The correct answer is a Negative charge.

Key Points

• When a plastic straw is rubbed with polythene, the kind of charge that the plastic straw would carry is a negative charge.
• In this question, we can see the concept of electric charge.
• It allows electrons and protons to stick together to form atoms.
• The stuff that has the same charge drives each other further and this is called the law of charges.

Additional Information

• There are two types of charges:
• Negative charge.
• Positive charge
• Opposite charges i.e positive charge and negative charge attract each other.
• The same charges i.e positive and positive charge and negative and negative charge repel each other.

The correct answer is During exhalation, ribs move outwards.

Key Points 

• During exhalation, ribs move outwards, this is an INCORRECT statement.
• The following table shows the distinction between inhalation and exhalation:

The correct answer is Polyester + Wool

Key Points 

• Poly wool is a mixture of two types of fibres which are Polyester + wool.
• Polyester is a synthetic fibre and wool is a natural fibre
• Polywool fabric is warm, body-friendly & colour dyes well.
• Due to the growing demand for economical & durable fabrics in textiles, a blend of poly & wool called polywool is a suitable fabric to cater the day to day needs of buyers.

Additional Information

• Characteristics of Polywool are:
• It is a fine, soft and luxurious fabric with good drape quality.
• Poly Wool is used in duster clothes, bedspreads and dress material for dolls.
• Polywool has excellent resistance and absorption properties towards heat, thermal and Noise
• It can also be used as an insulation material

The correct answer is Arteries carry oxygenated blood from the heart to different parts of the body.

Key Points 

• The walls of the arteries are thick and elastic because arteries carry oxygenated blood from the heart to different parts of the body.
• The blood emerges from the heart under very high pressure and in order to withstand this pressure the wall of arteries is thick and elastic.
• Veins are responsible for carrying deoxygenated blood from various parts of the body to our hearts.
• The blood emerges from various parts of the body under very low pressure, hence the walls of veins are thin.
• Certain veins like those which are present in the lower limbs or organs situated far away from the heart have valves present in them so that the blood does not flow back into the organ while moving against gravity.

The correct answer is Satpura National Park

Key Points 

• Pachhmarhi biosphere consists of one national park named Satpura National park.
• National Park is an area protected and established by the Government to conserve the entire set of the ecosystem i.e landscape, flora, fauna, etc of that region.
• Panchmarhi biosphere is located in the Hoshangabad district of Madya Pradesh.
• Panchmarhi is called the Queen of Satpura or Satpura ki Rani and it has an old association with the epic 'Mahabharata".
• In the year 2009, Panchmarhi was declared as part of the UNESCO (United Nations Educational, Scientific and Cultural Organization) Biosere Reserve because it is home to various species of flora and fauna.
• The word Panchmarhi can be divided into 'Panch" (Five) and Marhi (Caves) which were built by the Pandava brothers of Mahabharata during their thirteen years of exile.

Additional Information

The correct answer is carbon dioxide.

Key Points 

• A gas X turns lime water milky. This gas is a raw material for the process of photosynthesis. It is called Carbon dioxide.
• The complete chemical reaction that takes place is Ca(OH)2+CO2-> CaCO3(+)+H2O.
• The insoluble calcium carbonate is formed due to the passage of carbon dioxide gas.
• The lime water (calcium hydroxide solution) when reacts with carbon dioxide a white precipitate of calcium carbonate is formed and it turns lime water milky or cloudy white.

Additional Information 

• Calcium hydroxide is sparingly soluble in water producing an alkaline solution known as limewater.
• When carbon dioxide gas is passed through or over limewater, it turns milky due to the formation of calcium carbonate.

The correct answer is basic in nature.

Key Points 

• An aqueous solution of Sodium hydrogen carbonate is basic in nature.
• The pH scale depicts whether the solution is acidic or basic in nature.
• It is a 14-point scale where points 0 to 7 show if the solution is acidic, 7 shows neutral, and 7 to 14 shows if the solution is basic.
• The pH scale was invented by Danish chemist S. P. L. Sorenson in the year 1909.
• The pH scale is significant for measurement in all fields such as medicine, forestry, food science, etc.
• The Buffer solution refers to the solution whose pH value does not change when a small amount of an acid or base is added to it.
• The most common method used to determine whether the solution is acidic or basic is the litmus test.
• If the solution is acidic then it will turn blue litmus paper into red color and if the solution is basic then it will turn red litmus paper into blue color.
• An aqueous solution of Sodium Hydrogen Carbonate is basic in nature, having a pH value between 8 to 9.

Image of pH scale:

The correct answer is One billionth of a second.

Key Points 

• A nanosecond is one billionth of a second
• ​It is equal to 1/1000000000 of a second or 10^-9s.
• The time units of this granularity are commonly found in telecommunications, pulsed lasers, and related aspects of electronics.
• A nanosecond is sometimes written in short form as nsec.
• A nanosecond is called by some scientists as Lightfoot.

The correct answer is Plane Mirror.

Key Points

• ​When a person stands in front of a mirror, an erect image where ‘right appears left and left appears right’ is obtained. This mirror is an example of a Plane Mirror.
• The plane mirror refers to the mirror which is having a flat reflective surface.
• The image formed by a plane mirror is virtual and erect, behind the mirror and the size of the image is equal to the size of the object.
• When a person stands in front of a mirror, an erect image where ‘right appears left and left appears right’ is obtained and this is called a Laterally inverted image.

Image of the plane mirror:

Additional Information 

Convex Mirror:

• If the outer surface of the spherical mirror is the reflecting surface then it is called a convex mirror. It is also called the diverging mirror.
• It reflects the light outwards.
• The nature of the image formed by a convex mirror does not depend on the distance of the object from the mirror.
• These images are always virtual, smaller than the object, and situated behind the mirror.

Concave Mirror:

• If the inner surface of the spherical mirror is the reflecting surface, then it is called a concave mirror. It is also called a focusing mirror or converging mirror.
• The size of the image produced by these mirrors can be larger or smaller than the object, depending upon the distance of the object from the mirror.
• The concave mirror can form both real as well as virtual images of any object.
• The concave mirror has a negative focal length.

The correct answer is Egg ­-> Caterpillar­ -> Pupa­ -> Adult.

Key Points 

• The life cycle of a silkworm is Egg ­-> Caterpillar­ -> Pupa­ -> Adult.
• Silkworm arises after the eggs crack and they are hairy.
• They feed on mulberry leaves and consume a large amount of these leaves for around thirty days.
• The Silkworms spin a cocoon around themselves which protects them.
• This cocoon is made up of a single thread of soil.
• Cocoon appears as a small cotton ball.
• The pupa is a motionless stage.
• The last stage is when the Pupa changes into an adult moth.

Additional Information

• The egg is the first and primary stage of the life cycle of a Silkworm.
• The egg is laid by a  female moth and the egg is the size of small dots.
• More than 350 eggs are laid by a female moth at a time.
• The eggs hatch in the springtime due to the warmth in the air.
• This procedure takes place once a year.
• The study of the cultivation of silkworms to produce silk is called Sericulture.
• Silk was invented around 3500 BC in China.

The correct answer is Light-colored clothes as they absorb less heat.

Key Points 

• In summer, people prefer wearing light-coloured clothes as they absorb less heat and keeps their bodies cool.
• Cotton is a good absorber of water which helps in absorbing sweat and brings it in contact with the surrounding atmosphere for easy evaporation hence it is recommended to wear cotton clothes at the time of the summer season.
• Summer is the hottest season of the year and in order to avoid dehydration and health problems because of the excessively warm atmosphere the people prefer wearing light-colored clothes.
• In winter, people prefer wearing dark-coloured clothes as they absorb more heat and keeps their bodies warm.

The correct answer is the Chemical effect of electric current.

Key Points 

• When current is passed through a conducting solution, bubbles of gas are formed on the electrodes. This shows the Chemical effect of electric current.
• This experiment was shown by British Chemist William Nicholson in the year 1800.
• The chemical reaction takes place when an electric current is passed through a conducting solution and this results in the formation of bubbles of gas on the electrodes.
• Deposits of metal may be seen on electrodes and sometimes colour changes in solutions may occur.
• This reaction totally depends upon what solution and electrodes are used and also some chemical effects of the electric current may occur.

The correct answer is Lateral Inversion.

