MPPEB Group 2 Subgroup 4 Labour Inspector Official Paper(Held On: 8th Jan 2017 Shift 1) (Previous Year Paper)

The correct answer is Canopy.

Key Points

• The branches of tall trees cover the other plants of the forest like a rooftop. This is called a canopy.
• Shade trees have a dense canopy that restricts light from reaching low-growing plants.
• The canopy of a rainforest is about 10 meters thick and absorbs about 95% of the sunlight.
• The highest terrestrial biodiversity resides in the canopy of tropical rainforests.
• The photosynthesis process of canopy trees is relatively quick due to abundant light.

Additional Information

• The crown of a plant refers to the aboveground part of a plant, including the stems, leaves, and reproductive structures.
• In botany, the trunk is the main woody axis of a tree, which is an important feature in tree identification, and which is often markedly different from the bottom to the top of the trunk depending on the species.
• A stem is one of the two main structural axes of a vascular plant, the other being the root.
• It supports leaves, flowers, and fruits, transports water and solutes in the xylem and phloem between roots and shoots**, stores nutrients,** and builds new living tissue.

The correct answer is Fractional Distillation.

Key Points

• Crude petroleum oil is refined by a process known as Fractional distillation.
• It is the process by which oil refineries separate crude oil into different, more useful hydrocarbon products based on their relative molecular weights in a distillation tower.
• This is the first step in the processing of crude oil, and it is considered to be the main separation process as it performs the initial rough separation of the different fuels.
• The different components that are separated during this process are known as fractions.
• Fractions that are separated include gasoline, diesel, kerosene, and bitumen.
• Fractional distillation allows a lot of useful products to be made from crude oil, with many environmental consequences for the use of those useful products.
• It is used since the difference in the boiling points is very less.
• Vacuum distillation is used for separating mixtures having a high boiling point difference.​

Additional Information

• Evaporation is a type of vaporization that occurs at the surface of a liquid as it changes into the gas phase.
• A high concentration of the evaporating substance in the surrounding gas slows evaporation significantly, such as when humidity affects the rate of evaporation of water.
• Destructive distillation is a process involving the decomposition of a solid by heating it in a closed container and collecting the resulting volatile components, mainly used for the distillation of coal.
• Simple distillation is a method of separating mixtures based on differences in their volatility in a boiling liquid mixture.
• The components in a sample mixture are vaporized by the application of heat and then immediately cooled by the action of cold water in a condenser.

The correct answer is Acids, Bases & Salts.

Key Points

• Most liquids that conduct electricity are solutions of Acids, Bases & Salts.
• Conduction of electricity in liquids:
• When an acid, base, or salt is dissolved in water, the molecules become electrically charged particles called ions.
• Ion-containing solutions conduct electricity. Since it contains few ions, pure water is a poor conductor.
• Ions have the ability to pass through a solution and create an electric current when they are present.
• Acids, bases, and salts ionize in an aqueous solution in order to conduct electricity.
• That is why tap water is a good conductor of electricity because it contains salts but distilled water does not conduct electricity.

The correct answer is Very rich in plant nutrients like N.P.K.

Key Points

• Very rich in plant nutrients like N.P.K is associated with the property of fertilizers.
• Fertilizers are additional substances supplied to crops to increase their productivity.
• These are used by farmers every day to increase crop yield.
• These fertilizers contain essential nutrients needed by plants, including nitrogen, potassium, and phosphorus.

Additional Information

• Fertilizers for plants may be required in the following ways:
• Fertilizers make plants more resistant to pests. As a result, they are using fewer pesticides and herbicides, resulting in healthier crops. Therefore, fewer diseases are present, giving crops an aesthetic value.
• The amount of potassium present in the fertilizers provides strength to the straws and stalks of the plants.
• Phosphorus present in fertilizers helps in the rapid development of roots and the formation of seeds in plants.
• Nitrogen in fertilizers promotes plant growth, which is seen in the green color of plants.

The correct answer is Cockroach.

Key Points

• Tiny openings called spiracles which allow air to move into the body is characteristic of Cockroach.
• The spiracle is an external respiratory pore present on the side of the cockroach's body.
• It contains a series of pores through which air passes directly through the body into a system of branching tubes.

Additional Information

• When you study the anatomy of a cockroach, there are 10 spiracles in a cockroach.
• These spiracles are located in different regions in different numbers.
• Some are found on parts of the thorax and legs.
• Rests are found in the abdominal regions.
• The largest spiracle found in cockroaches is the first thoracic spiracle.

The correct answer is Fuse.

Key Points

• A fuse is a safety device that prevents damage to electrical devices and possible fires.
• When the current is higher than the critical level, the fuse wire melts causing a break in the circuit thus removing the current.
• Fuse is a device that works on the heating effect of electric current.
• It has a fuse wire which has a low melting point.
• It is connected in series with the equipment in a circuit.
• Whenever there is a high current, more heat will be generated and it starts melting the fuse wire.

The correct answer is Very elastic & strong.

Key Points

• Conveyor belts are made from terylene because it is Very elastic & strong. 
• Terylene fiber is used as a fashion apparel fabric in the form of polyester tricot knits.
• It is also used to make wrinkle-free fabric (silk).

Additional Information

• Properties of Terylene:
• Since it is a strong fiber, bleaching or dry cleaning agents have no effect on it.
• Since it absorbs very less amount of water, it dries quickly and can also be washed easily.
• Terylene is abrasion resistant due to its high tensile strength.
• Terylene is stable at high temperatures.
• It is resistant to acids and alkalis due to its insolubility in most organic solvents.
• Terylene is a synthetic polyester fabric that when blended with wool is known as terywool.

The correct answer is Asiatic Lion.

Key Points

• Asiatic Lion is endemic to Gir National Park.
• The Asiatic Lion is one of the five big cat species, found in India, a single population exists in the Gir National Park of Gujarat state.
• The scientific name of the Asiatic lion is Panthera Leo Persica.
• It is listed as endangered species under the red list on the IUCN list.

Additional Information

The correct answer is Diatoms.

Key Points

• The seabed contains large deposits of silica derived from diatoms.
• Diatoms are photosynthesizing algae with cell walls composed of transparent, opaline silica.
• Diatoms are used to monitor past and present environmental conditions and are commonly used in studies of water quality.

Additional Information

• Diatoms are the main producers in the marine environment.
• Hence, they are also known as 'pearls of the sea'.
• Since diatom walls are made of silica, they leave large amounts of cell deposits in their habitats.
• This accumulation is called diatomaceous earth.
• Diatomaceous earth is gritty in nature and hence is used in polishing and in the filtration of oils and syrups.

The correct answer is Rhizobium.

Key Points

• The bacteria found in the roots of plants, which can convert atmospheric nitrogen to a soluble form that can be utilized by the plants is Rhizobium.
• Rhizobium bacteria are soil microbes that can convert atmospheric nitrogen into a dissolved compound.
• They are found in the root nodules of woody plants.
• It plays a major role in the nitrogen cycle as well as in ecosystem services.

Additional Information

• Streptococcus is a genus of Gram-positive coccus or spherical bacteria belonging to the family Streptococci, in the order Lactobacillus, in the phylum Bacillota.
• Cell division in streptococci occurs along an axis, so as they grow, they form pairs or chains that may appear twisted or folded.
• Pneumococcal disease is the name for any infection caused by bacteria called Streptococcus pneumoniae, or pneumococcus.
• Pneumococcal infections can range from ear and sinus infections to pneumonia and bloodstream infections.
• There are vaccines to help prevent pneumococcal disease.
• Lactobacillus is a genus of gram-positive, aerotolerant anaerobes or microaerophilic, rod-shaped, non-spore-forming bacteria.

The correct answer is Frictional force increases as mass increases.

Key Points

• The Frictional force will increase as mass increases.
• The friction experienced by an object is directly proportional to its weight, i.e. as the weight increases, the friction experienced by the body also increases and vice versa.
• Friction is the opposing force or resistance experienced by two objects sliding against each other.
• Friction is the result of interaction between the surfaces of two objects.
• When the weight of the object increases, this interaction becomes stronger due to which the resistance also increases.

Important Points

• The force of friction always acts in a direction opposite to that in which the body tends to move, which means against the direction of the force.
• Till the limiting value is reached, the magnitude of friction is exactly equal to the force which tends to move the body.

The correct answer is Iron & calcium.

Key Points

• Menstruating girls need to have foods rich in Iron & calcium.
• The body needs iron to make hemoglobin, an important component of blood.
• During the postmenstrual years, the body's need for iron increases because more blood needs to be made to compensate for blood loss during menstruation.

Additional Information

• ​Reproductive age in women:
• In females, the reproductive phase of life begins at puberty (10 to 12 years of age) and generally lasts till the age of approximately 45 to 50 years.
• The ova begin to mature with the onset of puberty.
• One ovum matures and is released by one of the ovaries once in about 28 to 30 days.
• During this period, the wall of the uterus becomes thick so as to receive the egg, in case it is fertilized and begins to develop.
• If fertilization occurs, it results in pregnancy.
• If fertilization does not occur, the released egg and the thickened lining of the uterus along with its blood vessels are shed off.
• This causes bleeding in women known as menstruation.
• The first menstrual flow begins at puberty and is termed menarche.
• At 45 to 50 years of age, the menstrual cycle stops.
• The stoppage of menstruation is termed menopause.

