The correct answer is Adrenal.

Key Points

• There are various organs in the human body that produce specific substances like hormones.
• These are known as glands, which can be endocrine or exocrine.

Exocrine glands:

• Glands that have ducts are called exocrine glands.
• They secrete their secretions into the ducts.
• Example: Sweat and oily glands (of skin) and salivary glands .

Endocrine glands:

• These are ductless glands i.e., lack ducts. Hormones are secreted by these glands.
• They secrete hormones directly into the blood.
• Example: Adrenal gland, Pituitary gland, Thyroid gland

Adrenal gland

• Our body has a pair of adrenal glands. Each located at the anterior part of each kidney.
• When the pituitary gland sends instructions to the adrenals via its hormones, the adrenals release hormones.
• The adrenal gland is the endocrine gland responsible for the production and secretion of aldosterone hormones.
• The major mineralocorticoid hormone, aldosterone (Salt-retaining Hormone), is a steroid hormone produced by the adrenal cortex's zona glomerulosa in the adrenal gland.
• This hormone helps in the maintenance of the body's salt and water levels, which regulates blood pressure.
• Aldosterone has an impact on the body's ability to regulate blood pressure.
• It sends the signal to organs like the kidney and colon, which may raise the quantity of salt in the bloodstream or the amount of potassium in the urine.
• The hormone also causes the body to reabsorb water and sodium in order to raise blood volume.
• All of these actions are necessary for increasing and lowering blood arteries.
• Indirectly, the hormone helps in the maintenance of blood salt and electrolyte levels.

The correct answer is 1 to 2 weeks.

Key Points

• Peels of vegetables and fruits, leftover food items, all these are called organic waste.
• Organic Waste -
• Due to the very fast (one to two weeks) action of bacteria on such waste, it gets decomposed quickly and mixes in soil, water, and air.
• It does not cause any kind of pollution.
• Agricultural waste, crop plants, peels of fruits and vegetables, dry leaves and wood, feces, urine, etc. are organic waste.
• Compost and biogas can be made from organic waste.

Additional Information

• ​Non-organic wastes -
• Bacterial action on such waste is slow.
• Some substances take hundreds of years to decompose, such as glass, plastic, polythene, etc.
• These substances remain in the environment for a long time and produce toxic substances in the environment.

The correct answer is Transpiration.

Key PointsTranspiration: 

• It is the process by which water leaves the body of a living plant and reaches the atmosphere as water vapour.
• Transpiration is measured by a potometer.

Evaporation: 

• It is the process in which a liquid changes to the gaseous state at the free surface below the boiling point through the transfer of heat energy.
• Evaporimeter measures evaporation.

Precipitation:

• It is condensed water vapours that fall to the earth.
• Most precipitation occurs as rain, but also snow, hail, fog drip, graupel, and sleet.

Respiration is a chemical change as new substances like carbon dioxide and water are formed.

The Correct answer is Plastic cans, sticks, packets.

Key Points

• Bar screens are used to remove large objects like rags, sticks, cans, plastic packets napkins, etc. in wastewater treatment plant.
• The wastewater is allowed to pass through bar screen so that large solid objects such as rags, napkins, sticks, cans, plastic bags, polythene, etc. present in wastewater can be removed.
• A wastewater bar screen is a coarse screen made of vertical steel bars spaced 1-3 inches apart.
• The most basic wastewater bar screen uses nothing but vertical bars that allow water to pass through but stop larger objects. They're effective but not as efficient as other types. Objects can build up on them, preventing flow and elevating backwater levels.
• There are 4 types of mechanical bar screens; chain-drive, reciprocating rake, catenary, and continuous belt screens.

The correct answer is chemical effect of electric current.

Key Points

• When an electric current is passed through a conducting liquid,
• It dissociates into its positive and negative ions.
• This effect is called the chemical effect of electric current and the phenomenon is called electrolysis.

Additional Information

• Magnetic effect of electric current -
• When an electric current is passed through a conductor, A magnetic field is produced around it.
• This phenomenon is called the magnetic effect of electric current.
• Heating effect of electric current -
• ​In an electric circuit in which pure resistance is connected to the battery, then
• The entire energy of the source is dissipated in the form of heat in the former form, this is called the heating effect of the electric current.
• ​Electrolysis -
• This is the process by which chemical bonds are broken by passing an electric current through a chemical compound.
• When an electric current is passed through water, water decomposes into hydrogen and oxygen.
• This is called the electrolysis of water.

The correct answer is Gravitational force.

Key Points

• In the case of a moving satellite, the gravitational pull provides the necessary centripetal force to the satellite to move the satellite on the circular orbit.
• If the gravitational pull disappears suddenly then there will be no centripetal force acting on the satellite. So the satellite will not move in the circular orbit.

The satellite will move with the same speed and path is tangential to the circular orbit at that point where the gravitational pull disappears.

The correct answer is Tsunamis.

Key Points

• Tsunamis are giant waves caused by earthquakes or volcanic eruptions under the sea.
• Out in the depths of the ocean, tsunami waves do not dramatically increase in height. But as the waves travel inland, they build up to higher and higher heights as the depth of the ocean decreases.
• The speed of tsunami waves depends on ocean depth rather than the distance from the source of the wave. Tsunami waves may travel as fast as jet planes over deep waters, only slowing down when reaching shallow waters.

The correct answer is **L.P.G.**We know that heat is produced when fuels are burnt. The amount of heat produced by burning or combustion of 1Kg of fuel is expressed in terms of calorific value. 

• • It is also known as energy value or heat of combustion.
• It is measured in units of energy per amount of material, e.g. KJ/g or kJ/kg, where KJ is Kilo Joules.

The correct answer is From right to left.

Key Points

• Friction always acts in the opposite direction to the motion.
• Hence the force of friction will be from Right to Left.

Additional Information

• ​Friction Force -
• ​It is a force that opposes relative tangential motion between two planes.
• The value of this force depends on the normal force between the two planes.
• There are two types -
• Static friction and Kinetic friction.
• Static friction acts in a direction parallel to the contact surface of the two bodies.
• Kinetic friction does not depend on the direction of motion.

The correct answer is Bharatpur.

Key Points

• Formerly known as the Bharatpur Bird Sanctuary, the Keoladeo National Park is recognised as one of the world’s most important bird breeding and feeding grounds.
• It originated in as a royal hunting reserve during the 1850s and was a game reserve for Maharajas and the British.
• In 1982, Keoladeo was declared a national park and then later listed as a World Heritage Site by UNESCO in 1985.
• The park is home to over 370 species of birds and animals such as the basking python, painted storks, deer, nilgai and more.
• Noted Indian ornithologist and naturalist Salim Ali used his influence to garner government support to create Keoladeo National Park.
• It was also known as the breeding ground for the rare and elusive to spot Siberian crane.

Additional Information

• The Thattekkad Bird Sanctuary, covering an area of barely 25 km2, and located about 12 km from Kothamangalam (Kerala state, India), was the first bird sanctuary in Kerala.
• Ranganathittu Bird Sanctuary (also known as Pakshi Kashi of Karnataka), is a bird sanctuary in the Mandya District of the state of Karnataka in India.
• Sultanpur National Park is located at Sultanpur village on Gurugram-Jhajjar highway, Haryana.

The correct answer is Weed plants.