Key Points 

• ​When we stand in front of our dressing table combing our hair, our left hand appears to be on the right and right appears to be on the left in the image. This phenomenon is known as Lateral Inversion
• The convex mirror is also called a diverging mirror.
• It reflects the light outwards.
• The focal length of the convex mirror is positive.
• A spherical mirror has a focal length of + 25 cm.
• The concave mirror and have a negative focal length.
• The plane mirror refers to the mirror which is having a flat reflective surface.
• The image formed by a plane mirror is virtual and erect, behind the mirror and the size of the image is equal to the size of the object.

The correct answer is Bile juice.

Key Points 

• Major part of  fat digestion is done with the help of Bile Juice.
• Bile juice is a digestive fluid that is produced by the liver.
• Gallbladder stores bile juice in the body.
• The major function of bile juice is to change fats in food into fatty acids, which are assimilated in the gut.
• It is a bitter-tasting dark green to the yellowish-brown fluid that helps in the digestion of lipids in the human body.
• Bile Juice is important for the absorption of fat, vitamins, iron, and calcium.

Additional Information

• Gastric Juice is a mixture of hydrochloric acid (HCL), lipase, and pepsin.
• The major duty of Gastric Juice is to inactive swallowed microorganisms, thereby stopping infectious agents from reaching the intestine.
• Gastric Juice is a digestive fluid that is produced within the lining of the stomach.
• Gastrin regulates the production of Gastric Juice.
• It is a peptide hormone and it is produced by G cells in the pyloric antrum of the stomach.
• Hydrochloric Acid (HCL) is also known as muriatic acid, the spirit of salt, hydronium chloride, and chlorhydric acid.
• The digestive juice in our stomach consists mainly of hydrochloric acid.
• It has no color and it is a transparent liquid that fumes in the air if concentrated and it has a very strong smell.
• It is acidic in nature and forms an acidic salt.
• It is used for refining and pickling of steel, production of inorganic compounds, pH (Hydrogen potentials) control, and neutralization, Regeneration of ion exchangers, and other laboratory use.
• Pepsin enzyme aids in converting proteins into polypeptides.
• Pepsinogen is converted to pepsin through hydrochloric acid.
• It helps in the digestion of proteins into peptones.
• Pepsin was recognized as the first enzyme to be discovered in the 18^th century and was named by T. Schwann in the year 1825.

The correct answer is Loamy soil.

Key Points

• The best soil for growing plants is Loamy soil.
• The best topsoil for growing plants is loam.
• Loamy soil is a mixture of sand, clay and another type of soil particle known as silt.
• Silt occurs as a deposit in riverbeds.
• The size of the silt particles is between those of sand and clay.
• The loamy soil also has humus in it.
• It has the right water holding capacity for the growth of plants.

Additional Information

• Clayey soil:
• The proportion of fine particles is relatively higher, then it is called clayey soil.
• Clayey soils have less air.
• Clayey soil is used to make pots, toys and statues.
• Sandy soil:
• If soil contains a greater proportion of big particles it is called sandy soil.
• This kind of soil has a low nutrient level.
• The water holding capacity of this soil is low.
• Silty soil:
• Filtration of water can be a problem in this kind of soil.
• It has a higher proclivity for forming a crust.
• It has the potential to become compact and firm.

The correct answer is Haemoglobin.

Key Points

• Haemoglobin -
• ​It is a metal protein that makes red blood cells,
• Which works to carry oxygenated blood inside the body from lungs and gills,
• It plays an important role in carrying out all the processes of the body smoothly.

Additional Information

• ​Red blood cells (RBC)-
• They are formed in the bone marrow but in the embryonic stage it is formed in the liver.
• Anthocyanin -
• ​It is colored water-soluble pigments.
• It is belonging to the phenolic group.
• It is responsible for the colors, red, purple, and blue, are in fruits and vegetables.
• Berries, currants, grapes, and some tropical fruits have high anthocyanins content.
• Chlorophyll -
• ​It is a proteinaceous complex chemical compound.
• This pigment is the reason for the green color of the leaves.
• It is the main pigment of photosynthesis.
• It is also called photosynthetic pigment.
• Plasma -
• ​It is a fluid present in the blood.
• It is yellow in colour.
• With its help, cells and proteins carry blood to different parts of the body.
• Its quantity in the body ranges from 52 to 62 percent.
• Whereas red blood cells range from 38 to 48 percent.

The correct answer is Light wave.

Key Points

• The wave of  light is a transverse wave.
• ​The components of a light wave vibrate perpendicular to its direction of propagation.
• Light waves do not require any medium for transmission.
• Propagation of sound waves, sea waves and seismic waves requires a medium.

Additional Information

• Longitudinal Waves -
• These are those waves in which the displacement of the particles of the medium is in the same direction as or opposite to the direction of wave motion.
• These are also called "L waves".
• The primary waves responsible for earthquakes are also longitudinal.
• Sound waves are also longitudinal in nature.
• Transverse Wave -
• These are the waves in which the speed of vibration of the particles is perpendicular to the speed of propagation of the wave.

The correct answer is Binary fission.

Key Points

• Amoeba reproduces asexually through binary fission.
• Binary Fission -
• The division of a cell into two parts to form two new cells is called binary fission.
• Asexual reproduction is found in amoeba and yeast.

Additional Information

• ​Budding -
• ​In the cells of the outer surface of the body of an organism, a protrusion is formed by mitosis, which is called a bud.
• The method of asexual reproduction by bud formation is called budding.
• The bud develops into a complete organism.
• Spore formation -
• ​This process takes place in plants.
• In spore formation, the parent plant produces hundreds of reproductive units called 'spores' in its spore case.
• When this spore sac of plants bursts, these spores are scattered on the wind, ground, food, or soil.
• This is where they grow and give birth to new plants.
• Multiple fission -
• ​When a cell gives rise to many daughter cells, the process is called multiple fission.

The correct answer is Before flowering & seed formation .

Key Points

• Weeding is the process of removing unwanted plants from an area of land.
• It is best to remove before flowering and seed formation.
• They grow alongside the main crops and compete with the main crop for nutrients, sunlight, fertiliser, space and water.

Additional Information

• Weed -
• These are unwanted plants that grow in someplace without being sown.
• Their presence is more harmful than beneficial to the farmer.
• Motha, Savari, Agia grass and Doob etc. come under this category.

The correct answer is Option4

Key Points

• The heat generated when a current flows through a wire depends on the following factors -
• The length of the wire depends on the density, nature of the material, the amount of current flowing and the duration of the current flowing.

Additional Information

• ​The amount of heat (h) produced in the wire is directly proportional to the square of current (I) passing through the wire, (h ∝ I²).
• The heat generated in a conductor depends on its resistance.
• The resistance of the wire further depends on the length and thickness of the wire.
• The amount of heat (h) produced in the wire is directly proportional to the resistance (R) of the wire, (h ∝ R).

The correct answer is Carbon dioxide.

Key Points

• **Stomata -**​ 
• It is a pore found in the epidermis of leaves, stems and all other parts of the plant found above the ground.
• Through which plants take up carbon dioxide (CO₂) and release oxygen (O₂).​

Additional Information

• Following are the main functions of stomata-
• In exchange for gases
• It transports gases such as oxygen (O2), carbon dioxide (CO2), or water vapor (H2O gas) between the inner and outer surfaces of plant tissues.
• Removal of Water -
• Stomata also participates in the elimination of excess water in plant tissues,
• Thus it maintains the water balance of the plants.

The correct answer is Gets heated quickly and melts.

Key Points

• Fuse -
• It is used for the protection of electrical circuits.
• The melting point of the fuse wire material is very low.
• When too much current flows in the circuit, the fuse wire gets heated and melts.
• As a result of which the circuit breaks and the current stops flowing in it.
• It works on the principle of the heating effect of electricity.

Additional Information

• ​Fuse wire -
• It is an alloy made by mixing metals called tin and lead.
• In sometimes a metal called cadmium is also added.
• The melting point of fuse wire is low.
• It remains closed in a vessel made of porcelain which is called Kitkat.

The correct answer is Gravitational Force.

Key Points

• Gravity, also called gravitation, in mechanics, is the universal force of attraction acting between all matter.
• On Earth all bodies have a weight, or downward force of gravity, proportional to their mass, which Earth’s mass exerts on them. Gravity is measured by the acceleration that it gives to freely falling objects.