The correct answer is Chemical tablets or bleaching powder.

Key Points

• One of the chemical methods used to purify water at home is Chemical tablets or bleaching powder. 
• Chlorination is a commonly used chemical method to purify water.
• This is done by adding chlorine tablets or bleaching powder to the water.
• Chlorine is a powerful chemical that has been used for many years to treat water for domestic consumption.
• Chlorine is an effective water purification method that kills germs, parasites, and other disease-causing organisms found in ground or tap water.
• Water can be purified with chlorine tablets or liquid chlorine.

The correct answer is Ascorbic acid. 

Key Points

• Amla is a rich source of Ascorbic acid.​
• Vitamin C is also known as Ascorbic acid.
• It is a water-soluble vitamin.
• Vitamin C deficiency leads to Scurvy disease.
• Sources:- Citrus fruits such as orange, kiwi, lemon, and vegetables such as broccoli, cauliflower, Brussels sprouts, and capsicums.

Additional Information

The correct answer is Vas deferens.

Key Points

• The tube that carries sperm to the urethra is called Vas deferens.
• Vas deferens: This is a tube in which the sperm is stored and it carries the sperm out of the scrotal sac.
• The vas d efer ens are between the epididymis and the urethra and connect these together.
• The vas deferens carries mature sperm to the urethra, the tube that carries urine or sperm out of the body in preparation for ejaculation.

Additional Information

• The testes are responsible for making sperm and are also involved in producing a hormone called testosterone.
• The epididymis is a narrow, tightly coiled tube attached to each testicle (the male sex glands that produce sperm).
• Sperm cells (the male reproductive cells) move from the testicles to the epididymis, where they mature and accumulate.
• The scrotum is a part of the male body that is located below the penis.
• The scrotum is a pouch that contains the testes, the epididymis, and the lower part of the spermatic cord (the blood vessels and vas deferens).

The correct answer is Loamy soil.

Key Points

• A mixture of sand, silt, and clay form Loamy soil.
• Loamy soil is a mixture of 40% sand, 20% clay, and 40% silt.
• Loamy soil contains more nutrients, moisture, and humus than sandy soil.
• Because of their ability to retain nutrients and water, these soils are suitable for growing most varieties of plants.

Additional Information

• Clayey soil:
• If the proportion of fine particles is relatively higher, then it is called clayey soil.
• Clay particles, being much smaller, pack tightly together, leaving little space for air.
• Unlike sandy soil, water can be held in the tiny gaps between the particles of clay.
• Sandy soil:
• If soil contains a greater proportion of big particles it is called sandy soil.
• Sand particles are quite large.
• They cannot fit close together, so there are large spaces between them.
• A wet soil or fully saturated soil is the soil in which all the pore spaces are filled with water and devoid of air.
• For example, a sponge that is completely filled with water and no air would be considered fully saturated.
• Roots need air - even in high-humidity plants.

The correct answer is Saturn.

Key Points

• The ‘Ringed’ planet surrounded by distinctive rings of dust & rocks is Saturn.
• Saturn is surrounded by a system of rings that stretches out into space for thousands of kilometers.
• The Rings of Saturn was discovered by Galileo Galilei in the year 1610.
• Saturn has the most extensive ring system in the solar system, Saturn is surrounded by a total of 7 rings.
• The rings of Saturn is made up of ice, dust, and particles.

Additional Information

• Solar system:
• ​ It is the collection of eight planets and their moons in orbit around the sun, together with smaller bodies in the form of asteroids, meteoroids, and comets.
• The planets of the solar system are (in order of distance from the sun).
• The planets are characterized into two: 
• The terrestrial planets (Mercury, Venus, Earth, Mars), and
• The Jovian planets (Jupiter, Saturn, Uranus, Neptune).
• The Terrestrial planets have rocky and solid compositions.
• They are close to the Sun and have few or no Moons.
• Also, they have no rings around them.
• The Jovian planets are also known as Gas planets.
• They are larger and composed of gas and liquid.
• They have multiple Moons.
• They all have some form of rings around them.
• Mercury is the smallest planet and Jupiter is the biggest planet.

The correct answer is Coastal areas.

Key Points

• The process of Rusting of Iron is faster in Coastal areas.
• Iron rusts only when iron comes in contact with moist air.
• In coastal areas, the percentage of moisture in the air is high due to sea or ocean, while in the desert the air is dry and hot.
• Corrosion is faster due to higher percentage of moisture in the air in the coastal region as compared to the desert.

Additional Information

• Corrosion occurs when a refined metal is converted into a more stable form such as its oxide, hydroxide or sulfide state, causing the material to corrode.
• It can be the result of some chemical process or it can also occur naturally.
• Rust is a form of corrosion, but it specifically refers to the oxidation of iron or its alloys.
• Rusting can occur only in metals containing iron or alloys.
• Rust refers to the iron oxide that is produced in the process.
• Iron undergoes this reaction in the presence of oxygen and moisture or water and forms a series of iron oxides.

The correct answer is Frictional force.

Key Points

• Worn-out steps of foot-over bridges on railway stations are due to frictional force.
• Due to the high number of railway passengers per day, the footfall on railway bridges is high.
• Therefore, due to friction between the soles of the shoes and the stairs, the steps of foot over bridges at railway stations wear out quickly.

Additional Information

• Gravitational Force: According to Newton's universal law of gravitation, the force of attraction between any two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The correct answer is Chlorine.

Key Points

• The nonmetal used in disinfecting water is Chlorine.
• Chlorine is used to disinfect water for all purposes i.e. from swimming pool water to drinking water.
• It kills bacteria and other germs present in the water.
• It also treats mold, algae, slime, bacteria and other organisms that are present in the water.
• When chlorine is added to swimming pools, it forms a weak acid known as hypochlorous acid that kills bacteria like salmonella and E. coli, and it also kills germs that cause diarrhea and the swimmer's ear.
• The hypochlorite ion, also known as bleach, is very active in killing pathogens.

Additional Information

• Bromine is a chemical element with the symbol Br and atomic number 35.
• It is the third lightest halogen and is a reddish-brown liquid at room temperature that evaporates readily to form a uniformly colored gas.
• It is a non-metal which remains liquid at room temperature.
• Iodine is a chemical element with the symbol I and atomic number 53.
• Iodine is a trace element that is naturally present in some foods, added to some types of salt, and available as a dietary supplement.
• Fluorine is a chemical element with the symbol F and atomic number 9. 
• It the most reactive chemical element and the lightest member of the halogen elements, or group 17 (group VIIa) of the periodic table.

The correct answer is Convection.

Key Points

• Sea breeze is a result of convection.
• Sea breezes blow on hot, summer days because of the unequal heating rates of land and water.
• During the day, the land surface heats up faster than the water surface.
• Therefore, the air over the land is warmer than the air over the ocean.
• Warm air is lighter than cold air.

Additional Information

• In conduction, heat is transferred between objects by direct contact. Heat transfer takes place due to the difference in temperature.
• In convection, heat transfer takes place within a fluid. Heat transfer occurs due to the difference in density.
• In radiation, heat transfer occurs through electromagnetic waves without the involvement of particles. Heat transfer occurs in all objects with a temperature greater than 0 K.

The correct answer is Vibrations.

Key Points

• When a tightly stretched band is plucked, it produces sound due to vibration.
• These vibrations are responsible for the production of sound.
• An elastic rubber band is stretched between two points.

Additional Information

• The sound wave is longitudinal mechanical.
• Longitudinal mechanical waves which are in the range of 20 Hz to 20,000 Hz are called audible or sound waves.
• Longitudinal mechanical waves with a frequency of less than 20 Hz are called infrasonic.
• These are generated by earthquakes, volcanoes, eruptions, ocean waves, elephants and whales.
• Longitudinal mechanical waves with a frequency greater than 20,000 Hz are called ultrasonic waves.
• The speed of sound depends on the elasticity and density of the medium.

The correct answer is 7 colors.

Key Points

• White light consists of 7 colors.
• White light consists of seven component colors**: violet (V), indigo (I), blue (B), green (G), yellow (Y), orange (O), red (R)**.
• In order from lowest to highest, the wavelengths of colored light are given by the acronym VIBGYOR (V < I < B < G < Y < O < R)
• The wavelength range of visible light is 400 to 700 nm.

Additional Information

• Electromagnetic Waves are generated due to the vibration between the electric field and the magnetic field and do not require any medium to travel. It can run in a vacuum.
• Light is a form of energy that is an example of an electromagnetic wave.
• Wavelength: The distance between two successive crests or troughs is called the wavelength of a wave.

The correct answer is Wind blows from ocean to land, in summer.