Key Points

• The superorder Caryophyllanae contains ubiquitous and allergenically important chenopod and amaranth weeds of the family Amaranthaceae, as well as the lesser docks and sorrels of family Polygonaceae. 
• The Amaranthus genus includes over 60 species and many more hybridized species that can be found throughout the world. Commonly referred to as “pigweeds,” they are annual weeds with prolific seed production that allows them to easily colonize disturbed areas in paddocks, on field edges, and along fences, ditches, and roads.
• Historically they were used as food by native populations, and some species have again gained favor for use as a natural food source. However, A. retroflexus (red pigweed) and several additional species of this genus are toxic to cattle, sheep, goats, pigs, and, rarely, horses.
• Several potential toxins, including nitrates, oxalates, and several unknown nephrotoxic and myocardiotoxic factors, have been associated with Amaranthus poisoning in livestock.

Additional Information

• Leguminous plants are plants in the family Fabaceae (or Leguminosae), which includes the plants that produce beans, peas, and lentils.
• They are notable in that most of them have symbiotic nitrogen-fixing bacteria in structures called root nodules.
• For that reason, they play a key role in crop rotation.
• Plantation crops are perennial crops that are grown on a large scale by an individual or a company.
• They are also known as cash crops because they are grown for their commercial value.
• Plantation crops are typically grown in tropical or subtropical regions and require a lot of land, labor, and capital.

The correct answer is Option 1.

Key Points

• Caterpillar Tracks -
• ​In this method, the area of contact with the ground is more.
• Due to this the average pressure on the land decreases.
• Because of this, the battle tank can easily walk on soft and sandy ground without sinking into the ground.

Additional Information

• ​Battle tanks move on the ground, due to which there is a chance of their sinking on the ground.
• Caterpillar tracks are used in battle tanks instead of tires, as they greatly increase the area of contact.
• The larger the area of contact, the smaller the effect of the force.
• A caterpillar track helps a battle tank distribute its weight more evenly over a larger surface area than wheels.
• Nowadays it is used on the wheels of all heavy vehicles.

The correct answer is -18°C.

Key Points

• Food products should not spoil for months, for this food should be stored at a temperature of -180C.
• Generally, to keep the food in the fridge for a long time, its temperature should be from 00C to 4⁰C.

Additional Information

• ​Keeping food in the fridge does not spoil quickly whereas food kept outside starts spoiling very quickly.
• That's why food items are kept in the fridge to keep them safe and are used as per the requirement in a fixed time.
• Bacteria grow in the outside temperature and spoil the food.
• The refrigerator temperature is lower than the outside temperature.
• Due to this bacteria do not thrive in the low temperature inside the fridge.
• Because of this, the food kept in the fridge remains safe for a certain time.

The correct answer is Carbon monoxide.

Key Points

• Carboxyhaemoglobin or carboxyhaemoglobin (symbol COHb or HbCO) is a complex of carbon monoxide and haemoglobin (Hb) that forms in red blood cells upon contact with carbon monoxide.
• Carbon Monoxide inhibits body stability to distribute O2.
• Haemoglobin has a higher affinity for CO.
• Haemoglobin that binds CO becomes 'poisoned' and can no longer bind oxygen, destroying its function.

The correct answer is 37.8°.

Key Points

• Fahrenheit to Celsius -
• Fahrenheit and Celsius measurements start at a different number—where 0° Celsius is the freezing point,
• For eg, The equivalent temperature in Fahrenheit is 32°.
• The freezing point to boiling point is (0-100°) in degrees Celsius,
• And the same degree is (32-212°) Fahrenheit.
• 100⁰F - 32 = 68
• 68 % 1.8 = 37.77⁰C

The correct answer is Lactic acid.

Key Points

• Cellular respiration is a breakdown of a complex molecule into simpler forms and also results in the release of energy.
• In the presence of oxygen aerobic respiration occurs.
• In the absence of oxygen anaerobic respiration occurs.
• Anaerobic respiration in our body muscles produces Lactic acid and energy.
• In the absence of oxygen, pyruvate is converted to form lactic acid, and energy is released.
• It leads to muscle cramps and pain.

The correct answer is China.

Key Points

• China is the world's largest producer of silk, while India is in second place.
• India and China are the leading countries in silk production in the world.
• India is the largest consumer of silk in the world.
• The majority of Chinese silk is produced from the mulberry silkworm.

Additional Information

• ​Japan -
• The cities of Tokyo, Nagoya, Kobe, Kyoto, and Osaka are silk production centers here.
• Here silk thread is extracted from the cocoon.
• Fukui and Ishikawa's cities are also major centers of silk fabric production.
• Indonesia -
• It is the fourth most populous country in the world and the country with the largest Muslim population in the world.
• It is a vast country located in Southeast Asia and Oceania.
• The capital of the country is **Jakarta.**​
• India -
• Karnataka, Andhra Pradesh, and Assam are the top three states in terms of silk production.
• Mulberry silk is produced maximum in India as compared to other varieties.
• Karnataka is the largest silk-producing state in India.

The correct answer is Living jungles.

Key Points

• Living jungles -
• It is a habitat for various species of wild animals and birds.
• Here a vast land area covered by dense trees, shrubs, mosses, and different types of plants is known as a habitat forest.

Additional Information

• ​Ecosystem -
• It is a natural unit that includes all the living beings, ie plants, animals, and microorganisms of a particular area.
• It interacts with its abiotic environment to form a complete biological unit.
• Thus ecosystem is a unit of interdependent components that share the same habitat.
• The term 'ecosystem' was coined by the British ecologist **Tensile in 1935.**​
• Biodiversity -
• It is the variety of species present in a given area and the diversity of the ecosystems of these species.
• Biome -
• It refers to a large area of land or sea.
• In which all parts have the same weather, geography, and living organisms.
• A biome consists of a single type of ecosystem,
• Whose plants adopt similar methods to thrive in the same type of conditions.

The correct answer is Soil erosion.

Key Points

• Soil erosion -
• It is the upper surface of the land that moves from one place to another due to water or wind.
• It is a naturally occurring physical process.
• It affects all types of landforms.​

Additional Information

• ​Deforestation -
• It means burning or cutting trees in forest areas.​
• Afforestation -
• It is the conversion of any barren, waste, arid, or semi-arid land into a forest area.
• This is done by planting trees and sowing the seeds of plants.
• Weathering -
• It is the process by which the rocks present on the surface of the earth break down.
• It is different from erosion because there is no transfer or transport of land materials formed by breaking down from one place to another.

The correct answer is Amplitude.

Key Points

• When we turn the volume of the TV, the amplitude of sound wave increases.
• Volume -

It is the intensity of a sound wave. 

It is directly related to amplitude, 

It is the height of a sound wave.

Additional Information

• The pitch of a sound depends on its frequency
• The pitch of the higher frequencies is higher.
• The pitch of the women's voice is higher than that of the men.
• Frequency -
• It is the number of occurrences of a repeating event per unit of time.
• It is expressed in units of Hertz (Hz) which is equal to one per second.

The correct answer is Regular reflection takes place.

Key Points

• Laws of reflection: The angle of reflection equals the angle of incidence.

• The incident ray, the reflected ray and the normal lie in the same plane.

• When light rays strike on a smooth plane surface then the reflection is called regular reflection.

• When light reflects at many angles after the incidence on the surface, such a reflection is called as diffuse reflection.

• Light rays are not parallel to each other after irregular reflection, but they obey laws of reflection at each point of reflection.

• When light is incident on a polished surface, regular reflection takes place.