Additional Information

• The electrostatic force is an attractive as well as repulsive force caused by the electric charge particles. It is also known as Columb's force.
• The magnetic force is a consequence of the electromagnetic force, one of the four fundamental forces of nature, and is caused by the motion of charges. Two objects containing charge with the same direction of motion have a magnetic attraction force between them.
• Muscular force is a force produced by muscle action and is a contact force because there is contact between the surfaces.

The correct answer is Coal tar.

Key Points

• Coal tar -
• It is derived from coal.
• It is a byproduct of the production of coke,
• It is a solid fuel that contains mostly carbon, and coal gas.
• It is used primarily for the production of refined chemicals and coal-tar products, such as creosote and coal-tar pitch.
• It is used to treat various skin conditions, such as eczema, psoriasis, and dandruff.

Additional Information

• Charcoal -
• It is a blackish-brown, porous, solid substance,
• Which is made by heating wood, bone, etc. in the absence of
• oxygen and extracting water and other volatile substances from it.
• ​This process is called "Pyrolysis".
• Charcoal has a high carbon content (about 80%).
• It is made by heating wood to 400 °C to 700 °C in the absence of air.
• Uses of charcoal -
• As a fuel in metallurgy,
• As an industrial fuel,
• As cooking fuel,
• For making gunpowder,
• For purification and filtration,
• Used for art, medicine, etc.
• Coke -
• It is a solid fuel prepared from coal.
• It is low ash, low sulfur fuel. ,

The correct answer is Water.

Key Points

• Bawri (water temple steps or step well) -
• These are social wells, which were mainly used as a source of drinking water.
• Most of these are very old and many were built by nomads.
• Water remains in them for a long time. Because the rate of evaporation is very less.

Additional Information

• ​This is a structure that is found only in India.
• It has been quite popular in the dry regions of India.
• It is used for rainwater harvesting and continuous availability of drinking water.
• The idea of making such wells came because of the problem of drought.
• Their names are different in different regions like Vav, Vavdi, Bawri, Baoli, and Bawdi.

संस्कृत भाषा के ऐसे शब्द जिनका हिन्दी भाषा में प्रयोग करने पर रूप बदल जाता है, वे "तद्भव शब्द" कहलाते हैं।

Key Points

तद्भव शब्द-

• दुग्ध —-> दूध
• अग्नि —-> आग
• कार्य —> काम
• कर्पूर —> कपूर
• हस्त —-> हाथ

Additional Information

दिए गए विकल्पों में से  शुद्ध वर्तनी "सुराख " की है।

Key Pointsअन्य विकल्प -

Additional Information

वर्तनी -

• शब्दों के ठीक-ठीक लिखने की ढंग को वर्तनी कहा जाता है।
• हिंदी में इसे अक्षरी भी कहा जाता है।
• उर्दू में इसे हिज्जे और अंग्रेजी में स्पेलिंग कहा जाता है।

शब्दों की शुद्ध अशुद्ध वर्तनी के कुछ उदाहरण -

दिए गए विकल्पों में से 'प्रभा' का पर्यायवाची है- "दामिनी"

• प्रभा के अन्य पर्यायवाची शब्द - रश्मि, दीप्ति, मरीचि, किरण, ज्योति।

Key Pointsअन्य विकल्प -

• कांता के पर्यायवाची शब्द - सुंदरी, औरत, वनिता, स्त्री, अबला, नारी, महिला, रमणी, कामिनी।
• कृश का पर्यायवाची शब्द - दुबला, क्षीणकाय, कमजोर, दुर्बल, कृशकाय।
• वल्लभा  के पर्यायवाची शब्द - पत्नी, संगिनी, प्रियतमा, बीवी,जोरू,जीवनसंगिनी,प्राणप्रिया।

Additional Information

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

कुछ पर्यायवाची शब्द -

• अधर्म- पाप ,अनाचार, अनीत, अन्याय, अपकर्म, जुल्म।
• कर्ण- सूर्यपुत्र, राधेय, कौन्तेय, पार्थ, अंगराज, सूतपुत्र।
• खेल- क्रीड़ा, केलि, तमाशा, करतब।
• गन्ना- ईक्षु, ऊख, ईख, पौंड़ा।
• घी- हव्य, अमृतसार, क्षीरसार, आज्य।
• चर्म- खाल, चमड़ी, त्वचा, त्वक्।
• छाछ- गोरस, मठा, दधि स्वेद, मट्ठा।
• जहर- हलाहल, विष, गरल, कालकूट, गर।
• झूठ- मिथ्या, अनृत, मृषा, असत्य।
• डरावना- भयंकर, भीषण, करालै।
• तरुण- युवा,जवान, युवक।

दिए गए विकल्पों में "ई" 'आमदनी' में प्रत्यय है।

• आमदनी का अर्थ है: कमाई
• आमदन मूल शब्द है जिसका अर्थ है- 'आना'
• ​इसमें 'ई' भाववाचक फारसी कृदंत प्रत्यय के योग से आमदनी शब्द बना है।

Confusion Points

• आमद शब्द में अ' प्रत्यय लगने पर आमद शब्द बनता है।
• अतः आमदन + ई = आमदनी
• अन्य उदाहरण-
• रफतन(जाना) इसमें 'ई' प्रत्यय के योग से रफतनी शब्द का निर्माण होता है।

Key Points

• यह उर्दू के कृत या कृदंत प्रत्यय के द्वारा निर्मित शब्द है ।
• "ई" प्रत्यय से बनने वाले अन्य शब्द - रेती, हँसी,बोली, फाँसी आदि।

Additional Information

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

प्रत्यय के दो भेद हैं-

कृत् प्रत्यय-

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

कृत् प्रत्यय कुछ उदाहरण -

तद्धित प्रत्यय-

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

तद्धित प्रत्यय कुछ उदाहरण-

सुरेंद्र ने सुंदर गीत लिखे हैं - "कर्तृ वाच्य" का प्रकार है।  

Important Points

• वाक्य में कर्ता के साथ ने हो तथा क्रिया का लिंग, वचन कर्म के अनुसार हो तो कर्तृ वाच्य होता है।
• अगर कर्ता के साथ कोई कारक चिन्ह का प्रयोग न हुआ हो और क्रिया का लिंग, वचन कर्ता के अनुसार हो तो कर्तृ वाच्य होता है।

Key Points

कर्मवाच्य ​-

• क्रिया के जिस रूप में कर्म प्रधान हो, उसे कर्मवाच्य कहते हैं या जहाँ क्रिया का संबंध सीधा कर्म से हो तथा क्रिया का लिंग तथा वचन कर्म के अनुसार हो, उसे कर्मवाच्य कहते हैं। मीरा ने दूध पीया। मीरा ने पत्र लिखा।

**जैसे -**​

• नौकर द्वारा चाय लाई जाएगी।
• मेरे द्वारा रामायण पढ़ी जा रही है।

Additional Information

• वाच्य- क्रिया के जिस रूप से यह जाना जाए कि वाक्य में क्रिया का मुख्य सम्बन्ध कर्ता, कर्म या भाव से है, वह वाच्य कहलाता है।

वाच्य के भेद - कर्तृवाच्य, कर्मवाच्य, भाववाच्य।  

दिए गए विकल्पों में से  शुद्ध वर्तनी "पूज्य" की है। 

Key Points 

अन्य विकल्प -

Additional Information

वर्तनी - 

• शब्दों के ठीक-ठीक लिखने की ढंग को वर्तनी कहा जाता है।
• हिंदी में इसे अक्षरी भी कहा जाता है। उर्दू में इसे हिज्जे और अंग्रेजी में स्पेलिंग कहा जाता है।

शब्दों की शुद्ध अशुद्ध वर्तनी के कुछ उदाहरण -

दिए गए विकल्पों में से "घात-निघात" सही विलोम युग्म नहीं है।  

Key Points

• घात का विलोम शब्द --> प्रतिघात
• शेष विकल्पों के सही विलोम युग्म है।

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

'सूर्य' शब्द उत्पति के आधार पर "तत्सम" प्रकार का है। 

Key Points

तत्सम- जो शब्द संस्कृत भाषा से हिन्दी म���ं बिना किसी परिवर्तन के ले लिए गए हैं वे तत्सम कहलाते हैं।

जैसे-

• अग्नि, क्षेत्र, वायु, रात्रि, आदि।

Additional Information

जब वह आएगा, तब मैं जाऊँगा'। प्रस्तुत वाक्य में "समय वाचक"  क्रियाविशेषण उपवाक्य है। 