Key Points

• Monsoon winds happen when wind blows from ocean to land in summer.
• Monsoon winds are when the winds blow from sea to land in summer.
• ​They are formed when the air above the land gets heated and rises to cause the winds to blow from sea to land.
• Monsoon always flows from cold regions to hot regions.
• The summer monsoon and the winter monsoon determine the climate of India and Southeast Asia.

Additional Information

• Seasonal winds are a movement of air repetitively and predictively driven by changes in large-scale weather patterns.
• Planetary Winds: The winds that flow throughout the year from one latitude to another latitude because of latitudinal differences in the air pressure are called planetary winds.
• Local Winds: There are winds that affect local weather. Local winds usually affect small areas and are confined to the lower levels of the troposphere.

The correct answer is Light travels in straight line.

Key Points

• Shadows are formed because light travels in straight lines.
• A shadow is formed when an opaque object or substance is placed in the path of rays of light.
• Opaque material does not allow light to pass through it.
• Light rays passing through the edges of the material form the outline of the shadow.

युग्म शब्द ऐसे शब्द हैं जिनका उच्चारण मात्रा या वर्ण के हल्के से हेर फेर के सिवा प्रायः समान है किन्तु अर्थ में भिन्नता है।

उदाहरण -

• तरणि - सूर्य
• तरणी - नाव
• नीरज - कमल
• नीरद - बादल
• परिणाम - नतीजा, फल
• परिमाण - मात्रा
• सर - तालाब
• शर - तीर

Key Points

अर्थ के आधार पर वाक्यों के भेद है - 'इच्छावाचक वाक्य'

• "भगवान आपको सदुबद्धि दे।"

(यहां वक्ता किसी व्यक्ति के लिए भगवान से कामना कर रहा है कि आपको भगवान सद्‌बुद्धि यानि समझदारी दे। अतः यह इच्छावाचक वाक्य के अंतर्गत आयेगा।)

• वे वाक्य जिसमें हमें वक्ता की कोई इच्छा, आकांक्षा, आशीर्वाद, कामना इत्यादि का पता चलता है, उन वाक्य को इच्छा वाचक वाक्य कहते हैं।

उदाहरण -

• तुम्हारा कल्याण हो।
• ईश्वर करे सब कुशल लौटें।

Key Pointsअर्थ के आधार पर वाक्य के आठ भेद होते हैं -

1. विधानवाचक वाक्य
2. इच्छावाचक वाक्य
3. निषेधवाचक वाक्य
4. आज्ञावाचक वाक्य
5. प्रश्नवाचक वाक्य
6. संकेतवाचक वाक्य
7. संदेहवाचक वाक्य
8. विस्मयादिबोधक वाक्य

Additional Information

उद्धरण चिह्न वाले शुद्ध वाक्य - माँ ने कहा- "मैं देर से घर लौटूंगी। तुम अपना पाठ अवश्य याद कर लेना"।

• (जब हम किसी अन्य व्यक्ति द्वारा कही गई बात को, लिखित रूप में, हू-ब-हू प्रस्तुत करते हैं तो अवतरण चिह्न का प्रयोग किया जाता है।)
• किसी महत्वपूर्ण कथन को ज्यों-का-त्यों लिखने के लिए जिस संकेत चिह्न का प्रयोग किया जाता है उसे अवतरण चिह्न (”…”) कहते हैं।

जैसे - 

• महावीर ने कहा, “अहिंसा परमो धर्म"।

Mistake Points 

• वाह**!** तुमने जो कमाल कर दिखाया। {(विस्मयादिबोधक चिह्न (!)}
• महात्मा गाँधी महापुरूष थे**,** सभी स्त्री पुरूष बच्चे उन्हें अपना मार्गदर्शक मानते थे। {अल्प विराम-(,)}
• मरता**,** क्या न करता। {अल्प विराम-(,)}

Important Points 

‘काम अपनी अवधि में ही पूर्ण हो सकता है, पहले नहीं' यह लोकोक्ति का सही अर्थ है - 'हथेली पर सरसों नहीं जमती'

• वाक्य प्रयोग - जैसे ही नौकरी की सूचना मिली उसने आवेदन पत्र लिखना शुरू कर दिया तब सब ने कहा अरे "हथेली पर सरसों नहीं जमती'।

Key Points

• जब कोई पूरा कथन किसी प्रसंग विशेष में उद्धत किया जाता है तो लोकोक्ति कहलाता है।
• इसी को कहावत कहते है।
• लोकोक्ति वाक्यांश न होकर स्वतंत्र वाक्य होते हैं।

Important Points कुछ महत्वपूर्ण लोकोक्ति, अर्थ और वाक्य प्रयोग:-

• यह मुँह और मसूर की दाल - जब कोई अपनी हैसियत से अधिक पाने की इच्छा रखने वाला

          वाक्य प्रयोग - सोहन कहने लगा कि मैं तो सिल्क का सूट बनवाऊँगा। मैंने कहा - जरा आईना देख आओ - "यह मुँह और मसूर की दाल"।

• सहज पके सो मीठा पकवान - जो काम धीरे - धीरे होता है वह संतोषप्रद और पक्का होता है।

          वाक्य प्रयोग - तुम हर काम में जल्दीबाजी क्यों करती हो? जल्दी का काम तो शैतान का होता है और काम बिगड़ जाता है। यह बात ध्यान रखो "सहज पके सो मीठा होय"।

• नाम बड़े पर दर्शन छोटे - नाम बहुत हो परन्तु गुण कम या बिल्कुल नहीं हों

          वाक्य प्रयोग - लखपति बुआ ने विदा के समय भतीजों को बस एक-एक रुपया दिया। ये तो वही बात हुई - "नाम बड़ा और दर्शन छोटे"।

• आँख के अन्धे गाँठ के पूरे - मूर्ख धनवान

           वाक्य प्रयोग- वकीलों की आमदनी के क्या कहने, उन्हें आँख के "अन्धे गाँठ के पूरे रोज ही मिल जाते हैं"।

• उतर गई लोई तो क्या करेगा कोई - इज्जत जाने पर डर किसका?

          वाक्य प्रयोग - जब लोगों ने उसे बिरादरी से ख़ारिज कर दिया है अब वह खुलेआम आवारागर्दी कर रहा है- "उतर गई लोई तो क्या करेगा कोई"।

कुछ लड़के जा चुके हैं। इस वाक्य में शब्द “कुछ” के विशेषण का भेद है - 'अनिश्चित संख्यावाचक'

• (यहाँ पर **'**कुछ लड़के' में कुछ शब्द से हमें निश्चित संख्या का बोध नही हो पा रहा है। अतः यह शब्द अनिश्चित संख्यावाचक विशेषण के अंतर्गत आएगा।)
• ऐसे विशेषण जो हमें किसी संज्ञा या सर्वनाम का निश्चित बोध नहीं करा पाते एवं उनमें अनिश्चितता बनी रहती है,
• ऐसे विशेषण शब्द अनिश्चित संख्यावाचक विशेषण कहलाते हैं।
• अनिश्चित संख्यावाचक शब्द: कई आदमी, कुछ छात्र, बहुत लोग, सब जानवर आदि।

जैसे - 

• मुझे कुछ फल चाहिए।
• यहाँ तक आने में मुझे अनेक मुश्किलों का सामना करना पड़ा।

Confusion Points

• परिणामवाचक से किसी संज्ञा या सर्वनाम की निश्चित या अनिश्चित मात्रा या नाप के बारे में पता चलता है,
• जबकि संख्यावाचक से किसी संज्ञा या सर्वनाम की निश्चित या अनिश्चित संख्या के बारे में पता चलता है।

Key Points

दूध पीकर**,** दीदी से कहानी सुनकर**,** बच्चा सो गया है। यह वाक्य अल्प विराम चिह्न को सम्बोधित करता है। 

• (उपर्युक्त वाक्य में उपवाक्यों को अलग करने के लिए अल्प विराम चिह्न का प्रयोग किया जाता है।)
• अल्प विराम का अर्थ थोड़ी सी देर के लिए रुकना होता है।
• बोलते समय वाक्य को अर्थपूर्ण, भावपूर्ण और स्पष्ट बनाने के लिए, वाक्य के बीच में हम थोड़ी देर के लिए रुकते हैं,
• इसी ठहराव को लिखते समय जिस चिह्न (,) का प्रयोग किया जाता है, उसे अल्पविराम कहते हैं।

जैसे -

• विजय ने बच्चों के लिए आम**,** अमरूद**,** केले आदि ख़रीदे।
• मैं आया**,** खाना खाया और वापस चला गया।

Key Points

विसर्ग के साथ स्वर या व्यंजन की संधि को विसर्ग संधि कहते हैं।

उदाहरण -

• नि: + चल = निश्चल
• मनः + भाव = मनोभाव
• निः + गुण = निर्गुण

Key Points

‘पढ़वइया’ में प्रत्यय - 'इया'

