल रूप में प्रेषक को वापस लौटाना हो,
• या उसकी प्रति जानकारी कार्यवाही निहितार्थ या सूचना के लिए या आदेश के लिए किसी अन्य विभाग,
• या अधिकारी या कार्यालय को भेजनी हो, तो पृष्ठांकन का कार्य संपन्न किया जाता है।
• किसी पृष्ठांकन में कोई संबोधन या समापन नहीं होता, केवल जो अधिकारी पृष्ठांकन पर हस्ताक्षर करता है,
• उसका नाम, पदनाम और संपर्क नंबर आदि लिखे जाते हैं।

Additional Information

दिए गए विकल्पों में से 'कुटेव' में उपसर्ग है- "कु"

Key Points

• कु + टेव = कुटेव
• "कु" उपसर्ग से बने अन्य शब्द - कुपुत्र, कुरूप, कुख्यात, कुचक्र, कुरीति।

Important Pointsउपसर्ग के प्रकार - 

Additional Information

• शब्दांश या अव्यय जो किसी शब्द के पहले आकर उसका विशेष अर्थ बनाते हैं, उन्हें उपसर्ग कहा जाता है।

उदाहरण - 

आश्चर्य, हर्ष और घृणा आदि का बोध कराने के लिए निम्न में से "विस्मयादिबोधक चिन्ह" का प्रयोग किया जाता है।

Key Points

• विस्मयाधिबोधक चिह्न ( ! )
• जैसे - वाह! हम यह मैच भी जीत गए।
• अरे! वह पास हो गया।
• वाह! वाह! फिर साइकिल चलाइए।

Additional Information

• वाक्यों के बीच-बीच में थोड़ी देर के लिए रुकने का संकेत करने वाले चिह्नों को विराम-चिह्न कहते हैं।

हिंदी में प्रयोग किए जाने वाले प्रमुख विराम-चिह्न- 

दिए गए विकल्पों में से "दनुज" शब्द 'अग्नि' का पर्यायवाची नहीं है। 

• शेष विकल्प (दहन, पावक, अनल) अग्नि का पर्यायवाची शब्द है।

Key Points

• दनुज के पर्यायवाची शब्द - असुर, दानव, दैत्य, राक्षस, निशाचर।
• अग्नि के अन्य पर्यायवाची - शब्द ज्वलन, धूमकेतु, कृशानु, हुताशन, वैश्वानर, शुचि, ज्वाला, आग।

Additional Information

• समान अर्थ प्रदान करने वाले शब्द पर्यायवाची शब्द अथवा समानार्थक शब्द कहलाते हैं।

उदाहरण - 

• अतिथि- मेहमान ,पाहुन ,आगंतुक, अभ्यागत।
• उत्पत्ति- उद्भव, जन्म, जनन, आविर्भाव ।
• औषधि- दवा, दवाई, भेषज।
• किनारा- तट, कूल, तीर, कगार, पुलिन।
• खेल- क्रीड़ा, केलि, तमाशा, करतब।
• गुप्त- गूढ़, रहस्यपूर्ण, परोक्ष, छिपा।
• घी- हव्य, अमृतसार, क्षीरसार, आज्य।
• चर्म- खाल, चमड़ी, त्वचा, त्वक्।
• छाछ- गोरस, मठा, दधि स्वेद, मट्ठा।
• तरुण- युवा,जवान, युवक।
• दया- कृपा, अनुकंपा, करुणा, अनुग्रह।

दिए गए विकल्पों में से 'अधिष्ठाता' में उपसर्ग "अधि" है। 

Key Points

• अधि उपसर्ग के अन्य शब्द - अधिनियम, अधिनायक, अधिकृत, अधिकरण।
• अध उपसर्ग से बने शब्द - अधपका, अधमरा, अधजला।

Important Points

• उपसर्ग उन शब्दाशों  को कहते है,
• जो किसी शब्द के पूर्व में जुडकर उस शब्द के अर्थ में  पूर्णत: परिवर्तन  अथवा विशिष्टता ला देते है।