• Reflection is a phenomenon in which the direction of the incident ray changes when it falls on a smooth, reflecting surface.

• The light ray that was reflected is called reflected ray.

• In the case of a plane mirror, the angle of reflection and angle of incidence is the same.

The correct answer is Option 3.

Key Points

• Distance-Time Graph -
• The line slope of this graph shows the rate of distance traveled by the object over time.
• This rate is called the speed or movement of an object.
• The greater the slope of a line on a distance-time graph, the faster the object is moving.

Additional Information

• ​If an object covers equal distances in equal intervals of time, then the motion of that object is called uniform motion.
• Distance -
• The numerical measurement of the space between any two points is called.
• That is, it is the measure of the length of the path between those two points.
• The length of the path covered by a moving object in a given time is also called the distance traveled by that object.

The correct answer is Lactic acid.

Key Points

• Milk is converted into curd or yoghurt by the process of fermentation.
• Milk consists of globular proteins called casein.
• The curd forms because of the chemical reaction between the lactic acid bacteria and casein.
• During fermentation, the bacteria use enzymes to produce energy (ATP) from lactose.
• The byproduct of ATP production is lactic acid.
• Lactic acid acts on the globular proteins present in the milk and denatures them.
• Thus giving a thick texture to the milk due to the coagulation of the proteins.
• Curd may contain a wide variety of bacteria like Lactobacillus acidophilus, Lactococcus lactis, Lactococcus lactis cremoris, etc.

The correct answer is Sodium.

Key Points

• At room temperature sodium reacts vigorously with water to form sodium hydroxide and hydrogen gas.

Additional Information

• Sodium -
• It is the second element of the first main group of the periodic table.
• The total charge on this atom is 23.​
• ​Aluminium -
• It is found in metallic form.
• It is the most abundant metal found in the earth's crust.
• One of its main ores is **bauxite.**​
• Calcium -
• It is a metallic element of the second main group of the periodic table.
• It is an alkaline earth metal and is not available in **pure form.**​
• Magnesium -
• It is an alkaline earth metal like calcium and barium.
• It is the Eighth most abundant element on earth.

The correct answer is Methane, Hydrogen & Carbon monoxide.

Key Points

• Coal gas is obtained during the processing of coal(destructive distillation) to get a coke.
• Coal gas is a product of coal.
• Coal gas is a mixture of Methane(CH4), Carbon Monoxide(CO), and Hydrogen(H2).
• Coal gas is used as a fuel in many industries.

दिए गए विकल्पों में से "तत्" ‘तत्त्व’ में उपसर्ग है।

Key Points

• तत् + त्व
• तत् उपसर्ग के अन्य शब्द - तत्काल, तत्सम, तत्पर।

Additional Information

• 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।
• जैसे- प्रसिद्ध, अभिमान, विनाश, उपकार।
• इनमे कमशः ‘प्र’, ‘अभि’, ‘वि’ और ‘उप’ उपसर्ग है।

उपसर्ग  के  प्रकार - 

सीमित क्षेत्र में बोली जाने वाली भाषा को "बोली"  जाता है।

Key Points

Additional Information 

• एक भाषा के अंनर्गत कई उपभाषाएँ होती हैं तथा एक उपभाषा के अंतर्गत कई बोलियाँ होती है।
• हिन्दी क्षेत्र की समस्त बोलियों को 5 वर्गों में बाँटा गया है। इन वर्गों को उपभाषा कहा जाता है।
• इन उपभाषाओं के अंतर्गत ही हिन्दी की 18 बोलियाँ आती है।

‘अधजल गगरी छलकत जाए' निम्न में से इस लोकोक्ति का सही अर्थ है - कम ज्ञान वाला स्वयं को अधिक दिखाने का प्रयास करता है।

• वाक्य वाक्य - अजय खुद तो आठवीं क्लास पास है लेकिन गुरु जी सामने बढ़ चढ़ के बात कर रहा है, इसे ही कहते हैं कि अधजल गगरी छलकत जाये।

Key Pointsअन्य विकल्प - 

Additional Informationकुछ लोकोक्तियाँ- 

राम ने लंका के राजा रावण को मार गिराया। प्रस्तुत वाक्य में "संज्ञा पदबंध" है। 

Key Points

• उपर्युक्त वाक्य में  लंका के राजा रावण  संज्ञा पदबंध' है। में चार पद है।
• किन्तु वे मिलकर एक ही पद अर्थात संज्ञा का कार्य कर रहे हैं।
• पदबंध का अंतिम अथवा शीर्ष शब्द रावण संज्ञा है अन्य सभी पद उसी पर आश्रित है।

Additional Information

• जब दो या दो से अधिक पद मिलकर एक पद का कार्य करते हैं तब उन्हें पदबंध कहा जाता है।

मुख्य पद के आधार पर पदबंध के पाँच प्रकार होते हैं-

दिए गए विकल्पों में से विस्मयादि बोधक वाक्य है -  "अरे! यह पत्र मोहन ने लिखा है।"

Key Points

• जिन  वाक्यों में विस्मय, आश्चर्य, घृणा, प्रेम, हर्ष, शोक आदि भाव प्रकट होते हैं। विस्मयादि बोधक वाक्य कहते  है।
• शब्दों के बाद विस्मयादिबोधक चिह्न (!) का प्रयोग होता है।

अन्य विकल्प -

• मेरी इच्छा है कि मोहन यह पत्र लिखे - इच्छावाचक वाक्य
• शायद मोहन पत्र लिख ही दे - संदेहवाचक वाक्य
• क्या मोहन पत्र लिखता है? - प्रश्नवाचक वाक्य

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

दिए गए विकल्पों में से 'गायन' का संधि विच्छेद है- "गै + अन"

Key Points

• गायन में संधि का प्रकार - अयादि संधि
• इस संधि को बनाने का नियम - ऐ + अ= आय
• अयादि संधि में जब ए,ऐ,ओ,औ के साथ कोई अन्य स्वर हो तो ” ए- अय “, ” ऐ- आय”, “ओ- अव ” , “औ- आव”  मैं हो जाता है।

Additional Information

• दो वर्णों के मेल से होने वाले विकार को संधि कहते हैं।
• दो शब्दों के मेल से बने शब्द को पुनः अलग अलग करने को संधि विच्छेद कहते हैं।
• संधि के तीन प्रकार होते हैं-  (A) स्वर संधि, (B) व्यंजन संधि और (C) विसर्ग संधि
• जब स्वर के साथ स्वर का मेल होता है तब जो परिवर्तन होता है वह स्वर संधि कहलाता है।

स्वर संधि के निम्नलिखित पाँच भेद हैं-

दिए गए विकल्पों में से रिक्त स्थान के लिए सही वर्तनी वाला शब्द "अवधि" है। 

अतः वाक्य -  'चौदह वर्ष की अवधि समाप्त होने पर श्री राम अयोध्या लौटे।

Key Points

• अन्य विकल्प वर्तनी की दृष्टि से अशुद्ध है।
• किसी भाषा के शब्दों को शुद्ध या अशुद्ध लिखने के ढंग को वर्तनी कहते हैं।
• वर्तनी को अक्षर या स्पेलिंग भी कहते हैं।