• पढ़ना + इया = पढ़वइया
• 'पढ़ना' मूलशब्द और **'**इया' प्रत्यय
• अर्थ: जो पढ़ता रहता है।

Key Points

• प्रत्यय शब्द के अंत में जुड़ता है।

Additional Informationकुछ महत्वपूर्ण प्रत्यय शब्द:-

• इया - लठिया, बिटिया, दुनिया, नचनिया, गवइया।
• आना - नजराना, हर्जाना, घराना, तेलंगाना, राजपूताना।
• इक - लौकिक, धार्मिक, वार्षिक, ऐतिहासिक।
• अक - लेखक, पाठक, कारक, गायक।
• पन - अपनापन, मोटापन, कालापन, नीलापन।
• इया - छलिया, जड़िया, बढ़िया, घटिया।
• आई - लड़ाई, सिलाई, पढ़ाई, चढ़ाई।

‘वाह! कैसा सुंदर दृश्य है' यह वाक्य है - 'विस्मयादि वाचक'

'वाह! कैसा सुन्दर दृश्य है।' यह विस्मयादिवाचक वाक्य का उदाहरण है। 

• (यहां पर आश्रर्य के भाव का बोध हो रहा है। साथ ही साथ विस्मय सूचक चिन्ह का प्रयोग भी हुआ है। अतः यह विस्मयादिबोधक वाक्य के अंतर्गत आएगा।)
• वाक्य में हर्ष, विवाद, विस्मय, घृणा, आश्रर्य, करुणा, भय इत्यादि का बोध कराने के लिए विस्मयादिवाचक चिह्न का प्रयोग किया जाता है,

अर्थात विस्मयादिबोधक चिन्ह (!) का प्रयोग अव्यय शब्द से पहले किया जाता है। 

जैसे - 

• आह! कितना सुहावना मौसम है।
• अरे! यह अचानक क्या हो गया।

Key Points

'तनु' का पर्यायवाची शब्द है - 'शरीर'

• तनु का अन्य पर्यायवाची शब्द है- देह, काया, कलेवर, वपु, गात्र, अंग, गात।

Key Pointsझील:-

• अर्थ: सरोवर, कूल, सर।

चंद्रमा:-

• अर्थ: चन्द्र, शशि, हिमकर, राकेश, रजनीश, हिमांशु, चाँद, म��ंक, विधु, सुधाकर, कलानिधि।

खटिया:-

• अर्थ: बाध (पतली रस्सी) से बुनी हुई खाट, चारपाई।

‘निस्तेज’ का संधि विच्छेद है - 'निः + तेज'

• ‘निस्तेज’ शब्द में विसर्ग संधि है।
• निस्तेज - जिसमें आभा या तेज का अभाव हो।

Mistake Points

• यदि प्रथम पद के अंत में किसी भी स्वर के बाद विसर्ग आये तथा दूसरे पद के प्रारंभ में 'त्‌ /थ्‌' आये तो
• विसर्ग दन्त्य 'स्‌' में और 'च्‌ /छ' आये तो विसर्ग तालव्य 'श' में और यदि 'ट्‌/ठ्‌' आये तो विसर्ग मूर्धन्य 'ष्' में बदल जाता है।

Key Pointsविसर्ग:-

• जब संधि करते समय विसर्ग के बाद स्वर या व्यंजन वर्ण के आने से जो विकार (परिवर्तन) उत्पन्न होता है, हम उसे विसर्ग संधि कहते हैं।

उदाहरण-

• नि: + चल = निश्चल
• धनु: + टकार = धनुष्टकार
• नि: + तार = निस्तार

‘महौदार्य’ का संधि विच्छेद है - 'महा + औदार्य'

• महा + औदार्य = महौदार्य (आ + औ = औ)
• महौदार्य में 'वृद्धि स्वर संधि' है।

Key Pointsवृद्धि संधि:-

• संधि करते समय जब (अ, आ) के बाद (ए, ऐ) आए तो ‘ऐ’ बनता है,
• जब (अ, आ) के बाद (ओ, औ) आए तो ‘औ’ बनता है, उसे वृद्धि संधि कहते हैं।

उदाहरण -

• सदा + एव = सदैव (आ + ए = ऐ)
• महा + ऐश्वर्य = महैश्वर्य (आ + ऐ = ऐ)
• जल + ओघ = जलौघ (अ + ओ = औ)
• परम + औषध = परमौषध (अ + औ = औ)

'छि: कैसी लज्जा की बात है'। यह वाक्य में चिह्न को सम्बोधित करता है - 'विस्मयसूचक चिह्न'

• 'छि:! कैसी लज्जा की बात है'। इस वाक्य से घृणा का बोध हो रहा है। अतः यह विस्मयादिसूचक चिह्न के अंतर्गत आएगा।
• वाक्य में हर्ष, विवाद, विस्मय, घृणा, आश्रर्य, करुणा, भय इत्यादि का बोध कराने के लिए विस्मयादिबोधक चिह्न का प्रयोग किया जाता है
• अर्थात विस्मयादिबोधक चिन्ह (!) का प्रयोग अव्यय शब्द से पहले किया जाता है।
• जैसे -
• अरे! तुम यहां कब पहुंचे।
• हे भगवान! यह तुमने क्या किया है।

Key Points

Confusion Points

• निर्देशक चिह्न का प्रयोग किसी विषय के साथ उससे सम्बंधित अन्य बातों की जानकारी देने के लिए किया जाता है,
• जबकि योजक चिह्न का प्रयोग दो समान या विपरीत अर्थ वाले शब्दों को जोड़ने के लिए किया जाता है।

​जैसे -

• निर्देशक चिह्न - तुलसी ने कहा है –“परहित सरिस धरम नहिं भाई।”
• योजक चिह्न - जीवन में उतार - चढ़ाव तो आते ही हैं।

‘मिठबोला' में समास है - **'**बहुव्रीहि'

• 'मिठबोला' का समास विग्रह - मीठी है बोली जिसकी (कोयल )
• वह समास जिसके समस्त पदों में से कोई भी पद प्रधान नहीं होता एवं दोनों पद मिलकर किसी तीसरे पद की ओर संकेत करते हैं वह समास बहुव्रीहि समास कहलाता है।

उदाहरण -

• पीतांबर - पीला है अम्बर (वस्त्र) जिसका अर्थात् श्रीकृष्ण
• श्वेतांबर - श्वेत है जिसके अंबर (वस्त्र) अर्थात् सरस्वती जी

Confusion Points

• मिठबोला' का समास विग्रह - मीठी है बोली जिसकी (समानाधिकरण बहुब्रीहि समास)
• जिस बहुब्रीहि समास में दोनों पदों की विभक्ति समान हो, समानाधिकरण बहुब्रीहि समास कहलाता है।

उदाहरण -

• कलहप्रिय = कलह है प्रिय जिसको
• पीताम्बर = पीत है अम्बर जिसका अर्थात कृष्ण

Key Points

'आवट' प्रत्यय नहीं है - 'घबराहट'

• घबरा + आहट = घबराहट
• 'घबरा' मूल शब्द और 'आहट' प्रत्यय
• अर्थ: घबराने की अवस्था, व्यग्रता।

Mistake Points 

Key Points

• प्रत्यय शब्द के अंत में जुड़ता है।

Additional Information कुछ महत्वपूर्ण प्रत्यय शब्द:-

• आवट - लिखावट, मिलावट, महावट।
• आहट - बौखलाहट, घबराहट, हरबराहट, तड़फड़ाहट।
• ता - प्रसन्नता, सफलता, उत्कृष्टता, कुशलता।
• इक - लौकिक, वार्षिक, सैनिक, ऐतिहासिक।
• अक - लेखक, पाठक, कारक, गायक।
• पन - अपनापन, मोटापन, कालापन, नीलापन।
• इया - छलिया, जड़िया, बढ़िया, घटिया।
• आई - लड़ाई, सिलाई, पढ़ाई, चढ़ाई।

“पंचामृत” शब्द में समास है- 'द्विगु समास'

• 'पंचामृत' शब्द का समास-विग्रह - पाँच अमृतों का समाहार
• वह समास जिसका पहला पद संख्यावाचक विशेषण होता है तथा समस्तपद किसी समूह या फिर किसी समाहार का बोध करता है तो वह द्विगु समास कहलाता है।

उदाहरण -

• त्रिराहा = तीन रास्तों का समाहार
• नवरत्न = नौ रत्नों का समूह

Mistake Points

• यहाँ पर पंचामृत में पहला वर्ण है, 'पंच' जिसका मतलब पाँच होता है।
• पाँच शब्द एक संख्यावाचक विशेषण है। अतः यह द्विगु समास के अंतर्गत आएगा।

Important Points 

शुद्ध वाक्य है - मैं आपके दर्शन करने आया हूँ।

• अन्य सभी विकल्प व्याकरण की दृष्टि से अशुद्ध है।

Key Points

• मैं दर्शन करने आया हूँ। **(**सर्वनाम संबंधी अशुद्धि)
• मैं आपका दर्शन करने आया हूँ आपका। (सर्वनाम और वचन संबंधी अशुद्धि)
• दर्शन करने आया हूँ आपके। (सर्वनाम और पदक्रम संबंधी अशुद्धि)