• उपर्युक्त वाक्य में शब्द मुख्य उपवाक्य की क्रिया विशेषता (समय) बता रहा हैं।

Key Points

क्रिया-विशेषण उपवाक्य- 

• जो उपवाक्य किसी क्रिया की विशेषता बताते हैं, उन्हें क्रिया-विशेषण उपवाक्य कहते हैं।
• ये उपवाक्य क्रिया का समय, स्थान, कारक, प्रयोजन परिमाण आदि बताते हैं।
• इनकी शुरुआत जब, जहाँ, क्योंकि जिससे, अतः, अगर, यद्यपि, चाहे, जो, त्यों, ज्यों, मानों इत्यादि से होती है।

Additional Information

क्रिया-विशेषण उपवाक्य पाँच भेद होते हैं-

• काल सूचक उपवाक्य - जब मैं घर पहुँचा, तब वह जा रही थी।
• स्थानवाचक उपवाक्य- जिधर हम जा रहे हैं, उधर एक शेर है।
• रीतिवाचक उपवाक्य- बच्चे वैसे ही करते हैं, जैसा वे बड़ों से सीखते हैं।
• परिमाणवाचक उपवाक्य- जैसे-जैसे गर्मी बढ़ेगी, वैसे-वैसे पसीना आयेगा।
• परिणाम अथवा हेतु सूचक उपवाक्य- वह इसलिए आएगा ताकि आपसे शादी कर सके।

"जल" शब्द का रूप बहुवचन में नहीं बदलता है। 

Key Points

• "जल" शब्द में वचन परिवर्तन का प्रभाव नहीं होता वह एकवचन एवं बहुवचन दोनों में ही एक-सा रहता है।
• कुछ शब्द ऐसे हैं; जो एकवचन तथा बहुवचन में समान होते हैं। उनके रूप नहीं बदलते।
• जैसे- घी, चाय, गिरि, छाया, क्षमा, पानी, याचना, कल आदि।

अन्य विकल्प -

Additional Information

• वचन की परिभाषा- शब्दों के संख्यावाचक रुप को वचन कहते हैं।

वचन के प्रकार-

'कलम तोडना' मुहावरे का अर्थ-"बहुत अच्छा लिखना"।

वाक्य प्रयोग- सौरब ने अपनी आत्मकथा लिखने में "कलम तोड़ दी"।

Mistake Points 

1. ​दिन-रात लिखना।
2. लिखते-लिखते रुक जाना।
3. लेखनी से संन्यास ले लेना।

ये सभी पंक्ति मुहावरों की श्रेणी में नहीं आती।

Key Points

1. मुहावरा एक अरबी शब्द है।
2. हिंदी में इसे वाग्धारा कहते।
3. मुहावरों का प्रयोग सामान्य-सी बात को 'विशेष वाक्य' में कहने में होता।

Additional Information कुछ अन्य महत्वपूर्ण मुहावरे-

1. बन्दर के हाथ में आईना - नासमझ व्यक्ति कीमती चीज़ों की क़दर नहीं कर सकता।

वाक्य प्रयोग- जिस प्रकार बन्दर के हाथ में आईना आने पर वह उसमे अपनी सकल देख कर उसे दूसरा बन्दर समझ के तोड़ देगा। 2. दिन दूनी रात चौगनी- खूब उन्नति होना।

           वाक्य प्रयोग- रामनरेश की शहर जाकर "दिन दूनी रात चौगनी" हों गयी।

"चौराहा" में "द्विगु समास" है।

चौराहा "चार राहो का समूह"।

Key Points

द्विगु समास- 'उत्तर पद प्रधान होता'।

1. पहचान- पहला पद "संख्यावाचक" तथा इसमें "समूह या समाहार" का पता चलता है।
2. जैसे- 'चौराहा' शब्द में 'चार राहों के समूह' का ज्ञान हो रहा है।

 

तत्पुरुष समास- 'उत्तर पद प्रधान होता'।

1. पहचान- "कारक चिन्ह" का लोप हों जाना।
2. जैसे- 'गगनचुम्बी' "गगन को चूमने वाला" (कर्म कारक विभक्ति "को" का लोप)।

 

बहुब्रीहि समास- 'अन्य पद प्रधान होता'।

1. पहचान- 'दोनों पद' मिलकर किसी "तीसरे पद" की ओर संकेत देते हैं।
2. जैसे- 'लंबोदर' "लंबा है उदर जिसका" अर्थात् "गणेश जी"।

​

​कर्मधारय समास- 'उत्तर पद प्रधान होता'।

1. पहचान- 'दोनों पदों' के मध्य मे 'है जो' , 'के समान' आता हैं।
2. जैसे- 'नीलकंठ' "नीला है जो कंठ"।

Confusion Points

• द्विगु समास का पहला पद संख्यावाचक विशेषण होता।
• जैसे- 'चतुर्भुज' "चार भुजाओं का समूह"।
• जबकि, बहुव्रीहि समास का पूरा पद ही विशेषण का कार्य करता है।
• जैसे 'चतुर्भुज' "चार हैं भुजाएँ जिसकी" अर्थात् "विष्णु जी"।

Additional Information

समास-  "दो या दो से अधिक शब्दों से मिलकर बने नये सार्थक शब्द को समास कहते है"।

समास भेद- 6 भेद होते हैं।

1. अव्ययीभाव समास
2. तत्पुरुष समास
3. द्विगु समास
4. द्वन्द्व समास
5. कर्मधारय समास
6. बहुव्रीहि समास

जो मापा न जा सके' - "अपरिमेय"।

Key Pointsअनेक शब्दों के लिए एक शब्द- "किसी बात को संक्षिप्त मे कहना"।

• अप्रमेय- "जो प्रमाण देने के योग्य न हों"।
• अपलक-"बिना पलक झपकाए"।
• अभेद्य-"जो भेदा न जा सके"।

Mistake Points​ "जो मापा न जा सके" के लिए एक शब्द "अपरिमेय" होगा, न कि "अप्रमेय"।

1. अ(न)+ परिमेय(मापा) =अपरिमेय।
2. अ(न) प्रमेय(प्रमाण) = अप्रमेय।

Additional Information

 अनेक शब्दों के लिए एक शब्द-

1. अदेय- "जो दिया न जा सके"।
2. अनाहूत- "जो बिना बुलाये आया हों"।
3. गत- "जो बीत चुका हों"।
4. क्षम्य- "क्षमा पाने योग्य"।

"अनुशासन"- "अनु" उपसर्ग। 

अनु+शासन= अनुशासन (अनु=पीछे)

उपसर्ग- शब्द के प्रारंभ में लगते हैं।

Key Points

1. "अटल" ("अ" उपसर्ग) (अ=निषेध)।
2. "अनमोल" ("अन" उपसर्ग) (अन=निषेध)।
3. "अनुश" यह कोई उपसर्ग नहीं।
4. "अनुशासन" ("अनु" उपसर्ग)।

Additional Information

• उपसर्ग- शब्द के शुरू में लगते हैं।
• प्रत्यय- शब्द के अंत में लगते हैं।
• कुछ अन्य महत्वपूर्ण "उपसर्ग प्रत्यय"-

Mistake Points

1. अनुशासन में "अन" उपसर्ग नहीं होगा क्योकि,"अन" उपसर्ग का प्रयोग करने से उसका अर्थ बदल जायेगा।
2. "अनु" का प्रयोग ही सार्थक होगा।

संयुक्त वाक्य होगा- "वह बाज़ार में गया किन्तु कार्यक्रम में न जा सका"।

"संयुक्त वाक्य में दो या दो से अधिक वाक्य अव्यय से जुड़े रहते हैं"।

Key Points

• "वह बाज़ार में जाने के कारण कार्यक्रम में न जा सका"- 'सरल वाक्य'।

(एक उद्देश्य, एक विधेय)

• "वह बाज़ार गया था ताकि कार्यक्रम में न जा सके"- मिश्र वाक्य।

           (एक वाक्य तथा दूसरा उपवाक्य, दोनों 'ताकि' अव्यय से जुड़े हैं) 

• "वह बाज़ार गया कार्यक्रम में नही"- सरल वाक्य।

(एक ही उद्देश्य, एक विधेय)

Additional Information रचना के आधार पर वाक्य 3 प्रकार के होते है- 

1. सरल वाक्य- "एक उद्देश्य, एक ही विधेय"।
2. मिश्र वाक्य- "एक वाक्य,एक उपवाक्य/आश्रित वाक्य कि, जो, जिसका, जिसे,आदि शब्दों से जुड़े रहते"।
3. संयुक्त वाक्य- "दो या दो से अधिक सरल या मिश्र वाक्य अव्यय या योजक शब्द से जुड़े होते है" (जैसे-और, एवं, व, तथा आदि)।