Additional Informationअशुद्ध- शुद्ध वर्तनी के उदाहरण -

‘आँखों पर ठीकरी रखना' मुहावरे में निम्न में से "बेशर्म बन जाना" अर्थ सही है��� 

• वाक्य प्रयोग - चरित्रहीन व्यक्ति हमेशा आँखें पर ठीकरी रखे हुए होता है।

Key Points

Additional Informationकुछ मुहावरे - 

दिए गए विकल्पों में से जंगल में लगने वाली आग "दावानल"  कहलाती है। 

Key Points

• दावानल के लिए स्थिति तब उत्पन्न होती है जब वनस्पतियां और मिट्टी सूख जाते हैं।
• वन में वृक्षों की रगड़ से अपने आप से लगने वाली आग जो दूर- दूर तक फैल जाती है,
• उसे दावानल कहते है, ये आग अकसर जंगल में गर्मियों खुद लग जाती है।
• जठरानल - पेट की आग - जठराग्नि
• बड़वानल - समुद्र में लगने वाली आग

Additional Information

• जब किसी वाक्य में प्रयुक्त या स्वतन्त्र किसी वाक्यांश के लिए किसी एक शब्द का प्रयोग किया जाता है,
• जो उस वाक्यांश के अर्थ को पूरी तरह सिद्ध करता हो तो उसे वाक्यांश के लिए एक शब्द कहते हैं।

वाक्यांश के लिए एक शब्द के उदाहरण-

• जिसने आत्मा को जीत लिया हो - जितात्मा
• जहां सिक्कों की ढलाई होती है - टकसाल
• आकाश में विचरण करने वाले जंतु - नभचर
• दो भाषाएं बोलने वाला**- द्विभाषी**
• दूसरे के पीछे चलने वाला**-** अनुचर
• किसी पद का उम्मीदवार**-** प्रत्याशी
• कम जानने वाला**- अल्पज्ञ**
• जो बिन माँगे मिल जाए - अयाचित
• जिसके आने की तिथि निश्चित न हो - अतिथि
• जिस पुस्तक में आठ अध्याय हो  - अष्टाध्यायी

जिसके द्वारा हम अपने भावों एवं विचारों का आदान प्रदान करते हैं उसे "भाषा" जाता है।

Key Points

• जब हम अपने विचारों को लिखकर या बोलकर प्रकट करते हैं।
• और दूसरों के विचारों को सुनकर या पढकर ग्रहण करते हैं, उसे भाषा कहते हैं।

भाषा के भेद-

भाषा के कुछ अन्य भेद भी होते हैं-

• (1) मातृभाषा  (2) राजभाषा (3) राष्ट्रभाषा  (4) मानक भाषा

Additional Information

बोली -

• सीमित क्षेत्रों में बोली जाने वाली भाषा के रूप को बोली कहा जाता है अर्थात,
• स्थानीय व्यवहार में अल्पविकसित रूप में प्रयुक्त होने वाली भाषा बोली कहलाती है।

अलग-अलग राज्यों में अलग-अलग बोलियाँ बोली जाती हैं –

• पूर्वी उत्तर प्रदेश की बोली अवधी है, बिहार की भोजपुरी और मैथिलि,
• हरियाणा में हरियाणवी और बांगड़ू, राजस्थान में राजस्थानी,
• मारवाड़ी और गुजरात में गुजराती बोली बोली जाती है।

लिपि -

• 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।

व्याकरण- 

• मनुष्य मौखिक एवं लिखित भाषा में अपने विचार प्रकट कर सकता है और करता रहा है,
• किन्तु इससे भाषा का कोई निश्चित एवं शुद्ध स्वरूप स्थिर नहीं हो सकता।
• भाषा के शुद्ध और स्थायी रूप को निश्चित करने के लिए नियमबद्ध योजना की आवश्यकता होती है।
• और उस नियमबद्ध योजना को हम व्याकरण कहते हैं।

दिए गए विकल्पों में से ‘अज्ञ' का विपरीतार्थक शब्द "विज्ञ" है।

Key Points

• विज्ञ का अर्थ - जाननेवाला, सम��दार और पढ़ा लिखा।
• अज्ञ का अर्थ - ज्ञानशून्य, मूर्ख।

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 - 

यदि वह परिश्रम करता तो सफल हो जाता।

• अर्थ के आधार पर यह वाक्य "संकेतवाचक" वाक्य होगा।

Key Points

• इसमें एक वाक्य दूसरे वाक्य की संभावना पर निर्भर कर रहा है।
• अतः संकेतवाचक वाक्य होगा।
• संकेतवाचक वाक्य - जिसमें एक वाक्य दूसरे वाक्य की संभावना पर निर्भर करता है।
• जैसे - डॉक्टर न आता तो वह मर जाता।

Additional Informationअर्थ के आधार पर 8 प्रकार के वाक्य होते हैं -

दिए गए विकल्पों में से 'जो कहा न गया हो' के लिए एक शब्द होगा- "अकथित"

Key Pointsअन्य विकल्प -

• जिसका वर्णन नहीं किया जा सके -  अवर्णनीय
• जिसका कथन न किया जा सके - अकथनीय
• जिसे वाणी व्यक्त न कर सके - अनिर्वचनीय

Additional Information

• जब किसी वाक्य में प्रयुक्त या स्वतन्त्र किसी वाक्यांश के लिए किसी एक शब्द का प्रयोग किया जाता है,
• जो उस वाक्यांश के अर्थ को पूरी तरह सिद्ध करता हो तो उसे वाक्यांश के लिए एक शब्द कहते हैं।

वाक्यांश के लिए एक शब्द के उदाहरण- 

• जिस पुस्तक में आठ अध्याय हो  - अष्टाध्यायी
• कम जानने वाला- अल्पज्ञ
• कुछ दिनों तक बने रहने वाला- टिकाऊ
• किसी पद का उम्मीदवार- प्रत्याशी
• दाव (जंगल) में लगने वाली आग- दावानल
• किसी काम में दखल देना- हस्तक्षेप
• आकाश में विचरण करने वाले जंतु - नभचर
• जहां सिक्कों की ढलाई होती है - टकसाल
• जो किनारे से सटे हुए हो - तटवर्ती
• जिसने इन्द्रियों को वश में कर लिया हो - जितेन्द्रिय

दिए गए विकल्पों में से "प्राण" शब्द बहुवचन रूप में प्रयुक्त होता है। 

• शेष विकल्प एकवचन शब्द है।
• "प्राण" शब्द हमेशा बहुवचन में प्रयोग होता है।

Key Points

कुछ शब्दों का प��रयोग हमेशा ही बहुवचन में किया जाता है-

• जैसे - दाम, दर्शन, आँसू, लोग, अक्षत, होश, समाचार, हस्ताक्षर, दर्शक, अश्रु, आशीर्वाद आदि।

कुछ शब्दों का प्रयोग हमेशा ही एकवचन में किया जाता है-

• जैसे - बारिश, पानी, दूध, घी, दही, आकाश, जनता आदि।

Additional Information

• संज्ञा के जिस रूप से किसी व्यक्ति वस्तु स्थान के एक या एक से अधिक होने का बोध हो उसे वचन कहते हैं।

हिन्दी में वचन दो प्रकार के होते हैं-

निम्नलिखित मुहावरों में से "दूध का जला छाछ भी फूँक फूँक कर पीता है" 

मुहावरे का अर्थ 'एक बार धोखा खाने पर सावधान हो जाना' है।

• वाक्य प्रयोग- पिछली बार एक दिन की गैरहाजिरी में राजू को दफ्तर से जवाब मिला था;
• इसलिए अब वह देरी से जाने से भी डरता है, क्योंकि 'दूध का जला छाछ भी फूँक-फूँक कर पीता है'।