उपसर्ग  के  प्रकार- 

Additional Informationउपसर्ग के कुछ उदाहरण - 

दिए गए विकल्पों में से 'कोप' का विपरीतार्थक शब्द "कृपा"  है। 

• कोप शब्द का अर्थ गुस्सा करना होता है, अतः इसका विपरीत अर्थ 'कृपा करना' होता  है।

Key Pointsअन्य विकल्प - 

Additional Information

• जो शब्द किसी दूसरे शब्द का उल्टा अर्थ बताते हैं,
• उन्हें विलोम शब्द या विपरीतार्थक शब्द या विरुद्धार्थी शब्द कहते है।

उदाहरण - 

दिए गए विकल्पों में से राजस्थान में "मेवाती" भाषा बोली जाती है।

Key Points

• जार्ज ग्रियर्सन के अनुसार यह उत्तर-पूर्वी राजस्थान की एक बोली है।
• मेवाती राजस्थान में अलवर, भरतपुर, धौलपुर व करौली में बोली जाती हैं।
• तथा उत्तर प्रदेश के मथुरा हरियाणा के गुड़गांव तक बोली जाती है।
• मेवाती बोली शौरसेनी अपभ्रंश के उपनागर रूप से विकसित हुई है।
• यह ब्रजभाषा की एक उपभाषा/बोली या उपबोली है।
• मेवाती बोली पश्चिमी हिंदी एवं राजस्थानी के बीच सेतु का काम करती है।

Additional Information

पहाड़ी इलाके में इनमें से भाषा "गढ़वाली, कुमाऊँनी" बोली जाती है।

• उत्तराखण्ड लगभग सम्पूर्ण क्षेत्र मध्य पहाड़ी समूह में आता है।
• जिसके अन्तर्गत मुख्यतः कुमाऊंनी और गढ़वाली बोलियां आती हैं।

Key Points

• पहाड़ी बोली भारतीय-आर्य परिवार से जुड़ी भाषाओं का एक समूह है,
• जो मुख्यत: हिमालय के निचले क्षेत्रों में बोली जाती हैं।
• पहाड़ी का हिन्दी में शब्दार्थ ‘पहाड़ का’ है।

इस समूह को तीन वर्गों में वर्गीकृत किया गया है-

• पूर्वी पहाड़ी जिसमें नेपाली आती है।
• मध्यवर्ती पहाड़ी जिसमें कुमाऊंनी और गढ़वाली आती है।
• पश्चिमी पहाड़ी जिसमें हिमांचल प्रदेश की अनेक बोलियां आती हैं।

Additional Information

शिष्ट और सुनिश्चित लोगों द्वारा निश्चित प्रयुक्त तथा व्याकरण सम्मत भाषा रूप ही "मानक भाषा" कहलाता है।

Key Points

Additional Information

मैंने एक कृश काय व्यक्ति को देखा “कृश” शब्द का निम्न विकल्पों में से  उचित विलोम "हृष्ट-पुष्ट" होगा। 

• कृश शब्द का अर्थ - दुबला-पतला, कमज़ोर।
• हृष्ट-पुष्ट का अर्थ - हट्टा-कट्टा; तगड़ा; स्वस्थ; तंदुरुस्त।

Key Points

अन्य विकल्प -

Additional Information

• जो शब्द किसी दूसरे शब्द का उल्टा अर्थ बताते हैं,
• उन्हें विलोम शब्द या विपरीतार्थक शब्द या विरुद्धार्थी शब्द कहते है।

उदाहरण - 

दिए गए विकल्पों में से "दिनों के नाम"  प्रायः पुल्लिंग होते हैं। 

• दिनों के नाम पुल्लिंग होते हैं।
• जैसे- सोमवार, मंगलवार, बुधवार, गुरुवार, शुक्रवार, शनिवार, रविवार।

Key Points

• भाषाओं के नाम स्त्रीलिंग होते हैं।
• तिथियों के नाम स्त्रीलिंग में होते हैं।
• भारतीय नदियों के नाम स्त्रीलिंग में होते हैं।
• अपवाद- शोण, सिन्धु, ब्रह्यपुत्र नदी है, अतः पुंलिंग है।

Additional Information

• लिंग उन शब्दों का रूप होता है जिनसे स्त्री और पुरुष में अंतर किया जा सके।
• यानी अगर स्त्री और पुरुष का बोध कराते हो, उन्हें लिंग कहा जाता है।

Given:

(sin θ + cosec θ) = 4

Calculation:

(sin θ + cosec θ) = 4

Squaring on both sides

(sin θ + cosec θ)² = 4²

sin2θ + cosec2θ + 2sin θ cosec θ = 16      [cosec θ = \(\frac{1}{sin\ \theta}\)]

sin2θ + cosec2θ + 2 = 16

∴ sin2θ + cosec2θ = 14.