Confusion Points

• 'दर्शन' शब्द सदैव बहुवचन में ही प्रयोग किया जाता है।
• इसका एकवचन नहीं होता है।

Additional Information

‘मुरेला' में प्रत्यय है - 'एला'

• मोर + एला = मुरेला
• 'मोर' मूलशब्द और 'एला' प्रत्यय
• अर्थ: मोर से सम्बन्धित

Key Points

• प्रत्यय शब्द के अंत में जुड़ता है।

Additional Information कुछ महत्वपूर्ण प्रत्यय शब्द:-

• एला - बघेला, अकेला, सौतेला, करेला।
• ला - अगला, निचला, पहला, धुंधला।
• ईला - रसीला, जहरीला, पथरीला, कंकरीला, हठीला।
• आना - नजराना, हर्जाना, घराना, तेलंगाना, राजपूताना।
• इक - लौकिक, धार्मिक, वार्षिक, ऐतिहासिक।
• अक - लेखक, पाठक, कारक, गायक।
• पन - अपनापन, मोटापन, कालापन, नीलापन।
• इया - छलिया, जड़िया, बढ़िया, घटिया।

‘प्रतिध्वनि’ शब्द में प्रयुक्त उपसर्ग है - 'प्रति'

• प्रति + ध्वनि = प्रतिध्वनि
• 'प्रति' (प्रत्येक) उपसर्ग और **'**ध्वनि' मूलशब्द
• अर्थ: तल से परावर्तित होकर सुनाई पड़नेवाली ध्वनि-तरंगें।

Key Points

• उपसर्ग शब्द के शुरू में जुड़ता है।

Additional Information कुछ महत्वपूर्ण उपसर्ग शब्द:-​

• प्रति (प्रत्येक) - प्रतिदिन, प्रत्येक, प्रतिकूल, प्रतिहिंसा, प्रतिरूप।
• प्र (आगे) - प्रदान, प्रबल, प्रयोग, प्रसार, प्रहार, प्रयत्न।
• नि (बिना) - निडर, निगम, निवास, निषेध, निबन्ध, निषिद्ध।
• सु (अच्छा) - सुगन्ध, सुयश, सुमन,सुलभ, सुबोध, सुशील।
• उप (सहायक) - उपभोग, उपवन, उपमन्त्री, उपयोग, उपनाम, उपहार।
• सम् (अच्छी तरह) - सन्तोष, संगठन,संलग्न, संकल्प, संशय, संरक्षा।
• अनु (पीछे) - अनुचर, अनुकरण, अनुकूल, अनुनाद, अनुभव।

'इस वर्ष फसल अच्छी नहीं हुई है ______ अनाज महंगा है' रिक्त स्थान के लिए उचित अव्यय है - 'इसलिए'

• इस वर्ष फसल अच्छी नहीं हुई है इसलिए अनाज महंगा है।
• (यहाँ पर फसल अच्छी नहीं होने के कारण अनाज महंगा है।)
• इसलिए - अतः, अतएव, इस कारण से।

Mistake Points अन्य शब्दों का प्रयोग-

• वह अपने हाथ धो रही थी, लेकिन तब तक पानी खत्म हो गया।
• हमने खेल में अच्छा प्रदर्शन दिखाया, परन्तु हम हार गए।
• मैंने खाना नहीं खाया क्योंकि खाना नहीं बना था।

Additional Informationअव्यय:-

• ऐसे शब्द जिसमें लिंग, वचन, पुरुष, कारक आदि के कारण कोई विकार उत्पन्न नहीं होता वह शब्द अव्यय कहलाते हैं।
• जैसे - जब, तब, अभी, उधर, वहाँ, इधर, कब, क्यों, वाह, आह, ठीक, अरे, और, तथा, एवं, किन्तु, परन्तु, बल्कि, इसलिए, अतः, अतएव, चूँकि, अवश्��� इत्यादि।
• वह ठीक कहता है।

'आसमान से बातें करना' मुहावरे का अर्थ है - 'बहुत ऊँचा होना'

• वाक्य प्रयोग - बचपन में बाबा जब शीशम के पेड़ पर झूला डाल कर हमें झुलाते थे तो झूला "आसमान से बातें करता हुआ लगता था"।

Mistake Pointsकुछ महत्वपूर्ण मुहावरा, अर्थ और उनके वाक्य प्रयोग:-  

• खून-पसीना एक करना - अधिक परिश्रम करना

           वाक्य प्रयोग - ​"खून पसीना एक करके" विद्यार्थी अपने जीवन में सफल होते है।

• छोटा मुँह बड़ी बात करना - हैसियत से अधिक बात करना

           वाक्य प्रयोग - बच्चे ने अपने दादा और पिता को कहा कि आपस में झगड़ा मत करो, यह तो "छोटा मुँह बड़ी बात हो गई"।

Key Points

• मुहावरा एक ऐसा वाक्य होता है,
• जो वाक्य की रचना करने पर अपना एक अलग अर्थ या विशेष अर्थ प्रकट करता है,
• इनका प्रयोग करने से भाषा, आकर्षक, प्रभावपूर्ण तथा रोचक बन जाती है।

Additional Information कुछ अन्य महत्वपूर्ण मुहावरा, अर्थ और उनके वाक्य प्रयोग:- 

• आँख खुलना - भ्रम का दूर होना, नींद टूटना

           वाक्य प्रयोग - ‌‌‌राम ने श्याम से कहा की अब मै तुम्हारी बातों में  नही आऊंगा अब मेरी "आँखें खुल गई है"।

• घर घाट एक करना - कठिन परिश्रम करना

           वाक्य प्रयोग - नौकरी के लिए संजय ने "घर घाट एक कर दिया"।

• कान कतरना - बहुत चतुर होना

           वाक्य प्रयोग - वह तो अभी से बड़े-बड़ों के "कान कतरता" है। ​

• ईद का चाँद होना - बहुत दिनों बाद दिखाई देना

वाक्य प्रयोग- तुम्हारे विदेश जाने के बाद से तुम तो मानो ईद का चाँद हो गए हो।

शुद्ध वाक्य है - 'आज के समाचार अच्छे हैं।'

• अन्य सभी विकल्प व्याकरण दृष्टि से अशुद्ध है।

Key Points

• ​आज का समाचार अच्छा है। **(**वचन संबंधी अशुद्धि)
• समाचार अच्छे हैं आज के। (पदक्रम संबंधी अशुद्धि)
• अच्छे हैं आज के समाचार। (पदक्रम संबंधी अशुद्धि)

Confusion Points

• वाक्य में समाचार शब्द बहुवचन है।
• इसका हमेशा प्रयोग बहुवचन में होता है।

Additional Information

‘दिल मसोसकर रह जाना' मुहावरे का अर्थ है - 'खीझकर रह जाना'

• वाक्य प्रयोग - भ्रष्टाचार के इस युग में मेरे जैसे कुछ नेक और ईमानदार लोग "दिल मसोसकर रह जाते हैं"।

Key Points

• मुहावरा एक ऐसा वाक्य होता है
• जो वाक्य की रचना करने पर अपना एक अलग अर्थ या विशेष अर्थ प्रकट करता है
• इनका प्रयोग करने से भाषा,आकर्षक, प्रभावपूर्ण तथा रोचक बन जाती है।

Additional Information कुछ महत्वपूर्ण मुहावरा, अर्थ और उनके वाक्य प्रयोग:- 

• मुंह में पानी आना - लालच आना

          वाक्य प्रयोग - होली पर माताजी ने इतनी स्वादिष्ट गुजिया बनाई कि मेरे तो "मुंह में पानी आ गया"।

• मुँह लटकाना - निराश होना।

          वाक्य प्रयोग - पिता जी के डाँटने पर सीमा "मुँह लटकाकर बैठ गई"।​

• ईंट से ईंट बजाना- पूरी तरह से समाप्त कर देना

          वाक्य प्रयोग- यदि पकिस्तान भारत पर आक्रमण करने की कोशिश भी करेगा तो भारत की बहादुर सेना उनकी "ईंट से ईंट बजा देगी"।

• कान पर जूँ न रेंगना- किसी भी बात का असर न होना

           वाक्य प्रयोग- सीमा को कितना भी समझा लो पर उसकी "कान पर जूं तक नहीं रेंगती"।

• डूबते को तिनके का सहारा - थोड़ी-सी मदद

           वाक्य प्रयोग - मैंने मोहित की जब सौ रुपए की मदद की तो उसने कहा कि "डूबते को तिनके का सहारा" बहुत होता है।

कर्ता ‘मैं' एकवचन का बहुवचन है - 'हम'