Key Pointsअन्य विकल्प - 

Additional Informationकुछ मुहावरे - 

दिए गए विकल्पों में से 'गाँठ' का एक अर्थ है- "गिरह"

Key Points

• गाँठ के अन्य अनेकार्थी शब्द -  फंदा, गठरी, उलझन, मनमुटाव आदि।
• गंभीर का एक अर्थ "जटिल" होता है।
• गंभीर  के अन्य अनेकार्थी शब्द - गहरा, घना, भारी, चिंताजनक, शांत आदि।
• कील  का एक अर्थ "मेख" होता है।
• कील के अन्य अनेकार्थी शब्द - नाक का एक गहना, फोङा का अंकुर, किला, खंभा आदि।

Additional Information

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

अनेकार्थी शब्द -

दिए गए विकल्पों में से "उल्लास" शब्द “प्रगति” का पर्यायवाची नहीं है। 

Key Points

• अन्य विकल्प ( उत्कर्ष, अभ्युदय, उत्थान )  शब्द “प्रगति” का पर्यायवाची है।
• प्रगति के अन्य पर्यायवाच शब्द - समृद्धि , उन्नति , प्रशंसा , बढ़ती , उठान आदि।
• उल्लास के पर्यायवाची शब्द - हर्ष , सुख , आनंद , प्रसन्नता , मोद , प्रमोद आदि।

Additional Information

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

उदाहरण - 

• अतिथि- मेहमान ,पाहुन ,आगंतुक, अभ्यागत।
• आयुष्मान- चिरंजीव, दीर्घजीवी, शतायु, दीर्घायु।
• उत्पत्ति- उद्भव, जन्म, जनन, आविर्भाव ।
• औषधि- दवा, दवाई, भेषज।
• किनारा- तट, कूल, तीर, कगार, पुलिन।
• गुप्त- गूढ़, रहस्यपूर्ण, परोक्ष, छिपा।
• घी- हव्य, अमृतसार, क्षीरसार, आज्य।
• चर्म- खाल, चमड़ी, त्वचा, त्वक्।
• जहर- हलाहल, विष, गरल, कालकूट, गर।
• झूठ- मिथ्या, अनृत, मृषा, असत्य।
• तरुण- युवा,���वान, युवक।
• फूल- पुष्प, कुसुम,पुहुप, सुमन, प्रसून।

दिए गए विकल्पों में से 'चश्मा' शब्द "पुल्लिंग" है। 

Key Points

• 'चश्मा' शब्द निर्जीव पुल्लिंग शब्द है।
• 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।
• हिन्दी में दो लिंग होते हैं - (1) पुल्लिंग, (2) स्त्रीलिंग

Additional Informationलिंग के भेद - 

पुल्लिंग शब्द -

• सजीव - बकरा, घोड़ा, लड़का, आदमी, शेर, हाथी, भेड़िया, खटमल, बन्दर, कुत्ता, बालक आदि।
• निर्जीव -  रुमाल, कपड़ा, रक्त, रबर, शहद, सोना, वसंत, लगान, फल, धन, पत्थर, नशा आदि।

स्त्रीलिंग शब्द - 

• सजीव - माता, लड़की, भेद, गाय, भैंस, बकरी, लोमड़ी, बंदरिया, मछली, बुढिया, शेरनी आदि।
• निर्जीव - धोती, टोपी, सड़क, सजा, भीड़, छत, किताब, ईंट, ईर्ष्या, मंजिल, परत, झोंपड़ी आदि।

किसी पहले भेजे गये पत्र का उत्तर नहीं आने पर उस विषय में याद दिलाने के लिए लिखा जाने वाला "अनुस्मारक" पत्र कहलाता है।

Key Points

• जब किसी पत्र, ज्ञापन इत्यादि का उत्तर समय पर प्राप्त नहीं होता तो,
• याद दिलाने के लिए अनुस्मारक पत्र भेजा जाता है। इसे स्मरण पत्र भी कहते हैं।
• इसका प्रारूप औपचारिक पत्र की तरह ही होता है मगर आकार छोटा होता है।

Additional Information

दिए गए विकल्पों में से ‘अग्राह्य’ शब्द में "अ" उपसर्ग है। 

Key Points

• 'अ' उपसर्ग से बनने वाले अन्य शब्द - अछूता, अथाह, अटल आदि।
• 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 उदाहरण - 

दिए गए विकल्पों में से ‘पवित्र' का संधि विच्छेद है- "पो+इत्र"

Key Points

• पवित्र शब्द में अयादि संधि है।
• पो+इत्र = पवित्र  (ओ + इ = अव)

Additional Information

• दो वर्णों के मेल से होने वाले विकार को संधि कहते हैं।
• दो शब्दों के मेल से बने शब्द को पुनः अलग अलग करने को संधि विच्छेद कहते हैं।
• संधि के तीन प्रकार होते है- स्वर संधि, व्यंजन संधि और विसर्ग संधि।
• जब स्वर के साथ स्वर का मेल होता है तब जो परिवर्तन होता है वह स्वर संधि कहलाता है।

स्वर संधि के पांच प्रकार होते हैं-

दिए गए विकल्पों में से "गँवार" शब्द कि शुद्ध वर्तनी है। 

Key Pointsअन्य विकल्प - 

Additional Information

• भाषा के किसी शब्द को को लिखने में प्रयुक्त वर्णों के सही क्रम को वर्तनी कहते हैं।
• वर्तनी को अक्षरी या अँग्रेजी में ‘स्पेलिंग’ भी कहा जाता है।

शुद्ध अशुद्ध वर्तनी- 

दिए गए विकल्पों में से ‘सेवक' का पर्यायवाची है- "भृत्य"

• सेवक के अन्य पर्यायवाची शब्द - परिचारक, किंकर, अर्दली, अनुचर, आश्रित, गुलाम, नौकर, दास आदि।

Key Pointsअन्य विकल्प - 

• आर्त का पर्यायवाची शब्द -   दुःखी, पीड़ित, संतप्त, त्रस्त, दुःखित, परेशान, व्याकुल।
• विग्रह का पर्यायवाची शब्द - युद्ध, लड़ाई, समर, संग्राम, रण।
• खल का पर्यायवाची शब्द - दुष्ट, बदमाश, दुर्जन, गुंडा, विश्वासघाती,पापी, कमीना ।

Additional Information

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

कुछ पर्यायवाची शब्द - 

• अतिथि- मेहमान ,पाहुन ,आगंतुक, अभ्यागत।
• कंठ- गला, शिरोधरा, ग्रीवा, गर्दन।
• उपहास- परिहास, मजाक, खिल्ली।
• इज्जत-  मान, प्रतिष्ठा, आदर, आबरू।
• औषधि- दवा, दवाई, भेषज।
• कृतज्ञ- ऋणी, आभारी, अनुग्रहित, उपकृत ।
• गुप्त- गूढ़, रहस्यपूर्ण, परोक्ष, छिपा।
• घी- हव्य, अमृतसार, क्षीरसार, आज्य।
• चर्म- खाल, चमड़ी, त्वचा, त्वक्।
• छाछ- गोरस, मठा, दधि स्वेद, मट्ठा।
• जहर- हलाहल, विष, गरल, कालकूट, गर।
• तरुण- युवा,जवान, युवक।
• पथ- मग, मार्ग, राह, पंथ, रास्ता।