Given:

f(x) = 2x³ - 6x2 - 2x + 6

Given roots (a - b), a, (a + b)

Formulas Used:

Sum of roots of polynomial = \(\frac{-(coefficient \ of \ x^2)}{(coefficient \ of \ x^3)}\)

Product of roots of polynomial = \(\frac{-(constant \ term)}{(coefficient \ of \ x^3)}\)

Calculation:

f(x) = 2x3 - 6x2 - 2x + 6

Sum of roots of polynomial

⇒ a - b +a + a + b = \(\frac{-(coefficient \ of \ x^2)}{(coefficient \ of \ x^3)}\) 

⇒ a - b +a + a + b =  \(\frac{-(-6)}{2}\)

⇒ 3a = 3

⇒ a = 1

Product of roots of polynomial

⇒ (a - b) × a × (a + b) = \(\frac{-(constant \ term)}{(coefficient \ of \ x^3)}\)

⇒ (a² - b²)a = \(\frac{-6}{2}\)

⇒ a³ - ab² = - 3

⇒ 1 - b² = -3

⇒ b² = 4

⇒ b = \(\pm 2 \)

∴ The values of a and b is 1 and \(\pm 2 \).

Given:

the arithmetic mean of 8, 4, 15, x and 11 is 10.

Calculation:

the arithmetic mean of 8, 4, 15, x and 11 is 10.

⇒ \(\frac{8+4+15+x+11}{5}\) = 10

⇒ 38 + x = 50

⇒ x = 50 - 38

⇒ x = 12.

Given:

\(\rm \frac{(x^{a+b})^4(x^{b+c})^4(x^{c+a})^4}{(x^a.x^b.x^c)^4}\)

Calculation:

⇒ \(\rm \frac{(x^{a+b})^4(x^{b+c})^4(x^{c+a})^4}{(x^a.x^b.x^c)^4}\) = \(\frac{x^{4a+4b} . x^{4b+4c} . x^{4c+4a}}{x^{4a+4b+4c}}\)

⇒ \(\frac{x^{4a+4b+4b+4c+4c+4a}}{x^{4a+4b+4c}}\) = x^{8a+8b+8c-4a-4b-4c}  = x4(a + b + c)

Given:

one face of a cube has an area 64 cm2

Formula Used:

Volume of cube = Side3

Calculation:

one face of a cube has an area 64 cm2

Let the side of the cube = L

L² = 64

L = 8 cm

∴ Volume of cube = Side³

Volume of cube = L³ 

Volume of cube = 8³

Volume of cube = 512 cm³

Given:

A pack of 52 playing cards from which all the kings are removed and a card is selected at random

Concept used:

Probability = (the number of favorable outcomes) /(the number of total outcomes)

Calculation:

The total number of cards in the pack is 52, and after removing the kings, the number of cards left is 48.

A card can either be red or black, but not both.

The probability of an event is the ratio of the number of favorable outcomes to the number of total outcomes.

The probability of an event that cannot occur is 0.

The probability of selecting a card that is both red and black is 0.

∴ The probability that the card selected is both red and black is 0.

Given:

A = 48

Calculation:

Shortcut Trick For equal roots in the equation ax2 + bx − c = 0, the discriminant (D) must be 0. ⇒ D = b2 − 4(a)(−c) = 0 ⇒ b2 + 4ac = 0 Since we are given a = b + c, we can write b = a − c. Substituting this into the discriminant: ⇒ (a − c)2 + 4ac = 0 ⇒ (a + c)2 = 0 ⇒ a + c = 0 ⇒ a = −c ∴ The correct answer is a = −c.