• ‘मैं' एकवचन, उत्तम पुरुष सर्वनाम
• 'हम' बहुवचन, उत्तम पुरुष सर्वनाम

Mistake Points उत्तम पुरुष सर्वनाम**:-**

Important Pointsएकवचन:-

• शब्द के जिस रूप से उसके एक होने का बोध हो, वह एकवचन कहलाते हैं ।
• जैसे- स्त्री, घोड़ा, नदी, रुपया आदि।

बहुवचन:-

• शब्द के जिस रूप से उसके एक से अधिक होने का बोध हो, वह बहुवचन कहलाते हैं।
• जैसे- स्त्रियाँ, घोड़े, नदियाँ, रूपये आदि।

Additional Informationउत्तम पुरुष:-

• जिन सर्वनाम शब्दों का प्रयोग वक्ता स्वयं के लिए करता है, उन्हें उत्तम पुरूषवाचक सर्वनाम कहते हैं।
• उत्तम पुरुषवाचक सर्वनाम में मैं, हम, मुझे, मेरा, हमारा, हमें इत्यादि सर्वनाम शब्द आते हैं।

जैसे-

• मैं कल जयपुर जाऊँगा।
• हम घूमने जा रहे हैं।

‘शिथिल’ के पर्यायवाची शब्द हैं- 'सुस्त, ढीला, धीमा'

Key Points

• विलोम शब्द - 'गतिशील'
• अर्थ: निरंतर चलने, बढ़नेवाला।

Important Points वीर:-

• अर्थ: बहादुर, शूर, सूरमा, योद्धा, विक्रांत, पराक्रमी।
• विलोम शब्द - 'कायर'
• अर्थ: डरपोक, अशक्ति, बुजदिल, नासमझ, कापुरुष।

विनम्र:-

• अर्थ: सम्भ्रांत, शिष्ट, अनुशासित, सुशील, भद्र, सौम्य, शालीन, सभ्य।
• विलोम शब्द - 'उद्दण्ड'
• अर्थ: ढीठ, अशिष्ट, बेअदब, गुस्ताख़।

प्रचुर:-

• अर्थ:बहुत, अधिक, बहुल, विपुल, यथेष्ट, पर्याप्त, काफी।
• विलोम शब्द - 'एकल'
• अर्थ: अकेला, एकाकी, एकमात्र, सिंगल।

शक्तिहीन:-

• अर्थ: कमज़ोर, सामर्थ्यरहित, बलहीन, अशक्त।
• विलोम शब्द - 'शक्तिशाली'
• अर्थ: बलवान, ताकतवर, जोरदार, ओजस्वी, समर्थ।

Shortcut Trick Subtract the remainder from the dividend: (x2 + x − 4) − 2 = x2 + x − 6. The divisor g(x) is obtained by dividing (x2 + x − 6) by the quotient (x − 2). Using the constant term method: −6 (constant of dividend) ÷ −2 (constant of quotient) = +3. Only the expression x + 3 has a constant term of +3. ∴ The correct answer is x + 3. Alternate Method Given: Dividend p(x) = x2 + x − 4, Quotient q(x) = x − 2, Remainder r(x) = 2. Formula Used: Dividend = (Divisor × Quotient) + Remainder

⇒ p(x) = g(x) × q(x) + r(x) ⇒ x2 + x − 4 = g(x) × (x − 2) + 2 ⇒ x2 + x − 4 − 2 = g(x) × (x − 2) ⇒ x2 + x − 6 = g(x) × (x − 2) ⇒ g(x) = (x2 + x − 6) ÷ (x − 2) ⇒ g(x) = (x2 + 3x − 2x − 6) ÷ (x − 2) ⇒ g(x) = [x(x + 3) − 2(x + 3)] ÷ (x − 2) ⇒ g(x) = [(x − 2)(x + 3)] ÷ (x − 2) ⇒ g(x) = x + 3 ∴ The correct answer is x + 3. Additional Information Division Algorithm for Polynomials For any polynomial p(x) and non-zero g(x), there exist unique q(x) and r(x) such that p(x) = g(x)q(x) + r(x), where r(x) = 0 or degree(r) < degree(g). Relationship of Degrees The degree of the dividend is equal to the sum of the degrees of the divisor and the quotient: degree(p) = degree(g) + degree(q). Factor Theorem If a polynomial p(x) is divided by g(x) and the remainder is zero, then g(x) is a factor of p(x).

Given :

x = 30°

Formula used :

cos 30° = \(\dfrac{\sqrt{3}}{2}\)

Calculation :

4 cos3 x - 2 cos x

⇒  4 cos³ 30° - 2 cos 30°

⇒  \(4\times\bigg( \dfrac{\sqrt{3}}{2}\bigg)^3-2\times \dfrac{\sqrt{3}}{2} \)

⇒  \(4\times \dfrac{3\sqrt{3}}{8}-\sqrt{3} \)

⇒ \(\dfrac{3\sqrt{3}-2\sqrt{3}}{2} = \dfrac{\sqrt{3}}{2}\) 

So, cos 30° = sin 60° = \(\dfrac{\sqrt{3}}{2}\) 

∴ The answer is cos x .

Given :

The cumulative frequency distribution table

Concept used :

Cumulative frequency is the sum of all other previous frequencies up to the current given point.

Frequency of any class = Cumulative frequency of the class - Cumulative frequency of the preceding class

Calculation:

 

We can clearly observe in the Table that 50 - 60 has the highest frequency.

∴ The answer is 50 - 60.

Given :

f(x) = x2 + kx + 5

The difference between the square of the zeros = 16

Formula used :

For a polynomial ax² + bx + c = 0

Then, the Sum of roots = \(\dfrac{-b}{a}\)

Product of roots = \(\dfrac{c}{a}\) 

Calculation :

Let the roots of polynomial f(x) be 'α' and 'β'.

So, Product of roots = α x β = 5 

Sum of roots = α + β = \(\dfrac{-b}{a}\) = - k 

(α - β)² = α² + β² - 2αβ

⇒ 16 = α2 + β² - 2 x 5

⇒ α² + β² = 26

So ,(α + β)² = α² + β² + 2αβ 

⇒ k2 = 26 + 2 × 5 = 36

⇒ k = ±6

∴ The answer is ±6.

Given:

To find the probability of |x| >1 from the numbers -4, -3, -2, -1, 0, 1, 2, 3, 4

Calculation:

|-4| = 4, |-3| = 3, |-2| = 2, and |-1| = 1

So,

Total no. of numbers |x|>1 (4, 3, 2, 2, 3, 4) = 6

Total numbers given = 9

Probability of |x| >1 = \(\frac{6}{9} \) = \(\frac{2}{3}\)

∴ The answer is \(\frac{2}{3}\).

Given :

P(A̅) = \(\frac{2}{9}\) 

Calculation:

We know that,

P(A) + P(A̅) = 1

⇒ P(A) = 1 - P(A̅)

⇒ P(A) = 1 - \(\dfrac{2}{9}\) = \(\dfrac{7}{9}\)

P(A) ∶ P(A̅) = \(\dfrac{7}{9}\) : \(\dfrac{2}{9}\)  = 7 : 2

∴ The answer is 7 : 2.

Given :

Radius of right circular cone and cylinder(r) = 5 cm

Height of right circular cone and cylinder(h) = 9 cm

Formula used :

Volume of right circular cylinder(V₁) = πr²h

The volume of the right circular cone (V₂) = \(\dfrac{1}{3}\)πr2h

Calculation :

Volume of remaining solid = V₁ - V₂ 

⇒ \(π× 5^2× 9 - \dfrac{1}{3}× π× 5^2× 9\) 

⇒ π × 5² × 9 (1 - \(\dfrac{1}{3}\))

⇒ \(\dfrac{2}{3}× π× 5^2× 9\)

⇒ 150π

∴ The answer is 150π .

Given :

One of the solutions of the equation x(2x - 3b) - k = 0 is -2b

Concept used :

For (a, b) are roots of equation ax² + bx + c, then 

ax² + bx + c = 0

Calculation :

According to the question,

x(2x - 3b) - k = 0

⇒ - 2b(2 × - 2b - 3b) - k = 0     (x = -2b)

⇒ - 2b × - 7b - k = 0

⇒ k = 14b²

∴ The answer is 14b².

Given :

42x-16 × 4x-5 = 64

Calculation :

42x-16 × 4x-5 = 64

⇒ 42x-16 × 4x-5 = 4³

⇒ 4^{(2x - 16 + x - 5)} = 4³  

⇒ 4(3x - 21) = 43

⇒ 3x - 21 = 3

⇒ 3x = 24

⇒ x = 8

∴ The answer is 8 .

Given : 

The answer is 

The roots of quadratic equation x2 + kx + 42 = 0 are 'a' and 'b'

and a - b = 1

Concept used :

For a polynomial ax2 + bx + c = 0

Then, the Sum of roots = \(\dfrac{-b}{a}\)

Product of roots = \(\dfrac{c}{a}\)

Calculation :

Product of roots = 42 = a x b

Sum of roots = -k = a + b

So, (a - b)² = a² + b² - 2ab

or a² + b² = 1 + 2 x 42 = 85

(a + b)² = a² + b² + 2ab

⇒ (-k)² = 85 + 2 x 42

⇒ k² = 169

⇒ K = ±13

Product of roots = k = (a + b) = ±13

∴ The answer is ±13 .