Mistake Points

1. मिश्र वाक्य योजक शब्द- 'कि', 'जो',' जिसे',' जिसका', 'जब', 'तब' आदि।
2. संयुक्त  वाक्य योजक शब्द- 'किन्तु', 'परन्तु', 'बल्कि', 'और', 'अथवा', आदि।

'गजानन' में "बहुब्रीहि समास" हैं

 गजानन- "गज के समान आनन है जिसका" अर्थात् "गणेश जी"। 

Key Points

कर्मधारय समास- 'उत्तर पद प्रधान होता'।

1. पहचान- 'दोनों पदों' के मध्य मे 'है जो' , 'के समान' आता।
2. उदाहरण- 'कमलनयन' "कमल के समान नयन"।
3. उदाहरण- 'मुखचंद्र' "चन्द्र के सामान मुख"।

द्वंद्व समास- 'दोनों पद प्रधान होते'।

1. पहचान- योजक चिन्ह (-) का प्रयोग।
2. उदाहरण- अन्न-जल।

 Mistake Points

• ज्यादातर लोग गजानन को 'गज के समान आनन' मानकर कर्मधारय समास कर देते है परंतु ये सिर्फ गणेश जी  के लिए ही प्रयोग होता है। इसलिए ये बहुव्रीहि समास है।

Hint

• कर्मधारय समास में एक पद 'विशेषण' तथा दूसरा पद 'विशेष्य' होता है तथा बहुब्रीहि समास में पूरा पद ही 'विशेषण' का कार्य करता हैं।

Additional Information

समास-  "दो या दो से अधिक शब्दों से मिलकर बने नये सार्थक शब्द को समास कहते है"।

समास भेद- 6 भेद होते हैं।

1. अव्ययीभाव समास
2. तत्पुरुष समास
3. द्विगु समास
4. द्वन्द्व समास
5. कर्मधारय समास
6. बहुव्रीहि समास

कटैया मे प्रत्यय- "ऐया"।

• कट+ऐया=कटैया।
• प्रत्यय- शब्द के अंत में लगते हैं।

Key Points 

प्रत्यय- शब्द के अंत में लगते हैं। जैसे-लिखावट में "आवट" प्रत्यय।

• छलिया में "इया" प्रत्यय।
• उपसर्ग- शब्द के शुरू में लगते हैं।
• जैसे- परहित में "पर" उपसर्ग।

Mistake Points

• ईया, एया प्रत्यय से बना शब्द अशुद्ध होगा।

Additional Information कुछ अन्य महत्वपूर्ण "उपसर्ग- प्रत्यय"- 

निः + राशा = निराशा "गलत" है।

"निः+आशा=निराशा होगा" 

Key Points

1. निः+प्राण=निष्प्राण।
2. निः+धन= निर्धन।
3. निः+फल=निष्फल।
4. निः+आशा=निराशा

उपर्युक्त सभी संधि विसर्ग संधि का उदाहरण है।

Additional Information​संधि- 3 प्रकार की होती है।

• स्वर संधि- 'दो स्वरों के मिलने से जो परिवर्तन होता है, स्वर संधि कहते है'।
• जैसे- हिम+आलय=हिमालय।
• व्यंजन संधि- 'व्यंजन के बाद स्वर या व्यंजन आने पर जो परिवर्तन होता है,व्यंजन संधि कहते है'।
• जैसे- शरद् + चंद्र = शरच्चन्द्र ।
• विसर्ग संधि- 'विसर्ग के बाद स्वर या व्यंजन के आने से जो परिवर्तन होता है,विसर्ग संधि कहते है'।
• जैसे- निः+ध��=निर्धन।

Mistake Points 

• विसर्ग के पहले 'आ,अ' को छोडकर कोई दूसरा स्वर हों बाद मे तीसरा, चौथा, वर्ण या 'य', 'र', 'ल', 'व', हों तो विसर्ग का 'र' हों जाता है।
• जैसे- निः+धन= निर्धन।

शुद्ध वाक्य-"परिश्रम और सफलता का घोर संबंध है"।

Key Points

• "परिश्रम और सफलता का खूब संबंध है"- शब्द ज्ञान संबंधी त्रुटी।
• "खूब" की जगह "घोर" आयेगा।
• "परिश्रम, सफलता का घोर संबंध है"- अव्यय स���बंधी त्रुटी।
• "अल्पविराम"(,) की जगह "और" अव्यय आयेगा।
• "खूब संबंध परिश्रम और सफलता का है"- पदक्रम तथा शब्द ज्ञान सम्बंधित त्रुटी।

Additional Information

• "वाक्य-अशुद्धि" वाक्य को बनाते वक्त वाक्य मे 'संज्ञा','सर्वनाम', 'विशेषण', 'क्रिया', तथा
• 'अव्यय' सम्बंधित अशुद्धि हों सकती है।

1. 'संज्ञा' सम्बंधित अशुद्धि- "गोलियों की बाढ़" ('बौछार')।
2. 'सर्वनाम' सम्बंधित अशुद्धि- "मेरे से मत पुछो" ('मुझसे')।
3. 'विशेषण' सम्बंधित अशुद्धि- "मुझे बड़ी बुख लगी है" ('बहुत')।
4. 'क्रिया' सम्बंधित अशुद्धि- "पगड़ी ओढ़कर आओ" ('बाँधकर')।
5. ‘अव्यय' सम्बंधित अशुद्धि- "बह अत्यंत ही सुन्दर है" ('अत्यंत')।

Mistake Points

• "परिश्रम और सफलता का खूब संबंध है" शब्द ज्ञान सम्बंधित त्रुटी। 'विशेषण' सम्बंधित त्रुटी नहीं है।
• 'खूब' के जगह "घोर" शब्द आयेगा।

"नवरत्न" में ​'द्विगु समास' है।

 क्योंकि,पहला पद "संख्यावाचक" है।

Key Points 

द्विगु समास- 'उत्तर पद प्रधान होता',तथा 'समूह' का ज्ञान होता। 

• उदाहरण- 'नवरत्न' "नौ रत्नों का समूह"।

 तत्पुरुष समास- 'उत्तर पद प्रधान होता',तथा 'कारक चिन्ह' का लोप हों जाता है।

• उदाहरण- 'पथभ्रष्ट' "पथ से भ्रष्ट" (अपादान कारक की विभक्ति "से" का लोप हों रहा है)

बहुब्रीहि समास- 'अन्य पद प्रधान होता',तथा 'दोनों पद' मिलकर किसी "तीसरे पद" की ओर संकेत देते हैं।

• उदाहरण- 'पंकज' " पंक (कीचड़) मे जो उगता है" अर्थात् "कमल" (पंकज)

 द्वंद्व समास- दोनों पद प्रधान होते है तथा, मध्य में ”और”, “अथवा”, “या” लगते है।

• उदाहरण- 'जलवायु' "जल और वायु"।

Additional Information

समास-  दो या दो से अधिक शब्दों से मिलकर बने नये सार्थक शब्द को समास कहते है।

• समास भेद- 6 भेद होते हैं।

1. अव्ययीभाव समास- पूर्व पद प्रधान।
2. तत्पुरुष समास- उत्तर पद प्रधान।
3. द्विगु समास- उत्तर पद प्रधान।
4. द्वन्द्व समास- दोनों पद प्रधान।
5. कर्मधारय समास- उत्तर पद प्रधान।
6. बहुव्रीहि समास- अन्य पद प्रधान।

Confusion Points

• कारक चिन्ह- "से" करण विभक्ति मे 'साधन के तौर पर' तथा,अपादान विभक्ति में 'अलगाव होने का भाव' में लगता।
• जैसे- "पथभ्रष्ट" "पथ से भ्रष्ट" (पथ से अलग होने का भाव)।

सही उत्तर: सदुपदेश है ।

• सदुपदेश का संधि विच्छेद= सत्+उपदेश

          सदुपयोग में घोष व्यंजन संधि है, जिस कारण त् और उ मिलने से द हो जाता है। 

 Key Points

Additional Information

• जब दो शब्दों का योग होता है तो पहले शब्द की अंतिम ध्वनि और दूसरे शब्द की पहली ध्वनि आपस में मिलकर जो परिवर्तन लाती हैं उसे संधि कहते हैं, और इस प्रकार निर्मित शब्द, यौगिक शब्द कहलाते हैं।
• इस प्रकार अतिशयोक्ति, तत्त्व, प्रामाणिक, आशीर्वाद आदि शुद्ध शब्द हैं।