Alternate Method Given: Quadratic equation: ax2 + bx − c = 0 Condition: a = b + c ⇒ b = a − c Formula Used: For a general quadratic equation Ax2 + Bx + C = 0 to have equal roots, its discriminant must be zero (D = 0). D = B2 − 4AC = 0 Calculations: ⇒ Comparing ax2 + bx − c = 0 with Ax2 + Bx + C = 0, we get A = a, B = b, and C = −c. ⇒ D = b2 − 4(a)(−c) = 0 ⇒ b2 + 4ac = 0 Substituting the value of b = a − c in the above equation: ⇒ (a − c)2 + 4ac = 0 Expanding the squared term using the identity (x − y)2 = x2 + y2 − 2xy: ⇒ a2 + c2 − 2ac + 4ac = 0 ⇒ a2 + c2 + 2ac = 0 Using the algebraic identity x2 + y2 + 2xy = (x + y)2: ⇒ (a + c)2 = 0 Taking the square root on both sides: ⇒ a + c = 0 ⇒ a = −c ∴ The correct answer is a = −c.

Additional Information Nature of Roots For a quadratic equation ax2 + bx + c = 0, the discriminant is given by D = b2 − 4ac. If D > 0, the roots are real and distinct. If D = 0, the roots are real and equal. If D < 0, the roots are imaginary. Sum and Product of Roots If α and β are the roots of the equation ax2 + bx + c = 0, then the Sum of roots (α + β) = −b/a and the Product of roots (α×β) = c/a. Forming a Quadratic Equation If the roots α and β are already known, the quadratic equation can be written as x2 − (α + β)x + αβ = 0.

Given:

Equations 2ax + 6y = a + 3 and 3x + ay = a

Concept used:

Condition for infinitely many solutions,

Let a₁x + b₁y = c1 and a₂x + b₂y = c₂

then a₁**_/**a₂ = b₁/b₂ = c₁/c₂

Calculation:

2ax + 6y = a + 3

3x + ay = a

For infinite number of solutions

\(\frac{2a}{3} = \frac{6}{a} = \frac{a + 3}{a}\)

⇒ \(\frac{2a}{3} = \frac{6}{a}\)

⇒ 2a² = 18

⇒ a² = 9

⇒ a = 3.

∴ The value of a = 3 .

Given:

Number = \(\frac{3}{8}\)

Calculation:

equivalent rational number

\(\frac{3}{8}\) × \(\frac{5}{5}\) = \(\frac{15}{40}\) × \(\frac{25}{25}\) = \(\frac{375}{1000}\)

∴ Convert \(\frac{3}{8}\) to an equivalent rational number of the form \(\frac{c}{d}\) = \(\frac{375}{10^3}\) .

Shortcut Trick

Curved Surface Area (CSA) of a frustum can be calculated using the perimeters (circumferences) of its bases.

CSA = (Sum of Perimeters ÷ 2) × Slant Height

⇒ CSA = [(20 + 12) ÷ 2] × 8

⇒ CSA = (32 ÷ 2) × 8 = 16 × 8 = 128 cm²

∴ The correct answer is 128 cm².

Alternate Method

Given:

Slant height (l) = 8 cm

Perimeter of larger base (P₁) = 20 cm ⇒ 2πR = 20

Perimeter of smaller base (P₂) = 12 cm ⇒ 2πr = 12

Formula Used:

Curved Surface Area (CSA) of frustum = π(R + r)l

Calculations:

⇒ 2πR + 2πr = 20 + 12

⇒ 2π(R + r) = 32

⇒ π(R + r) = 16

⇒ CSA = π(R + r) × l

⇒ CSA = 16 × 8

⇒ CSA = 128 cm²

∴ The correct answer is 128 cm².

Additional Information

Total Surface Area of Frustum

TSA = π(R + r)l + πR² + πr². It includes the CSA and the area of both circular bases.

Volume of Frustum

Volume (V) = (1/3)πh(R² + r² + R×r), where h is the vertical height.

Slant Height Relationship

l = √[h² + (R − r)²], connecting vertical height, slant height, and radii.