दिए गए विकल्पों में से रोमन भाषा की "अंग्रेजी" लिपि है।

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 लिखी जाती है।
• हर वर्ण का आकार समान होता है।
• ये उच्चारण के अनुरूप लिखी जाती हैं।

दिए गए विकल्पों में से "स्वागत"  में "स्व" उपसर्ग नहीं है।

• अन्य विकल्पों में ( स्वावलंबी, स्वतंत्र, स्वचालित ) स्व उपसर्ग  है।

Key Points

• सु + आगत = स्वागत  (उ + आ = व्) - 'यण स्वर संधि'
• स्वागत में उपसर्ग है -  ‘सु’
• स्वागत में मूल शब्द है - आगत
• सु उपसर्ग के अन्य शब्द - सुकृत, सुगम, सुलभ, सुदूर सुवास, सुजन इत्यादि।

Important Pointsहिंदी भाषा में तीन प्रकार के उपसर्ग प्रयोग किए जाते हैं- 

Additional Information

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

उदाहरण -

Given:

Product of zero = 5

Concept used: 

Product of zeroes = \(\dfrac{c}{a}\)

Calculation:

In the given equation,

a = 2 and c = k

⇒ \(\dfrac{c}{a}\) = 5

⇒ c = 5a

On putting the values,

⇒ k = 5 x 2

⇒ k = 10

∴ The value of k = 10.

Given:

The mean weight of a group of 5 girls is 47.

The individual weights (in kgs) of 4 of them are 42, 46, 53 and 40.

Concept used: 

Average = Sum of observation / Number of observations

Calculation:

Let, the age of 5^th girl = m

⇒ Sum of weights = 42 + 46 + 53 + 40 + m

⇒ 181 + m

Average = \(\dfrac{181 + m}{5}\) = 47

⇒ 181 + m = 5 x 47

⇒ m = 235 - 181

⇒ m = 54

∴ The weight of the 5^th girl is 54 kg.

Given:

Diameter = 14 cm

Thickness = 0.75 cm

Total plates = 20

Concept used: 

Surface area of cylinder = 2πr(r + h)

Calculation:

⇒ r = 7 cm

⇒ h = 0.75 x 20

⇒ h = 15 cm

⇒ Surface area of the cylinder = 2 x \(22\over 7\) x 7 x ( 7 + 15)

⇒ 44 x 22

⇒ 968 cm²

∴ The total surface area of the cylinder so formed is 968 cm²

Given: 

\(\frac{1}{{{{\left( {√ 2 } \right)}^{ - 3}}}},, \times ,,\frac{1}{{{{\left( {√ 5 } \right)}^{ - 3}}}}\)

Concept used: 

\(\dfrac{1}{m^{-n}}\) = mⁿ 

√m x √n = √(mn)

Calculation: 

⇒ \(\frac{1}{{{{\left( {√ 2 } \right)}^{ - 3}}}},, \times ,,\frac{1}{{{{\left( {√ 5 } \right)}^{ - 3}}}}\) 

= (√2 x √5)³ 

⇒ (√10)³ 

⇒ (10)^\(3\over2\)

⇒ (1000)^\(1\over2\)

∴ The simplifies form of \(\frac{1}{{{{\left( {√ 2 } \right)}^{ - 3}}}},, \times ,,\frac{1}{{{{\left( {√ 5 } \right)}^{ - 3}}}}\) is 1000^\(1\over2\)

Given:

∠AOD = x + 25 and ∠BOC = 4x - 11

Concept used: 

Vertically opposite angles are equal.

Calculation:

⇒ x + 25 = 4x - 11

⇒ 3x = 36

⇒ x = 12

⇒ ∠AOC + ∠AOD = 180°

⇒ ∠AOC + (12 + 25) = 180°

⇒ ∠AOC = 180 - 37

⇒ ∠AOC = 143°

∴ ∠AOC = 143°

Given:

There are two flower baskets A and B.

If 12 flowers are transferred from A to B, then the number of flowers in each basket is the same.

If 23 flowers are transferred from B to A, then the number of flowers in A is double the number of flowers in B.

Calculation:

According to the question,

A - 12 = B + 12

⇒ A - B = 24  → (1)

2(B - 23) = A + 23 

⇒ A - 2B = - 69  → (2)

From Eqn (1) and (2), we get

⇒ B = 93

Putting the value of B in Eqn (1), we have

⇒ A - 93 = 24

⇒ A = 24 + 93 = 117

Total number of flowers = A + B

⇒ 93 + 117 = 210

∴ The total number of flowers is 210.

Given:

81, 52, 29, 73, 48, 33, 31

Concept used: 

If n is odd, the median is the middle value in the set:

Median = \(\dfrac{n+1}{2}\) value

Calculation:

On arranging the given data in decreasing order,

⇒ 81, 73, 52, 48, 33, 31, 29

Total number of observation = 7

⇒ Median = \(\dfrac{7+1}{2}\)

⇒ Median = 4^th observation

⇒ Median = 48

∴ The median of the above data is 48.

Given:

Volume = 98 cm³

height = 7 cm

Concept used: 

Volume = \(1\over3\)πr²h

Area of base = π r²

Calculation: 

⇒ \( \dfrac{1}{3} \times \dfrac{22}{7} \) x r² x 7 = 98

⇒ 22 r² = 98 x 3

⇒ 11 r² = 49 x 3

⇒ 11 r² = 147

⇒ r² = \(147\over11\)

⇒ Area of base = \( \dfrac{22}{7} \times \dfrac{147}{11}\)

⇒ Area of base = 2 x 21

⇒ Area of base = 42 cm²

∴ The area of the base is 42 cm².

Shortcut Trick

Volume of the box = (Length − 2 × cut side) × (Breadth − 2 × cut side) × cut side

Volume = (42 − 12) × (28 − 12) × 6

Volume = 30 × 16 × 6

Volume = 2880 cm³

∴ The correct answer is 2880 cm³.

Alternate Method

Given:

Length of the metallic sheet = 42 cm

Breadth of the metallic sheet = 28 cm

Side of the square cut from each corner = 6 cm

Formula Used:

Volume of a cuboid = Length × Breadth × Height

Calculations:

When the four corner squares are cut off and the remaining flaps are folded up, they form the sides of the open box.

⇒ Length of the newly formed box = 42 − (2 × 6) = 42 − 12 = 30 cm

⇒ Breadth of the newly formed box = 28 − (2 × 6) = 28 − 12 = 16 cm

⇒ Height of the newly formed box (which is the side of the cut square) = 6 cm

Now, finding the volume of the box:

⇒ Volume = 30 × 16 × 6

⇒ Volume = 480 × 6

⇒ Volume = 2880 cm³

∴ The correct answer is 2880 cm³.

Additional Information

Volume of a Cuboid

The total space occupied by a rectangular 3D object is measured by multiplying its three dimensions: Volume = l × b × h.

Total Surface Area of an Open Box

Since an open box has no top lid, its surface area calculation involves only the bottom base area and the lateral walls: TSA = lb + 2h(l + b).

Given:

a_n = 2n - 5

Concept used: 

a_n = (n - 1)d

S_n = \(n\over2\)(a + a_n)

Calculation:

⇒ a₁ = 2(1) - 5

⇒ a = - 3

⇒ S_n = \(n\over2\)(-3 + 2n - 5)

⇒ S_n = n(n - 4)

∴ The Sum of 'n' terms of an A.P, whose nth term is given by 2n - 5, is n(n - 4).