 Mistake Points

• चूंकि महत्त्व, महत्+त्व से बना है।अतः महत्व नहीं महत्त्व सही शब्द है।

सही उत्तर:" मां ने कहा मैं देर से घर लौटूंगी, तुम अपना पाठ अवश्य याद कर लेना। यह वाक्य उद्धरण चिह्न को संबोधित करता है ।

• किसी और के वाक्य या शब्दों को ज्यों-का-त्यों रखने हेतु उद्धरण चिह्न (" ") का प्रयोग किया जाता है।

 Key Points

• विस्मयसूचक चिह्न - भाषा में आश्चर्य,विस्मय,हर्ष,घृणा आदि का बोध कराने के लिए इस चिह्न (!) का प्रयोग किया जाता है।
• उदाहरण- अरे ! तुम आ गए ।
• योजक चिह्न - दो पुनरुक्त शब्दों, संयुग्मी पदों, विपरीतार्थक शब्दों को जोड़ने के लिए इस चिह्न (-) का प्रयोग किया जाता है।
• उदाहरण - कभी - कभी, माता - पिता, ��ट्टा - मीठा आदि।
• विवरण चिह्न - वाक्यांश में जानकारी, निर्देश या सूचना आदि को दर्शाने के लिए इस चिह्न (:-) प्रयोग किया जाता है।
• उदाहरण - कृपया निम्नलिखित नियमों का पालन करें :-

Additional Information

• ऐसे सभी चिह्न विराम चिह्न के अंतर्गत आते हैं।
• कुछ मुख्य विराम चिह्न इस प्रकार हैं - पूर्णविराम, अर्धविराम, अल्प विराम आदि।

Mistake Points 

• उद्धरण चिह्न 2 प्रकार के होते हैं - इकहरा और दोहरा उद्धरण चिह्न ।

सही उत्तर: उठन्ति में 'न्ति**'** प्रत्यय है।

• 'उठन्ति' का संधि विच्छेद = उठ+न्ति

Additional Information

• मूल शब्द के पीछे जुड़ने वाले शब्द प्रत्यय कहलाते हैं।
• जैसे - नन्दति= नं+दति

                     गुंजति= गुं+जति

सही उत्तर: 'आकाश पाताल का अंतर' मुहावरे का अर्थ है बहुत अधिक अंतर होना।

• वाक्य प्रयोग: शहरी और ग्रामीण जीवन शैली में आकाश पाताल का अंतर है ।

 Key Points

• बहुत मेहनत करना- दिन रात एक करना
• बहुत कम अंतर होना- उन्नीस-बीस का फ़र्क होना
• बहुत डर जाना- खून सूखना

Additional Information

• जो सीधे अर्थ का बोध न करा उसकी प्रतीति कराए, उसे मुहावरा कहते हैं।

सही उत्तर: 'अक्ल के घोड़े दौड़ाना' मुहावरे का अर्थ है बहुत सोचना विचारना ।

• वाक्य प्रयोग: मोहन के पिता, उसके विवाह के लिए अक्ल के घोड़े दौड़ा रहे हैं।

Key Points 

• निश्चिंत हो कर सोना- घोड़े बेचकर सोना
• सबसे अलग रहना- अपनी खिचड़ी अलग पकाना
• खतरा मोल लेना- आग से खेलना

Additional Information 

• जो सीधे अर्थ का बोध न करा उसकी प्रतीति कराए, उसे मुहावरा कहते हैं।

Given:

If the product of zeros of a cubic polynomial with integer coefficients = \(\frac{-11}{3}\)

Calculation:

For an equation ax³ + bx² + cx + d

Product of zeros of cubic polynomial = \(\frac{-d}{a}\)

So, the constant term of cubic polynomial = d = 11

∴The answer is 11 .

Given:

To find the probability of getting a prime or composite number from the first 15 natural numbers.

Formula used:

Probability = \(\dfrac{Favourable\ outcomes}{Total\ Outcomes}\)

Calculation:

The first 15 natural numbers N = {1, 2, 3, ………,14,15}

The composite numbers from 1 to 15 are: 4, 6, 8, 9, 10, 12, 14, 15

The prime numbers from 1 to 15 are: 2, 3, 5, 7, 11, 13

Hence, Total numbers of prime or composite numbers from the first 15 natural numbers = 14

Probability = \(\dfrac{14}{15}\)

∴The answer is \(\dfrac{14}{15}\) .

Given:

The frequency distribution of wages of 50 workers

Formula used:

Probability = \(\dfrac{Favourable\ outcomes}{Total\ Outcomes}\)

Calculation:

Favourable outcomes = 4 + 10 + 14 = 28

Total Outcomes = 6 + 4 + 10 + 14 + 16 = 50

Probability = \(\dfrac{28}{50}\) = \(\dfrac{14}{25}\)

∴The answer is \(\dfrac{14}{25}\)  .

Given:

In ||_gm ABCD, ∠AXB = 40°

Calculation:

In  ||gm ABCD,

∠AXB = ∠XAD (Alternate angle)       ------(1)

and ∠XAD = ∠BAX   (AX is the bisector of ∠A)     -----(2)

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

∠AXB = ∠BAX = 40

In △ AXB

⇒ ∠AXB  + ∠BAX + ∠ABX = 180°  (Sum of angle of triangle = 180°)

⇒ ∠ABX + 40 + 40 = 180

⇒ ∠ABX = 180 - 80 = 100° = ∠B

As, opposite angles of a ||_gm are equal so, ∠B = ∠D = 100°

∴The answer is 100° .

Given:

\(\rm\left(\frac{2}{x}-\frac{3}{y}\right)=a\) , \(\rm xy=\frac{3}{b^2}\)

Formula used:

(a - b)2 = a2 + b2 -2ab

Calculation:

Squaring both sides we get,

⇒ \(\rm\left(\dfrac{2}{x}-\dfrac{3}{y}\right)^2\)= a²

⇒ \(\dfrac{4}{x^2}+\dfrac{9}{y^2} \) -  \(2\times \dfrac{2}{x}\times \dfrac{3}{y}\) = a2

⇒ \(\dfrac{4}{x^2}+\dfrac{9}{y^2} \) - \(\dfrac{12}{xy}\) = a²

⇒ \(\dfrac{4}{x^2}+\dfrac{9}{y^2} \) - \(\dfrac{12\times b^2}{3}\) = a2

⇒ \(\dfrac{4}{x^2}+\dfrac{9}{y^2} \) - 4b² = a²

⇒ \(\dfrac{4}{x^2}+\dfrac{9}{y^2} \) = a2 + 4b2

∴The answer is a2 + 4b2 .

Given:

The weights of 10 oranges 

Number of class intervals = 8

Calculation:

So, from above table we get that, for a class interval of 8 we need a class size of 5

∴The answer is 5 .

Given:

Point P(x, y) is equidistant from points A(3, 2) and B(­-2, 3)

Formula used:

Distance formula = √{{x₁ - x₂)² + (y₁ - y₂)²}

Calculation:

Since point P is equidistant from points A and B.

So, AP = BP

⇒ AP² = BP²

⇒ (x - 3)² + (y - 2)² = (x + 2)² + (y - 3)²

⇒ x² + 9 - 6x + y² + 4 - 4y = x² + 4 + 4x + y² + 9 - 6y

⇒ 13 - 6x - 4y = 13 + 4x - 6y

⇒ - 6x - 4y = 4x - 6y

⇒ - 4y + 6y = 4x + 6x

⇒ 2y = 10x

⇒ y = 5x

∴The answer is 5x .

Given:

An A.P series 11, 15, 19, 23

Formula used:

a_n = a + (n - 1)d

Calculation:

Here a = 11, d = 15 - 11 = 4, n = 28

a₂₈ = 11 + (28 - 1)4 = 11 + 27 × 4 = 119

∴The answer is 119 .