Given:

the semi perimeter of a triangle is 21 cm and two of its sides are 13 cm and 15 cm . 

Formula Used:

Perimeter of the triangle = a + b + c = 2s

area of triangle = \(\sqrt {s(s-a)(s-b)(s-c)}\).

Calculation:

Let a = 13 cm and b = 15 cm and s = 21

a + b + c = 2s

⇒ 13 + 15 + c = 42

⇒ 28 + c = 42

⇒ c = 14 cm

∴ area of triangle = \(\sqrt {s(s-a)(s-b)(s-c)}\)

⇒ area of triangle = \(\sqrt {21(21-13)(21-15)(21-14)}\)

⇒ area of triangle = \(\sqrt {21(8)(6)(7)}\)

⇒ area of triangle = 7 × 3 × 4

⇒ area of triangle = 84 cm² .

Given:

α and β are zeros of the polynomial x2 - 9x + k and 3α + β = 17.

Calculation:

Given equation 3α + β = 17 → (1)

From the given quadratic equation x2 - 9x + k

a = 1, b = - 9 and c = k

α + β = \(\frac{-b}{a}\) = 9 → (2)

αβ = \(\frac{c}{a}\) = k → (3)

Subtract equations (1) and (2), we get

⇒ 3α + β - α - β= 17 - 9

⇒ 2α = 8

⇒ α = 4

α = 4 substitute in equation (2)

⇒ α + β = 9

⇒ β = 9 - 4

⇒ β = 5

∴ αβ = k ⇒ k = 20

Given:

∠CBQ = 70°

PBQ is a tangent to the circle with centre 'o'.

Calculation:

OB is the radius and BQ is the tangent to the circle

So, ∠OBQ = 90°

But ∠CBQ = 70°

∠OBC = 90° - 70° = 20°

From \(\triangle\)OBC

OB = OC (radius of circle)

⇒ ∠OBC = ∠OCB = 20°

∴ ∠BOC = 180 - ∠OBC - ∠OCB = 180 - 20 - 20 = 140°

∴ ∠BAC = ∠BOC / 2 = 70° .

Given:

The sum of two numbers is 12.

The sum of their reciprocals is \(\frac{4}{9}\).

Calculation:

a + b = 12

sum of reciprocals = \(\frac{1}{a} +\frac{1}{b} = \frac{4}{9}\)

⇒ \(\frac{a +b}{ab} = \frac{4}{9}\)

⇒ \(\frac{12}{ab} = \frac{4}{9}\)

⇒ ab = 27

Let the one number be x and the other number be 12 - x

Now there product is 27

⇒ x(12 - x) = 27

⇒ 12x - x² = 27

⇒ x² - 12x + 27 = 0

Given: 

A girl 4ft tall is standing in front of a 26ft high building.

At a certain time of the day, if the girl casts a 6ft long shadow.

Calculation:

Let the length of the shadow of the building = x.

In \(\triangle ABC\), AB || DE

\(\frac{AB}{DE} = \frac{BC}{EC}\)

⇒ \(\frac{26}{4} = \frac{x}{6}\)

⇒ x = 39ft.

Given:

The area of the circle is \(\frac{12}{5}\) of the area of its sector.

Formula Used:

Area of circle = \(\pi r^2\)

Area of sector = \(\pi r^2 [\frac{\theta}{360^\circ}]\)

Calculation:

Where \(\theta\) = x

The area of the circle is \(\frac{12}{5}\) of the area of its sector.

⇒ \(\pi r^2\) = \(\frac{12}{5}\) × \(\pi r^2 [\frac{\theta}{360^\circ}]\)

⇒ \(\theta\) = 150°

⇒ x = 150°

Given:

(x + \(\rm \frac{1}{x} \)) = 2z

Formula Used:

(a + b)³ = a³ + b³ + 3ab(a + b)

Calculation:

(x + \(\rm \frac{1}{x}\)) = 2z

Cubing on both sides

⇒ (x + \(\rm \frac{1}{x}\))³ = (2z)³

⇒ x³ + \(\frac{1}{x^3}\) + 3× \(\rm \frac{1}{x}\)× x(x + \(\rm \frac{1}{x}\)) = 8z³

⇒ x3 + \(\frac{1}{x^3}\) + 3(x + \(\rm \frac{1}{x}\)) = 8z3

⇒ x3 + \(\frac{1}{x^3}\) = 8z³ - 3(2z)

⇒ x3 + \(\frac{1}{x^3}\) = 8z3 - 6z

∴ x3 + \(\frac{1}{x^3}\) = 2z(4z² - 3) .