Given:

Two dice are thrown simultaneously

Concept used: 

Probability = Number of favorable outcomes / Number of possible outcomes

Calculation:

Number of favourable outcome on 1 dice = 5

Number of possible outcome on 1 dice = 6

⇒ P(number other than 2) = \( \dfrac{5}{6} \times \dfrac{5}{6} \)

⇒ \( \dfrac{25}{36} \)

∴ The required probability is \(25\over36\)

Given:

\(\dfrac{{1 - {{\sin }^2}45}}{{1 + {{\sin }^2}45}}\)

Concept used: 

sin 45 = \(\dfrac{1}{\sqrt2}\)

Calculation:

⇒ \(\dfrac{{1 - {{\sin }^2}45}}{{1 + {{\sin }^2}45}}\) 

= \(\dfrac{{1 - {{ (\frac{1}{\sqrt{2}} })^2}}}{{1 + {{( \frac{1}{ \sqrt{2} } })^2}}}\) = \(1\over3\) 

Now, tan² 30° & cot² 60° = \(1\over3\)

∴  \(\dfrac{{1 - {{\sin }^2}45}}{{1 + {{\sin }^2}45}}\) = cot²60°.

Given:

Quadratic equations

Concept used: 

D = b² - 4ac

If D > 0, the roots will be real and distinct.

If D > 0, D is a perfect square 

If D < 0, the roots will be complex and distinct

If D = 0, the roots will be real and equal.

Calculation:

Option (1):

⇒ D = 25 - 4(2)(-1)

⇒ D = 25 + 8 = 33

⇒ D > 0 but not a perfect square 

Option (2):

⇒ D = 64 - 4(6)

⇒ D = 64 - 24 = 40

⇒ D > 0 but not a perfect square 

Option (3):

⇒ D = 25 - 4(4)(2)

⇒ D = 25 - 32 = - 7

⇒ D < 0

Option (4):

⇒ D = 36 - 4(5)

⇒ D = 36 - 20 = 16

⇒ D > 0 and a  perfect square 

∴  has real and rational roots.

Given:

PQ = 18 cm

QR = 9 cm

Calculation:

According to the rhombus figure,

LN = NM = MQ = QL = a

⇒ In ΔPLN and ΔPQR

⇒ \(\dfrac{PL}{PQ}=\dfrac{LN}{QR}\)

\(\dfrac{18-a}{18}=\dfrac{a}{9}\)

18a = 162 - 9a 

⇒ 27a = 162 

⇒ a = 6 cm

Perimeter of Rhombus = 4a 

⇒ 4 × 6 = 24 cm

Given:

2, 3, 3, 4, 4, 4, 5, 5, 5, 5

Concept used: 

Average = Sum of observation / Number of observations

Probability = Number of favorable outcomes / Number of possible outcomes

Calculation:

⇒ Number of observations = 10

⇒ Sum of observations = 2 + 3 + 3 + 4 + 4 + 4 + 5 + 5 + 5 + 5

⇒ 40

⇒ Average = \(\dfrac{40}{10}\) = 4

⇒ Number of favorable outcomes = 3

⇒ Number of possible outcomes = 10

⇒ Probability(getting 4) = \(3\over10\)

∴ The probability, that the number selected is their average, is \(3\over10\)

Given:

 \(\frac{{{\rm{a}},{\rm{ + }},{\rm{b}}}}{2}\) = 4 and ab = 7

Concept used: 

(a - b)² = (a + b)² - 4ab

Calculation:

⇒ ab = 7

⇒ 4ab = 28

⇒ a + b = 8

⇒ (a + b)² = 64

(a - b)2 = (a + b)2 - 4ab

⇒ (a - b)² = 64 - 28

⇒ (a - b)² = 36

⇒ (a - b) = ±6

∴ The value of (a - b) = ± 6

Given:

r + R = 11 cm

Sum of area = 73π cm²

Concept used:  

Area of circle = π r²

Calculation:

Let, the radius of two circles be r and R.

⇒ r + R = 11 cm    

⇒ r = 11 - R       → (1)

⇒ π r² + π R² = 73 π 

⇒ r² + R² = 73

On putting the value of r from equation (1) in equation (2),

⇒ (11 - R)² + R² = 73

⇒ 121 + 2R² - 22R = 73

⇒ 2R² - 22R + 48 = 0

⇒ R² - 11R + 24 = 0

⇒ R² - 3R - 8R + 24 = 0

⇒ R(R - 3) - 8(R - 3) = 0

⇒ (R - 3)(R - 8) = 0

⇒ R = 3 or 8

The largest radius = 8 cm

∴ The radius of the larger circle is 8 cm

Given:

x² + kx + 9 = 0

Concept used: 

The equation has real roots if,

D ≥ 0

D = b² - 4ac

Calculation: 

⇒ D = k² - 4(9)

⇒ D = k² - 36 ≥  0

⇒ k² ≥  36

⇒ k ≥ 6

∴ The least possible value of k is 6.

Given:

Sum = - 6

Product = 24

Calculation:

Let, the 3 numbers be (m - d), m, and (m + d)

⇒ m - d + m + m + d = -6

⇒ 3m = - 6

⇒ m = - 2

⇒ (m - d)(m)(m + d) = 24

⇒ (-2 - d)(-2)(-2 + d) = 24

⇒ (4 + 2d)(d - 2) = 24

⇒ 4d - 8 + 2d² - 4d = 24

⇒ d² = 16

⇒ d = ± 4

On taking d = 4 (d = +ve)

⇒ m - d = - 2 - 4 = - 6

⇒ m = - 2

⇒ m + d = -2 + 4 = 2

The number is -6, -2, and 2.

∴ The smallest number is -6.

Given:

4x⁴ - 6kx³ + 7x² + 3x + 2k

Calculation:

⇒ x - 1 = 0

⇒ x = 1

And Remainder = 3k

F(x) = 4x4 - 6kx3 + 7x2 + 3x + 2k - Remainder = 0

F(1) = 4(1)⁴ - 6k(1)³ + 7(1)² + 3(1) + 2k - 3k = 0

⇒ 4 - 6k + 7 + 3 + 2k - 3k= 0

⇒ 14 - 7k = 0

⇒ k = 2

∴ The value of k = 2.

Given:

d = 15°

Concept used:  

Sum of angles of triangles = 180° 

Calculation:

Let, the three angles = m, (m + d) and (m + 2d)

⇒ m + m + 15 + m + 30 = 180

⇒ 3m = 180 - 45

⇒ 3m = 135

⇒ m = 45

∴ The smallest angle is of 45°.