Given :

The total number of times the coin is tossed = 500

Number of heads = 180

Number of tails = 360

Formula used :

Probability = \(\frac{Number\ of\ Favourable\ Outcomes}{Total\ no\ of\ Events\ in\ Sample\ Space}\)

Calculation :

Number outcomes of getting head = 180

Total number of events = 500

Probability = \(\dfrac{180}{500} = 0.36 \) 

∴ The probability of getting a head is 0.36.

Given :

In the given figure,

AP = 2 cm, AQ = 3 cm, PB = 4 cm, AC = 9 cm and RD = 3 cm

Formula used :

For  PQ || BC,

\(\dfrac{AP}{PB} =\dfrac{AR}{RD}=\dfrac{AQ}{QC}\)   ----(Thales theorem)

Calculation :

According to the question,

\(\dfrac{AP}{PB} =\dfrac{AR}{RD}\) or \(\dfrac{2}{4} =\dfrac{AR}{3}\)

AR = 1.5 cm

AD = AR + RD = 1.5 + 3 = 4.5 cm

∴ The answer is 4.5 cm.

Given:

The radius of the hemisphere = 7a

Formula used:

T.S.A of hemisphere = 3πr²  

Calculation:

T.S.A of hemisphere = 3πr2

⇒ \(3× \dfrac{22}{7}× (7a)^2\) 

⇒ 3 × \(\dfrac{22}{7}\) × 7a × 7a = 462 a² cm²

∴ The answer is 462 a².

Given :

\(\dfrac{27×3^n-3×3^{n+1}}{81×3^{n+1}-9×3^{n+2}}\)

Formula used:

a^m × aⁿ = a^{m + n}

am ÷ an = am - n

Calculation :

\(\dfrac{27×3^n-3×3^{n+1}}{81×3^{n+1}-9×3^{n+2}}\)

⇒ \(\rm \dfrac{3^3×3^n-3^1×3^{n+1}}{3^4× 3^{n+1}-3^2×3^{n+2}}\) 

⇒ \(\rm \dfrac{3^{3+n}-3^{n+2}}{3^{n+5}-3^{n+4}}\)

⇒ \(\rm \dfrac{3^{n+2}\times(3-1)}{3^{n+4}\times(3-1)}\) 

⇒ \(\rm \dfrac{3^{n+2}}{3^2× 3^{n+2}}\) = \(\dfrac{1}{9}\)

∴ The answer is \(\dfrac{1}{9}\) .

Given :

To find which term is not an A.P

formula used :

n^th term in an A.P = a + (n - 1)d

Where, a = first term and d = common difference

Calculation :

n^th term of an A.P does not involve the square of n, but rather the product of d and n - 1, so except 4n2 + 5, all others can be n^th term.

∴ The answer is 4n2 + 5 .

Given :

The weights of 10 girls are 48, 42, 49, 50, 40, 38, 51, 46, 39, 47

Formula used :

\(Mean=\dfrac{Sum\ of\ Observations}{Number\ of\ Obervations}\) 

Calculation :

Mean weight of 10 girls =

 \(\dfrac{48+42+49+50+40+38+51+46+39+47}{10} = 45\) 

As we can see only 6 girls have more weight than the mean weight of the girls.

∴ The answer is 6.

Given :

(cosecθ -cotθ )(1 + cosθ)

Calculation :

(cosecθ -cotθ )(1 + cosθ)

⇒ \(\bigg(\dfrac{1}{sin θ}-\dfrac{cosθ}{sin θ}\bigg)\)(1+cosθ) 

⇒ \(\bigg(\dfrac{1-cosθ}{sinθ}\bigg) \)(1+cosθ)

⇒ \(\dfrac{1-cos^2θ}{sinθ}\)

⇒ \(\dfrac{sin^2θ}{sinθ} \) = sinθ

∴ The answer is sinθ.

Given :

The volume of cylinder = 648π cm³

Ratio of radius(r) to height(h) of cylinder = 1 : 3

Formula used :

Volume of cylinder : \(π× r^2× h\)

Curved surface area = \(2× π× r× h\)

Calculation :

Let the radius and height of the cylinder be 'x' and '3x' respectively

Volume of cylinder = \(π× r^2× h\) = 648π 

or \(r^2× h = 648\)

or \(x^2\times 3x = 648\)

or x = 6

So, radius = 6 cm and height = 18 cm

Curved surface area = \(2× π× r× h\) = \(2\times π\times 6\times 18\) = 216π cm²

∴ The answer is 216π cm² .

Given :

Ratio of curved surface areas of two cones = 3 : 1

Ratio of radius of two cones = 1 : 2

Formula used :

C.S.A  of cone = \(\pi\times r\times l\)

Where, l = Slant height

Calculation :

Let the slant heights of two cones be 'a' and 'b' and radius be 'r' and 'R' respectively .

According to question,

\(\dfrac{\pi\times r\times a}{\pi\times R\times b} =\dfrac{3}{1}\)

or \(\dfrac{1\times a}{2\times b} =\dfrac{3}{1}\) 

or a : b = 6 : 1

∴ The answer is 6 : 1 .

Given :

Internal radius of the hemispherical bowl (R) = 6 cm

Radius of cylindrical bottles (r) = 2 cm

Height of cylindrical bottles (h) = 3 cm

Formula used :

Volume of a hemisphere = \(\dfrac{2}{3}\times \pi\times R^3\)

Volume of a cylinder = \(\pi\times r^2\times h\)

Calculation :

Volume of hemispherical bowl = \(\dfrac{2}{3}\times \dfrac{22}{7}\times 6^3\) = \(\dfrac{9504}{21}\) cm³

Volume of cylindrical bottle = \(\dfrac{22}{7}\times 2^2\times 3\) = \(\dfrac{264}{7}\) cm³

No. of bottles require to empty the bowl = \(\frac{\dfrac{9504}{21}}{\dfrac{264}{7}}\) = 12

∴ The answer is 12.

Given :

To find the pure recurring decimal 

Calculation :

A pure recurring decimal is a decimal in which all the digits after decimal point is repeated .

So, in options only \(0.\overline{3}\) is a pure recurring decimal as it leads to 0.33333333...

∴ The answer is  \(0.\overline{3}\) .

Given:

PQRS is a quadrilateral in which ∠P = a and ∠R = b. If the bisectors of ∠P and ∠R meet SR and QP produced at N and M respectively.

Concept used:

The "Z" Theorem:

If two lines are parallel then their alternate interior angles are equal. If the alternate interior angles of two lines are equal then the lines must be parallel.

Calculation:

PQRS is a quadrilateral

Figure 1:

According to the Z theorem:

∠N = ∠QPN = \(\dfrac{a}{2}\)

Figure 2:

∠M = ∠SRM = \(\dfrac{b}{2}\)

Now, ∠M + ∠N = \(\dfrac{a}{2}\) + \(\dfrac{b}{2}\) = \(\dfrac{1}{2}\)(a + b)

∴ ∠M + ∠N = \(\dfrac{1}{2}\)(a + b)

Given:

3a + 2b + c = 0

Formula used:

(a + b + c)³ = a³ + b³ + c³ + 3(a + b)(b + c)(c + a)

Calculation:

(3a + 2b + c)3 = 27a3 + 8b3 + c3 + 3(3a + 2b)(2b + c)(c + 3a)

⇒ 0 = 27a3 + 8b3 + c3 + 3(3a + 2b)(2b + c)(c + 3a)

3a + 2b + c = 0

So, 3a + 2b = - c, 3a + c = - 2b, and 2b + c = - 3a

⇒ 0 = 27a3 + 8b3 + c3 + 3 × - c × -3a × -2b

⇒ 27a3 + 8b3 + c3 = 18abc

∴ The answer is 18abc.

Given :

One angle is  \(\frac{1}{3}\) of the largest and the other is \(\frac{2}{3}\) of the largest.

So, ratio of angles of triangle = 3 : 2 : 1

Calculation :

Let the angles of the triangle be 3x, 2x, and x .

Sum of angles of a triangle = 180°

⇒ 3x + 2x + x = 180°

⇒ 6x = 180°

⇒ x = 30°

The largest angle = 3x = 3 x 30 = 90°

∴ The answer is 90° .

Shortcut Trick

In a parallelogram, the diagonals bisect each other.

⇒ OA = AC ÷ 2 = 30 ÷ 2 = 15 cm.

⇒ OB = BD ÷ 2 = 18 ÷ 2 = 9 cm.

The sides of ΔAOB are 9 cm, 12 cm, and 15 cm.

Since 9² + 12² = 15² (81 + 144 = 225), ΔAOB is a right-angled triangle at B.

⇒ Area = 1/2 × base × perpendicular = 1/2 × 12 × 9 = 54 cm².

∴ The correct answer is 54 cm².