Given:

x = a cosec θ ⇒ \(\frac{x}{a} \) = cosec θ

y = b cot θ ⇒ \(\frac{y}{b}\) = cot θ

Calculation:

\(\rm \frac{x^2}{a^2}-\rm \frac{y^2}{b^2}=\) cosec² θ - cot² θ

\(\rm \frac{x^2}{a^2}-\rm \frac{y^2}{b^2}=\) 1     (∵ cosec2 θ = 1 + cot2 θ)

Given:

A(1, -3) and B(-2, 3)

The point on the line, through A(1, -3) and B(-2, 3) that is twice as far from A as from B

Calculation:

Let the point on line P(x, y) 

∴ \(\frac{PA}{PB} = \frac{2}{1}\)

So, by using section formula

x = \(\frac{mx_2+nx_1}{m+n}\)  and y = \(\frac{my_2+ny_1}{m+n}\)

⇒ x = \(\frac{mx_2+nx_1}{m+n}\)

⇒ x = \(\frac{2(-2) + 1(1)}{3}\)

⇒ x = \(\frac{-4+1}{3}\)

⇒ x = - 1

y = \(\frac{my_2+ny_1}{m+n}\) 

⇒ y = \(\frac{2(3) + 1(-3)}{3}\)

⇒ y = \(\frac{6-3}{3}\)

⇒ y = 1

∴ The point on the line is P(-1, 1)

Shortcut Trick

The ratio in which the x-axis divides the line segment joining (x₁, y₁) and (x₂, y₂) is given by −y₁ : y₂.

Given points are (5, −4) and (−3, 2). Here y₁ = −4 and y₂ = 2.

Required ratio = −(−4) : 2 = 4 : 2 = 2 : 1.

∴ The correct answer is 2  ∶  1.

Alternate Method

Given: Points A(5, −4) and B(−3, 2).

Formula Used: Section Formula for y-coordinate: y = (m₁y₂ + m₂y₁) / (m₁ + m₂). On the x-axis, the y-coordinate of any point is always 0.

Let the x-axis divide the segment AB in the ratio k : 1 at point P(x, 0).

⇒ 0 = [k × 2 + 1 × (−4)] / (k + 1)

⇒ 0 × (k + 1) = 2k − 4

⇒ 0 = 2k − 4

⇒ 2k = 4

⇒ k = 4 / 2 = 2

⇒ Ratio = k : 1 = 2 : 1

∴ The correct answer is 2  ∶  1.

Additional Information

Division by Y-axis

The ratio in which the y-axis divides the segment joining (x₁, y₁) and (x₂, y₂) is −x₁ : x₂.

Internal Section Formula

For a segment divided in ratio m : n, the coordinates of the point are ((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n)).

Mid-point Formula

If the ratio is 1 : 1, the point is ((x₁ + x₂)/2, (y₁ + y₂)/2).

Given:

Total People = 1000

who likes the mango juice = 275

who dislikes the mango juice = 530

who undecided the mango juice = 195

Formula Used:

Probability = \(\frac{no. \ of\ outcomes}{Total\ no.\ of\ outcomes}\)

Calculation:

the probability that a person selected at random likes the taste = \(\frac{275}{1000}\) 

= \(\frac{11}{40}\).

Given:

Number = \(\frac{1}{7}\)

Calculation:

The smallest rational number by which \(\frac{1}{7}\) should be multiplied so that the decimal expansion of the resulting rational number terminates after 2 decimal places is

since, \(\frac{1}{7}\) × \(\frac{7}{100}\) = \(\frac{1}{100}\) = 0.01

∴ \(\frac{7}{100}\) should be multiplied to get the required number.