Given:

\(\dfrac{{{{\left( {0.05} \right)}^0} - {{\left( {0.2} \right)}^{ - 1}}}}{{{{\left( {\dfrac{5}{8}} \right)}^{ - 1}}{{\left( {\dfrac{5}{2}} \right)}^3} + {{\left( {\dfrac{{ - 1}}{3}} \right)}^{ - 1}}{{\left( {\dfrac{{ - 1}}{3}} \right)}^{ - 1}}}}\)

Concept used: 

m⁰ = 1

m^-1 = \(1\over m\)

Calculation:

⇒ \(\dfrac{{{{\left( {0.05} \right)}^0} - {{\left( {0.2} \right)}^{ - 1}}}}{{{{\left( {\dfrac{5}{8}} \right)}^{ - 1}}{{\left( {\dfrac{5}{2}} \right)}^3} + {{\left( {\dfrac{{ - 1}}{3}} \right)}^{ - 1}}{{\left( {\dfrac{{ - 1}}{3}} \right)}^{ - 1}}}}\) 

⇒ \(\dfrac{{1 - {{\left( {2\over10} \right)}^{ - 1}}}}{{{{\left( {\dfrac{8}{5}} \right)}}{{\left( {\dfrac{5}{2}} \right)}^3} + {{\left(-3\right)}}{\left(-3\right)}}}\)

⇒ \(\dfrac{{1 - {{\left( {10\over2} \right)}}}}{{{{\left( {\dfrac{8}{5}} \right)}}{{\left( {\dfrac{125}{8}} \right)}} + 9}}\)

⇒ \(\dfrac{{1 - 5}}{{{25} + 9}}\)

⇒ \(\dfrac{-4}{34}\) = \(-2\over 17\)

Shortcut Trick

Volume of hollow cylinder = π × (R² − r²) × h

Inner radius (r) = 7 cm, Outer radius (R) = 8 cm, height (h) = 7 cm

Volume = (22/7) × (8² − 7²) × 7 = 22 × (64 − 49) = 22 × 15 = 330 cm³

Weight = Volume × Density = 330 × 7.8 = 2574 gm = 2.574 kg

∴ The correct answer is 2.574 kg.

Alternate Method

Given:

Inner diameter = 14 cm ⇒ Inner radius (r) = 7 cm

Outer diameter = 16 cm ⇒ Outer radius (R) = 8 cm

Length (h) = 7 cm

Density = 7.8 gm/cm³

Formula Used:

Volume of material = π × (R² − r²) × h

Weight = Volume × Density

Calculations:

⇒ Volume = (22/7) × (8² − 7²) × 7

⇒ Volume = 22 × (64 − 49)

⇒ Volume = 22 × 15 = 330 cm³

⇒ Weight in gm = 330 × 7.8

⇒ Weight in gm = 2574 gm

⇒ Weight in kg = 2574 / 1000 = 2.574 kg

∴ The correct answer is 2.574 kg.

Additional Information

Hollow Cylinder Surface Area

Total Surface Area = 2πR h + 2πr h + 2π(R² − r²). This includes inner, outer, and base areas.

Density Conversion

1 gm/cm³ = 1000 kg/m³. To convert grams to kilograms, divide the value by 1000.

Volume of Solid Cylinder

The volume of a solid cylinder is given by πr²h, where r is the radius and h is the height.

Given:

\({\left( {\frac{{2\cos 70}}{{\sin ,20}}} \right)^2}\)

Concept used: 

sinθ = cos(90 - θ)

Calculation: 

\({\left( {\frac{{2\cos 70}}{{\sin ,20}}} \right)^2}\)

sinθ = cos (90 - θ)

⇒ \({\left( {\frac{{2\cos 70}}{{\cos(90-,20)}}} \right)^2}\)

⇒ \({\left( {\frac{{2\cos 70}}{{\cos 70}}} \right)^2}\) = 2² = 4

∴ \({\left( {\frac{{2\cos 70}}{{\sin ,20}}} \right)^2}\) = 4.

Given:

30 residents

Concept used: 

Probability = Number of favorable outcomes / Number of possible outcomes

Calculation:

⇒ Number of possible outcomes = 30

⇒ Number of favorable outcomes = 8 + 6

⇒ 14

⇒ Probability = \(14\over30\)

⇒ \(7\over15\)

∴ The probability that the chosen resident will be a student is \(7\over15\)

The correct answer is option 1 i.e. 'Irregardless'.

Key Points

• The error lies in 'irregardless'. There is no such word.
• With the word 'regard', only suffix is used.
• The correct word is 'regardless'(adverb) which means despite; without being affected by something.
• Ex. ​The man didn't deserve to be punished, regardless of his mischievous acts.
• Thus, the correct answer is Option 1.

The correct sentence is: Regardless of what you say, you will still be suspected.

Additional Information

• The prefix 'ir' when added to a word gives a word which is opposite in meaning to the root word.
• Ex. 'Responsible' means showing a sense of responsibility.

                           'Irresponsible' means not showing or lacking a sense of responsibility.

• The suffix 'less' means without.
• Ex. 'Doubtless' means without any doubt.

The correct answer is option 3 i.e. 'Whenever'.

Key Points

• The most suitable word to be filled in the blank is 'whenever'.
• 'Whenever' means **at whatever time; on whatever occasion (emphasizing a lack of restriction).**​
• Ex. You can ask for help whenever you need it.
• The sentence expresses that the person asked the other person to inform him at whatever time he is ready emphasizing a lack of restriction.

The correct sentence is: Whenever you are ready, please inform me over the phone.

Additional Information

• Yet means until the present or specified time. 
• Ex. I haven't seen the movie yet.
• Why is used to ask the answer of something. 
• Ex. Why didn't you study for the exams?
• Whether is used to express a doubt or choice between the alternatives.
• Ex. I will tell you whether I will go to the party or not.

The correct answer is option 2 i.e. A room has been reserved for you at the Grand Hotel.

Key Points

• The given Active voice is in Present Perfect Tense.
• ​The subject will become the object and the object will become the subject.
• While changing it into Passive voice, its structure will be as follows: Subj. + has/have + been + Verb₃ + object
• ​Ex. Active: The painter has painted the door.

​                           Passive: The door has been painted by the painter.

​The correct Passive voice is: A room has been reserved for you at the Grand Hotel.

Additional Information

• In Active voice, the emphasis is on the subject.
• In Passive voice, the emphasis is on the object or the action.
• While changing one voice into the other, we do not change the tense of the sentence.
• The subject and the object are interchanged.
• The pronouns are changed according to the rules.

The correct answer is option 2 i.e. It is a very hot weather.

Key Points

• It is an exclamatory sentence.
• While changing the exclamatory sentence into assertive form, the tense of the sentence will remain same.
• The given sentence is in the Present Tense, so the resultant assertive sentence will also be in the Present Tense.
• Structure of an exclamatory sentence: How + the adjective + subject + linking verb + !
• Example: How beautiful the dress is!
• ​Structure of an assertive sentence: Subject + linking verb + adjective (subject complement) + modifiers (optional).
• Example: The dress is very beautiful.

Therefore, the correct assertive sentence is: It is a very hot weather.

Additional Information

• Exclamatory sentences express sudden or strong emotions and feelings.
• These sentences end with an exclamation mark(!).

The correct answer is option 1 i.e. 're'.

Key Points

• The correct prefix that can be used with 'usable' is "re".
• 'Reusable' means that can be used again.
• All other prefix can not be used with 'usable'.

The correct sentence is: This tea cup is reusable as it is made of porcelain.

Additional Information

• Prefix is a letter or a word that is used before another word to change its meaning.
• Ex. 'Regular' means recurring at regular intervals or arranged in a definite pattern.

​                           'Irregular' means uneven or unbalanced in shape and arrangement.

• 'pre-' means means prior to something or before something.
• Ex. vent - prevent, fix - prefix, etc.
• ​'in-' means in, on or not. 
• Ex. flux - influx, decisive - indecisive, etc.
• 'un-' means not.
• Ex. occupied - unoccupied, certain - uncertain, etc.