Given:

Total number of marbles initially = 15

Number of red marbles = 3

Number of red marbles = 15 - 3 = 12

Calculation:

Probability of drawing white marble initially = \(\dfrac{3}{15}\) = \(\dfrac{1}{5}\)

When x white marble is added,

Number of white marble = x + 3

Total number of marble = 15 + x

Now, According to the question,

⇒ \(\dfrac{3+x}{15+x}\) = 2 × \(\dfrac{1}{5}\)

⇒ 15 + 5x = 30 + 2x

⇒ x = \(\dfrac{15}{3}\) = 5

∴The answer is 5 .

Given:

Height of the boy = 1.2m

Speed of the boy = 0.8 m/s

Calculation:

Distance travelled by boy in 6 sec = 0.8 × 6 = 4.8m

Total distance of shadow of boy and distance from base of lamp post = 2.4 + 4.8 = 7.2 m

Let the height of lamp post be 'x' m

According to question,

⇒ \(\dfrac{1.2}{2.4}\) = \(\dfrac{x}{7.2}\)

⇒ x = 3.6 m

∴ The answer is 3.6 m .

Given:

Value of 3 = 1.732

Calculation:

⇒ \(\dfrac{\sqrt6-\sqrt2}{\sqrt6}\) = \(\dfrac{\sqrt{2}(\sqrt{3} -1)}{\sqrt{2}\times \sqrt{3}}\) = \(\dfrac{1.732 -1}{1.732}\) = 0.432

∴The answer is 0.432 .

Given:

The mean of 8 observations = 15

Formula used:

Mean = \(\dfrac{Sum\ of\ Observations}{Total\ Observations}\)

Calculation:

According to question,

x + x + 2 + x + 4 + x + 6 + x + 8 + x + 10 + x + 12 + x + 14 = 120

⇒ 8x = 120 - 56

⇒ x = 8

Now mean of last 3 observations = \(\dfrac{18 + 20 + 22}{3}\) = 20

∴The answer is 20 .

Given:

∠AOP = 2x + 4, ∠POQ = 3x

Calculation:

∠BOQ = ∠POQ = 3x

Now, ∠AOP + ∠BOQ + ∠POQ = 180

⇒ 2x + 4 + 3x + 3x = 180

⇒ 8x = 176

⇒ x = 22

So, ∠POB = 6x = 6 × 22 = 132°

∴The answer is 132° .

Given:

ABC is a triangle, right angled at C.

BC = a, AB = c, and ‘p’ is the length of the perpendicular from C to AB.

AC = 2 BC

Calculation:

In ΔABC,

Sinθ = \(\dfrac{P}{H}\) = \(\dfrac{a}{c}\) →(1)

Again, In ΔACM,

Sinθ = \(\dfrac{p}{2a}\) →(2)

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

\(\dfrac{a}{c}\) = \(\dfrac{p}{2a}\)

⇒ p × c = 2a²

⇒ c = \(\dfrac{2a^2}{p}\)

Shortcut Trick

To find when they all meet again at the starting point, calculate the LCM of their individual times.

Meeting time = LCM(18, 24, 36) = 72 minutes.

Number of rounds completed by X = Total Time ÷ Time per round = 72 ÷ 18 = 4 rounds.

∴ The correct answer is 4 rounds.

Alternate Method

Given:

Time taken by X to complete one round = 18 minutes

Time taken by Y to complete one round = 24 minutes

Time taken by Z to complete one round = 36 minutes

Formula Used:

⇒ Time to meet again at the starting point = LCM of individual times taken to complete one round.

⇒ Number of rounds completed = Total time elapsed ÷ Time taken for one round.

Calculations:

Find the prime factorisation of the given times:

⇒ 18 = 2 × 3²

⇒ 24 = 2³ × 3

⇒ 36 = 2² × 3²

Determine the Least Common Multiple (LCM):

⇒ LCM(18, 24, 36) = 2³ × 3²

⇒ LCM = 8 × 9 = 72 minutes

Thus, they all meet again at the starting point after 72 minutes.

Calculate the number of rounds completed by X in 72 minutes:

⇒ Number of rounds completed by X = 72 ÷ 18

⇒ Number of rounds completed by X = 4 rounds

∴ The correct answer is 4 rounds.

Additional Information

LCM Application in Circular Tracks

When multiple objects move along a circular path starting together, they will next meet at the starting point at a time that is the LCM of their individual time periods.

Meeting for the First Time Anywhere

The time when two runners running in the same direction meet for the first time anywhere on the track is given by: Track Length ÷ Relative Speed.

Opposite Direction Movement

If two runners run in opposite directions with speeds S₁ and S₂, they will meet for the first time after a time equal to Track Length ÷ (S₁ + S₂).

Given:

Radius : Slant height = 3 : 5

CSA = 240π cm² 

Concept used: 

CSA(Cone) = πrl

Calculation:

Let, radius = 3m and slant height = 5m

⇒ 240π = π (3m) (5m)

⇒ 15 x m x m = 240

⇒ m x m = 240/15

⇒ m x m = 4 x 4

⇒ m = 4

⇒ slant height = 5m

⇒ 5 x 4 

⇒ 20 cm

∴ Its slant height is 20 cm.

Given:

Two angles are equal.

The third angle is 30° less than each of the equal angles. 

Concept used: 

Sum of interior angles of a triangle = 180° 

Calculation:

Let, the equal angle be m

⇒ Third angle = m - 30°

⇒ (m - 30°) + m + m = 180° 

⇒ 3m - 30° = 180° 

⇒ 3m = 180° + 30° 

⇒ m = 210°/ 3

⇒ m = 70°

The smaller angle = m - 30°

⇒ 70° - 30° 

⇒ 40°

∴  The smaller angle is 40°

Given:

Perimeter = 144 cm

Sides = 3 : 4 : 5

Rate = Rs. 5/cm² 

Concept used: 

Perimeter = sum of all sides

Area = \( \dfrac{1}{2} \) x base x height

Calculation:

Let's, take the three sides = 3m, 4m and 5m respectively.

⇒ 3m + 4m + 5m = 144

⇒ 12m = 144

⇒ m = 12

Three sides will be  

⇒ Hypotenuse = 5m = 5 x 12 = 60 cm

⇒ Height = 4m = 4 x 12 = 48 cm

⇒ Base = 3m = 3 x 12 = 36 cm

⇒ Area = (1/2) x 48 x 36

⇒ 24 x 36

⇒ 864 cm² 

⇒ Total cost = 5 x 864

⇒ 4320 Rs.

∴ The cost of painting the surface at the rate of Rs. 5/cm2, is Rs. 4320.

Given:

Side = 28 cm

Concept used: 

Area of square = side x side

Area of circle = πr² 

Calculation: 

⇒ Area of square = 28² 

⇒ 784 cm² 

⇒ Radius of sector = \( \dfrac{28}{2} \) 

⇒ 14 cm

⇒ Area of circle = \( \dfrac{22}{7} \) x 14 x 14 

⇒ 22 x 28

⇒ 616 cm² 

⇒ Area of cardboard wasted = Area of square - Area of circle

⇒ 784 - 616

⇒ 168 cm² 

∴ The area of the cardboard wasted is 168 cm².

Given:

The mean weight of 50 students = 46 kg

The mean weight of 20 students = 43 kg

Concept used: 

Mean = Sum of observation / Number of observations

Calculation:

Let, the weight of 20 students = m

⇒ \( \dfrac{m}{20} \) = 43

⇒ m = 20 x 43

⇒ m = 860

Let, the weight of the left 30 students = n

⇒ \( \dfrac{860 + n}{50} \) = 46

⇒ 860 + n = 46 x 50

⇒ n = 2300 - 860

⇒ n = 1440

The mean weight of the remaining 30 students = \( \dfrac{1440}{30} \)

⇒ 48 kg

∴ The mean weight of the remaining students of that class is 48 kg.

Given:

2x = y - 3 and \(\rm\frac{3}{x+y}=2\)

Calculation:

⇒ y = 2x + 3  → (1)

⇒ 3 = 2(x + y)

⇒ 3 = 2x + 2y

⇒ 2x + 2y = 3   → (2)

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

⇒ 2x + 2(2x + 3) = 3   

⇒ 2x + 4x + 6 = 3

⇒ 6x + 6 - 3 = 0

⇒ 6x + 3 = 0

⇒ 2x + 1 = 0

⇒ x = \( \dfrac{-1}{2} \)

⇒ y = 2 x \( \dfrac{-1}{2} \) + 3

⇒ y = -1 + 3

⇒ y = 2

∴ x = \( \dfrac{-1}{2} \), and y = 2.

Given:

9.6̅

Calculation:

Let, m = 9.66666...

⇒ 10m = 96.6666..