Given:

Ratio a ∶ b ∶ c = 2 ∶ 5 ∶ 3

Calculation:

a ∶ b ∶ c = 2 ∶ 5 ∶ 3

Let a = 2x, b = 5x, and c = 3x.

For a straight line angle will be always 180°

So, 2x + 5x + 3x = 180°

⇒ 10x = 180°

⇒ x = 18

Largest angle = 5x = 18 × 5 = 90

Smallest angle = 2x = 18 × 2 = 36

∴ Required sum = 90 + 36 = 126° .

Shortcut Trick

In cyclic quadrilateral PQRS, opposite angles are supplementary.

∠PQR + ∠PSR = 180° ⇒ ∠PQR = 180° − 100° = 80°.

In ΔPQT, sum of angles is 180°.

∠T = 180° − (∠P + ∠PQR) = 180° − (70° + 80°) = 30°.

∴ The correct answer is 30°.

Alternate Method

Given: ∠P = 70° and ∠PSR = 100° in the cyclic quadrilateral PQRS within ΔPQT.

Formula Used: Sum of opposite angles of a cyclic quadrilateral is 180°; Sum of angles in a triangle is 180°.

In cyclic quadrilateral PQRS:

⇒ ∠PQR + ∠PSR = 180°

⇒ ∠PQR + 100° = 180°

⇒ ∠PQR = 180° − 100° = 80°

Now, consider the triangle ΔPQT:

⇒ ∠P + ∠PQT + ∠T = 180°

⇒ 70° + 80° + ∠T = 180°

⇒ 150° + ∠T = 180°

⇒ ∠T = 180° − 150°

⇒ ∠T = 30°

∴ The correct answer is 30°.

Additional Information

Cyclic Quadrilateral Property

A quadrilateral is cyclic if all its vertices lie on a single circle. The sum of opposite angles is always 180° (∠A + ∠C = 180° and ∠B + ∠D = 180°).

Exterior Angle of Cyclic Quadrilateral

The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle. For example, if side PS is extended to T, then ∠TSR = ∠PQR.

Angle Sum Property of Triangle

For any triangle, the sum of all three interior angles is always exactly 180°.

The correct answer is 'Unless.'

Key Points

• Let us see the meanings of given conjunctions:
• When: We use "when" to refer to a future situation or condition that we are certain of.
• Example: When I see Gary, I'll tell him that you said hello.
• Unless: We use the conjunction "unless" to mean ‘except if.'
• Example: They won’t come unless you invite them.
• "Provided" is used to say what must happen or be done to make it possible for something else to happen, if, or only if.
• Example: He's welcome to come along, provided that he behaves himself.
• "Suppose" is used at the beginning of a sentence or clause to mean 'what would happen if'.
• Example: Suppose we miss the train - what will we do then?
• ​The sentence says that except if something happens, the person will see the other person the next day.
• Therefore, the correct answer is Option 2.​

Correct sentence: Unless something happens, I’ll see you tomorrow.

The correct answer is 'The money was added up and found to be correct.​'

Key Points 

• The given sentence is in Active Voice. As per the given question we have to change it into Passive Voice.
• The structure of the given sentence is as follows:
• Subject + V2 + Object. (Active Voice)
• Subject (objective case)+ was/were + V3 + Object (subjective case). (Passive Voice)
• Example:
• Their cousin showed them some rare photographs. (Active Voice)
• They were shown some rare photographs by their cousin. (Passive Voice)
• In the first part of the sentence:
• The subject of the given sentence is 'We'.​​
• The object of the given sentence is 'The money'.
• The subject will be put in place of the object and the object will be put in place of the subject.
• And 'added up' will be changed into 'was added up'.
• "Money" must use "was" with it.
• As the second part is connected with the help of the conjunction "and" so the same rules will be applied to the verb "found."
• Therefore, as per the points mentioned above, we find that the correct answer is Option 3.

​

Correct sentence: The money was added up and found to be correct.

The correct answer is 'are.' 