Alternate Method

Given:

AB = 12 cm, AC = 30 cm, BD = 18 cm.

Diagonals of a parallelogram bisect each other at intersection point O.

Formula Used:

Heron's formula for the area of a triangle: Area = √(s(s − a)(s − b)(s − c))

where semi-perimeter (s) = (a + b + c) ÷ 2

Calculations:

⇒ OA = AC ÷ 2 = 30 ÷ 2 = 15 cm

⇒ OB = BD ÷ 2 = 18 ÷ 2 = 9 cm

In ΔAOB, the lengths of the sides are a = 15 cm, b = 12 cm, c = 9 cm.

⇒ s = (15 + 12 + 9) ÷ 2

⇒ s = 36 ÷ 2 = 18 cm

⇒ Area = √(18 × (18 − 15) × (18 − 12) × (18 − 9))

⇒ Area = √(18 × 3 × 6 × 9)

⇒ Area = √(54 × 54)

⇒ Area = 54 cm²

∴ The correct answer is 54 cm².

Additional Information

Parallelogram Diagonals Property

The diagonals of a parallelogram bisect each other, cutting each other exactly in half. They also divide the parallelogram into four non-overlapping triangles of equal area.

Pythagorean Triplets

A set of three positive integers that strictly satisfy the rule a² + b² = c². Common triplets include (3, 4, 5) and its multiples like (9, 12, 15) which represent the sides of a right-angled triangle.

Heron's Formula

A mathematical formula to calculate the exact area of any triangle when all three side lengths are known without requiring the altitude: Area = √(s × (s − a) × (s − b) × (s − c)).

The correct answer is 'I don’t know; I haven’t seen him.'

Key Points 

• A contraction is a shortened form of a word (or group of words) that omits certain letters or sounds.
• In a contraction, an apostrophe ( ' ) represents missing letters.
• The most common contractions are made up of verbs, auxiliaries, or modals attached to other words:
• He would=He’d. I have=I’ve. They are=They’re. You cannot=You can’t.
• ​The contraction "-n’t" means not.
• So, we need to add an apostrophe ( ' ) in the words "dont" to make "don't" and "havent" to make "haven't."
• We use a semicolon ( ; ) to replace a period between related sentences when the second sentence starts with either a conjunctive adverb or a transitional expression, such as for example, for instance, that is, besides, accordingly, furthermore, otherwise, however, thus, therefore.
• In the given problem, we need to introduce semicolon ( ; ) after the sentence "I don't know" to replace a period as the second sentence starts a transitional expression "and."
• The full stop (.) represents the greatest pause and separation and it is used to mark the end of a declarative or an Imperative sentence.
• Example: I could reach just up to his waist.
• ​So, we must use a full stop (.) at the end of the sentence.
• Therefore, the correct answer is Option 4.

​

Correct sentence: I don’t know; I haven’t seen him.

The correct answer is 'He exclaimed with disgust that there was a fly in his soup and called the waiter.'

Key Points 

• The given sentence is in the Simple Present Tense.
• The reporting verb said/said to is changed in asked, demanded, ordered, exclaimed and enquired as per the nature of the sentence.
• The conjunction 'that' will be used.
• The first person in reported speech changes according to the subject of reporting speech.
• In Reported Speech, the change of the second person depends on the object of reporting speech.
• The third person remains unchanged.
• Simple Present Tense 'is' converted into Simple Past Tense 'was'.
• Structure: (Subject+ V1 + object) (Direct Speech)

                  (Subject+ V2 + object) (Indirect Speech)

• Example:  Navin said, “He is young.”

                                      Navin said that he was young.   

• Therefore, the correct answer is Option 2.

Correct sentence: He exclaimed with disgust that there was a fly in his soup and called the waiter.

Confusion Points

• Option 1 cannot be the correct answer as the correct reporting verb cannot be surprise as 'ugh' represents disgust or horror.
• Thus, 'disgust' is the correct word.

Here, the erroneous part is 'the tallest of the two .'

Key Points 

• Th error lies in the part "the tallest of the two."
• When two items/people/situations are compared, a comparative degree is used by putting ‘er’ to the adjective word or "more" with the adjective in association with the word ‘than’.
• There are some exceptions in forming comparative degree and superlative degree.
• The comparative degree of "tall" is "taller" and the superlative degree is "tallest."​
• In this sentence, we can see that we are comparing two boys.
• Therefore, we need replace the word "tallest" with "taller" to make the sentence grammatically correct.
• So, the correct answer is Option 4.

Correct sentence: Both Vijayan and Rajan are quite tall but Rajan is the taller of the two.

Here, the correct answer is 'Every.'

Key Points

• Let us explore the given options:
• "Any" is usually used for plural countable nouns and uncountable nouns in questions and negative statements.
• Example: Is there any bread in the house?
• "All" can be used with uncountable nouns and plural countable nouns by itself.
• Example: All the people in the room were silent.
• "Every" are both used with singular nouns to indicate quantity and it indicates three or more items.
• Example: I leave the house every morning.
• Most: When we are talking about the majority of something in general, we use most + noun.
• When we are talking about the majority of a specific set of something, we use most of the + noun.
• Example: Most desserts are sweet.
• Also the sentence "every cloud has a silver lining" is a quote which means even a very bad situation has a positive or hopeful side. (निराशापूर्ण स्थिति में भी आशा की किरण होती है)
• So, the correct answer is Option 3.

Correct sentence: Every cloud has a silver lining.

The correct answer is 'sub-.'

Key Points   

• According to the sentence, we are talking about crossing the roads.
• The meaning of the prefix "sub" is under. ((के) नीचे, आधो-).
• Example: subway, submarine
• ​The meaning of the word "subway" is a tunnel under a busy road or railway that is for people who are walking (pedestrians). (व्‍यस्‍त सड़क या रेलपटरी के नीचे पैदल जाने का रास्‍ता; सुरंगी रास्‍ता, सुरंग पथ, भूमिगत पैदल पारपथ, तलमार्ग)
• ​Thus, the correct answer is Option 1.

Correct sentence: The villager was thrilled to use the subway to cross the road.

The correct answer is 'All sorts of things are left in the bus by passengers.​'

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 + V1(s/es) + Object. (Active Voice)
• Subject (objective case)+ is/am/are + V3 + Object (subjective case). (Passive Voice)
• Example:
• Their cousin show them some rare photographs. (Active Voice)
• They are shown some rare photographs by their cousin. (Passive Voice)
• The subject of the given sentence is 'Passengers'.​​
• The object of the given sentence is 'all sorts of things'.
• The subject will be put in place of the object and the object will be put in place of the subject.
• And 'leave' will be changed into 'are left'.
• "All sort of things" is a plural noun so we must "are" with it.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 1.

​

Correct sentence: All sorts of things are left in the bus by passengers.

The correct answer is 'in, by.'

Key Points  

• Let us see the meanings of the given prepositions​:
• Under: We use "under" to talk about something that is below or lower than something else.
• Example: His shoes were under his bed.
• With: We can use "with" when you're talking about people, or things being together. It means relating to, or in the case of a person or thing. ​
• Example: Russia has just drawn up a trade agreement with Norway.
• In: We can use "in" to refer to a general, longer period of time, such as months, years, decades, or centuries.
• Example: We visited her in April.
• By: We use "by" meaning 'not later than' to refer to arrangements and deadlines.
• Example: They said that the plumber would be here by Monday.
• At: We use "at" when we refer to an address.
• Example: Education starts at home.
• For: We use "for" to talk about a purpose or a reason for something.
• Example: I bought that for you.
• Until: "Until" as a preposition means 'up to (the time that)'.
• Example: We played chess until midnight.
• ​​The first blank refers to to a general period of time, such as hour, so the correct answer is "in" for it.
• The second blank talks about not later than another hour, so the correct answer is "by" for it.
• ​Therefore, the correct answer is Option 2.

​

Correct sentence: I told mom that we’d be home in an hour or so, but we got late by another hour.

The correct answer is 'intrude.'

Key Points 

• Let us see the meaning of Encroach:
• Encroach: to use more of something than you should, trespass, intrude. (अतिक्रमण करना)
• Example: I do hope that I am not encroaching too much upon your free time.
• Let us see the meanings of the given options:
• Attack: to try to hurt or defeat somebody/something by using force. (हमला या आक्रमण करना)
• Bind: to unite people, organizations, etc. so that they live or work together more happily or with better effect. (जनसमूहों, संगठनों, आदि के बीच पारस्‍परिक संबंध; लोगों, समूहों आदि को संगठित करना कि वे सौहार्दपूर्ण वातावरण में काम करें)
• Intrude: enter with disruptive or adverse effect. (अतिक्रमण)
• Mediate: to try to end a disagreement between two or more people or groups. (व्‍यक्तियों या व्‍यक्ति समूहों के बीच मतभेद समाप्‍त करने का यत्‍न करना; मध्‍यस्‍थता करना)
• 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 "intrude."
• Hence, the correct answer is Option 3.