⇒ 10m - m = 96.6̅  - 9.6̅ 

⇒ 9m = 87

⇒ m = \( \dfrac{87}{9} \)

∴ 9.6̅  = \( \dfrac{87}{9} \)

Given:

If 7 students are extra in each row, there would be 2 rows less and if 2 students are less in each row, there would be 1 more row.

Calculation:

Let, the number of rows = m

Total number of students in 1 row = n

⇒ The total number of students = m x n

⇒ (n + 7)(m - 2) = mn

⇒ mn + 7m - 2n - 14 = mn

⇒ 7m - 2n = 14   → (1)

⇒ (n - 2)(m + 1) = mn

⇒ mn - 2m + n - 2 = mn

⇒ n = 2m + 2     → (2)

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

⇒ 7m - 2(2m + 2) = 14  

⇒ 7m - 4m - 4 = 14  

⇒ 3m = 18  

⇒ m = 6

⇒ n = (2 x 6) + 2

⇒ n = 14

⇒ Total students = mn

⇒ 6 x 14

⇒ 84

∴ The number of students in the class is 84.

Given:

Edges = 3 cm, 4 cm, and 5 cm

Concept used: 

Volume of cube = side³ 

The surface area of 1 side = side² 

Calculation:

⇒ Volume of single cube = Sum of volumes of 3 small cubes

⇒ side³ = 3³ + 4³ + 5³

⇒ side³ = 27 + 64 + 125

⇒ side³ = 216

⇒ side = 6 cm

The surface area of the top and bottom of the new cube formed = 2 x 6²

⇒ 2 x 36

⇒ 72 cm²

∴ The surface area of the top and bottom of the new cube formed is 72 cm².

Given:

∠B = 90° 

cos C = \(\rm \frac{a-b}{a+b}\)

Concept used:  

Pythagoras Theorem: In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

h = \(\sqrt {p^2 + b^2}\),

Where, h = Hypotenuse, b = Base, and p = Perpendicular

cos C = \( \dfrac{base}{hypotenuse} \)

tan C = \( \dfrac{perpendicular}{base}\)

Calculation:

Using Pythagoras Theorem,

AC² = AB² + BC²

⇒ AB² = AC² - BC²

⇒ AB² = (a + b)² - (a - b)²

⇒ AB² = a² + b² + 2ab - a² - b² + 2ab

⇒ AB² = 4ab

⇒ AB = 2\(\sqrt {ab}\)

⇒ tan C = \( \dfrac{AB}{BC} \)

⇒ tan C = \(\dfrac{2\sqrt {ab}}{a-b}\)

∴ tan C = \(\dfrac{2\sqrt {ab}}{a-b}\)

The correct answer is: 'all'.

Key Points

• 'All' is used to refer everything, the complete number or amount and the whole of something.
• It is used with plural noun and plural verb.
• ​Ex. All my friends are going to Goa.
• The context of the sentence tells us that the person enjoys every style of dance.
• So, t​he correct determiner that fits the blank is 'all' because it is followed by plural noun.
• Both every and each are followed by singular nouns. So, option 1 and 2 are incorrect.
• The use of 'a lot' will also be incorrect here.

​​Hence, the correct sentence is: He likes all dance forms.

The correct answer is: the lands collapses.

Key Points

• According to the rule of subject verb agreement, the verb is always used according to its subject.
• If the subject is singular, singular verb will be used and if the subject is plural, plural verb will be used.
• ​Example:
• The child is playing in the garden.
• Children are running here and there.
• Similarly, in the given sentence, 'collapses' should be replaced with 'collapse' because its subject i.e. 'lands' is plural.
• So, the error lies in 'the lands collapses'.

​Hence, the correct sentence is: When the limestone just below the ground surface dissolves, the lands collapse and form ponds.

The correct answer is: In 1986, SEIKO invented Kinetic, the world’s first watch to generate and save its own electricity. 

Key Points

• When a date or year appears at the beginning of a sentence, comma is used used after it.
• Ex. In 2002, the prime minister of India was Manmohan Singh.
• We also use comma in case of Apposition to show the description, designation or the post of the person.
• The post, description or designation is placed just after the name by using a comma.
• For example: Kaushal, the captain of our team, played a crucial role in today's match.
• Similarly, in the given sentence, comma will be used after 1986 and Kinetic.
• Apostrophe ('s) is used after a word to show its relation with something else. It is used to show possession or close relation of something with the other.
• So, in the given sentence, apostrophe ('s) will be used after 'world'.
• Apostrophe ('s) is also used to indicate contraction or omission of letters. 
• Ex. It's = It is, isn't = is not, shouldn't = should not, won't = will not, etc.
• But in option 1 and 3, apostrophe is used which is incorrect as It's = It is, but here possession is implied.
• In option 4, apostrophe is used after worlds which is incorrect. It should be before 's'.
• Hence, option 2 is correct.

 Thus, the correct sentence is:​ In 1986, SEIKO invented Kinetic, the world’s first watch to generate and save, its own electricity.

The correct answer is: on the contrary.

Key Points

• 'On the contrary' means opposite to something in nature. 
• Ex. It doesn't seem ugly to me; on the contrary, I think it's rather beautiful.
• 'Chilly' means cold.
• The context of the sentence suggests that the thing wasn't hot; in fact, it was really cool. Both hot and chilly are used for the same thing.
• Hence, a word which shows opposition to the other should be used in the blank.

​Therefore, the correct sentence is: No, it wasn't hot, on the contrary, it was quite chilly.

Additional Information

• Nevertheless means in spite of; not withstanding; despite something that has just been mentioned or said**.**
• Moreover means in addition to something. It is used to mention additional facts.
• Besides means in addition to.

The correct answer is: since.

Key Points

• Since is used to denote point of time or a specified time or event in the past.
• It shows the time from a point in the past to the present time.
• Ex. He has been playing cricket since 2004.
• The context of the sentence tells that the person hasn't seen a good comedy movie in a very long time.
• Here, a specified period of time is mentioned i.e. from the last time the person saw a decent comedy till now.
• So, since is the most suitable word to be filled in the blank.

​Hence, the correct sentence is: It's a long time since I saw a decent comedy film.

Additional Information

• Ago is used to indicate how long before the present time something happened.
• Ex. I arrived in Navi Mumbai six months ago.
• When is used to refer to a situation that we are certain of.
• ​Ex. When I meet Sonu, I'll tell him that you said hello.​

The correct answer is: 'are'.

Key Points

• As per the rule of subject verb agreement, singular subjects are followed by singular verbs and plural subjects are followed by plural verbs.
• ​Example:
• The students are reading books in the library.
• The principal is sitting in his office.
• In the given sentence, the subject of the sentence is plural, so plural verb i.e. 'are' will be used.
• All other verbs are singular and hence are incorrect.
• Also, the sentence is in Simple Present Tense.

Therefore, the correct sentence is: The children’s books are on the table.

The correct answer is: 'un'.

Key Points

• Unlocked means not locked.
• ​Ex. The thief unlocked the car in the owner's absence.
• The context of the sentence tells us that our homes are vulnerable to burglary if we do not lock the doors.
• So, the correct prefix to be used before locked is 'un'.
• All other prefixes can not be used with 'locked'.

​The correct sentence is: If we leave our doors unlocked, our houses are liable to be burgled.

Additional Information

• Prefix is a letter or a word used before another to add something to its meaning or give a different meaning.
• Ex. 'Treat' means to regard or deal with something in a particular way.

​                           'Retreat' means to withdraw from a position or a state.

The correct answer is: of, on.

Key Points

• 'Of' is used to relate something to the other or to show that something is the part of the other.
• Ex. The climate of Himachal is very pleasing.
• 'On' is used to denote a place.
• Ex. The book is on the table.
• The context of the sentence tells that an express bus had flipped over on the main highway and firefighters were trying to lift its debris.
• So, the correct prepositions to be filled in the blanks are of and on respectively.

Therefore the correct sentence is: Fire fighters were trying to lift the wreckage of an express bus that had overturned on the main highway.

Additional Information

• 'At' is used to denote a comparatively smaller place. 
• Ex. I live at Hudson Bay in New York.
• 'In' is to denote comparatively bigger places.
• Ex. The Taj Mahal is in Agra.
• 'Under' is used to denote a position lower than the other.
• Ex. There is a rat under the bed.
• 'Across' is used to denote from one side of something to the other.
• Ex. I took a ferry across the lake.