Key Points

• The given sentence is in the Simple Present Tense.
• Structure: Subject + is/am/are + V3
• The subject "people" is a plural noun and it always takes a plural verb.
• Therefore, the option "is, is being and will being" must be ruled out.
• As the blank is referring to the subject "People", so the correct answer is Option 2*.*

Correct sentence: The people of this town are educated.

The correct answer is 'begged.'

Key Points     

• Let us see the meaning of Implored:
• Implored: to ask somebody with great emotion to do something, because you are in a very serious situation. ((कठिनाई में फँसे व्‍यक्ति की) अन्‍य व्‍यक्ति से याचना करना, अनुनय-विनय करना)
• Example: She implored him not to leave her alone.
• Let us see the meanings of the given options:
• Assumed: to accept or believe that something is true even though you have no proof; to expect something to be true. (प्रमाण न होते हुए भी किसी बात को सत्‍य मान लेना; किसी बात के सत्‍य होने की आशा या अपेक्षा करना)
• Said: to speak or tell somebody something, using words. ((शब्‍दों की सहायता से) (किसी को कुछ) कहना; बोलना)
• Declared: to state something publicly and officially or to make something known in a firm, clear way. ((कोई बात) सार्वजनिक और आधिकारिक रूप से घोषित करना, (किसी बात की) घोषणा करना)
• Begged: to ask somebody for something strongly, or with great emotion. (बहुत भावुक होकर या दृढ़ता के साथ कुछ माँगना)
• From the meanings of the given words, we can say that the option that is closest in meaning to the highlighted word in the given sentence is 'begged.'
• Hence, the correct answer is Option 4.

Here, the erroneous part is 'I sincerely pardon.'

Key Points   

• The error lies in the part "I sincerely pardon" of the sentence.
• The meaning of the word "pardon" is forgive or excuse (a person, error, or offence). (किसी को क्षमा करना)
• The sentence wants to convey that I'd want to take this opportunity to express my heartfelt regret for the problems you've had.
• So, we need to replace "pardon" with "apologize" to make the sentence grammatically correct.
• The meaning of the word "apologize" is to say that you are sorry for something that you have done. ((किसी से) (किसी बात के लिए) क्षमा याचना करना)
• Therefore, the correct answer is Option 2.

Correct sentence: Once again, I sincerely apologize for the difficulties you have encountered.

The correct answer: Please, can we discuss this calmly? 

Key Points    

• A comma ( , ) is used to separate clauses and phrases.
• A comma ( , ) also separates words (from other words or the sentence on the whole) that are not essential to the meaning of the sentence.
• The given sentence requires a comma after the word "Please."
• "Please" is used as a polite way of asking for something or telling somebody to do something. ((किसी से विनम्र अनुरोध करने के लिए प्रयुक्त) कृपया)
• The sentence "Can we discuss this calmly" doesn't require a comma ( , ) in between.
• As it is an interrogative sentence, so we must use a question mark ( ? ) at the end of the sentence "Can we discuss this calmly."
• The word after the comma ( , ) must start with a letter in the lower case.
• ​Therefore, the correct answer is Option 1.

​

Correct sentence: Please, can we discuss this calmly?

The correct answer is Tom requests his mother if she can sew that button for him. 

Key Points   

• The given interrogative sentence is in the direct speech.
• The rules of Direct and Indirect speech for interrogative sentence conversions.
• Inverted commas are removed in indirect speech.
• We do not need to change the tense if the reporting verb is in the present, or if the original statement was about something that is still true.
• The given reporting verb "says" is in the present tense.
• The reporting verb "says" is changed to "asks, demands, orders, enquires" as per the nature of the sentence.
• The first person in the reported speech changes according to the subject of reporting speech.
• In Reported Speech change of the second person depends on the object of reporting speech.
• The third person remains unchanged.
• To make the indirect speech for questions that can be answered in YES/NO, the word "if" or "whether" is used before the reported speech within the sentence.
• "Can" remains "can."
• Structure: 
• (Can + Subject+ V1 + Object?) (Direct Speech)
• (If + Subject + can + V1 + Object ) (Indirect Speech)
• Example:  
• He says "Can you help me?"
• He says if I can help him.
• ​Therefore, the correct answer is Option 1.

Correct sentence: Tom requests his mother if she can sew that button for him.