The correct answer is Rolling friction.

Key Points

• Rolling friction is friction that acts on objects when they are rolling over a surface.
• So, when a ball moves on a surface, it is an example of Rolling friction.
• There are 4 types of friction
• Sliding Friction, Fluid friction, Static friction and Rolling friction.

Additional Information

• Sliding friction is friction that acts on objects when they are sliding over a surface.
• For example, you use sliding friction when you write with a pencil.
• Fluid friction is friction that acts on objects that are moving through a fluid.
• If you've ever tried to push your open hand through the water in a tub or pool, then you've experienced fluid friction.
• Static friction acts on objects when they are resting on a surface.
• Without this static friction, your feet would slip out from under you, making it difficult to walk.

The correct answer is Hypermetropia.

Key Points

• Far-sightedness, also known as long-sightedness, hypermetropia, or hyperopia, is a condition of the eye where distant objects are seen clearly but near objects appear blurred.
• This blurred effect is due to incoming light being focused behind, instead of on, the retina wall due to insufficient accommodation by the lens.
• Nearsightedness (myopia) is a common vision condition in which you can see objects near to you clearly, but objects farther away are blurry.
• It occurs when the shape of your eye causes light rays to bend (refract) incorrectly, focusing images in front of your retina instead of on your retina.

Additional Information

• Astigmatism is a common and generally treatable imperfection in the curvature of the eye that causes blurred distance and near vision.
• Astigmatism occurs when either the front surface of the eye (cornea) or the lens inside the eye has mismatched curves.
• Colour blindness usually involves the inability to distinguish between shades of red and green.
• There is no treatment for inherited colour blindness.

The correct answer is ​Plastics are bad conductor of electricity.

Key Points

• Plastic is the bad conductor of electricity and it is nonresponsive towards electricity.
• Plastic is a good insulator it does not allow current to flow through it.

Additional Information

• Conductors are materials that permit electrons to flow freely from particle to particle.
• Insulators are materials that impede the free flow of electrons from atom to atom and molecule to molecule.
• Examples of conductors include metals, aqueous solutions of salts (i.e., ionic compounds dissolved in water), graphite, and the human body.
• Examples of insulators include plastics, Styrofoam, paper, rubber, glass and dry air.

The correct answer is Carbon dioxide is liberated.

Key Points

• The reaction between acetic acid and sodium hydrogen carbonate/sodium bicarbonate is shown below:
• CH3COOH(aq)+NaHCO3(aq)→CH3COONa(aq)+H2O(l)+CO2(g)↑
• When acetic acid is added to an aqueous solution of sodium bicarbonate, an acid-base reaction takes place (neutralisation reaction)
• Which leads to the formation of a salt of sodium acetate and water along with the evolution of carbon dioxide. 
• When carbon dioxide is evolved, it appears as a brisk effervescence. Carbon dioxide gas is colourless and odourless.
• It can be identified by passing it through lime water. If on passing a gas through lime water it turns milky, the gas is carbon dioxide gas.

The correct answer is Pitcher plant.

Key Points

• Insect-eating plants are called insectivorous plants and they derive nutrition by consuming insects and likewise other organisms.
• Insectivorous plants examples include Venus flytrap, bladderwort, cobra lily, drosera or sundews and pitcher plant.
• Pitcher plants belong to large carnivorous plants and have modified leaves acting as pitfall traps that have sugary nectar and make insects fall via slippery surfaces into digestive juices.
• Insectivorous Plants found at nitrogen deficient soils.

Additional Information

• Cuscuta, commonly known as dodder is a genus of over 201 species of yellow, orange, or red (rarely green) parasitic plants.
• Cuscuta is known as Amarbel in India.
• A mushroom or toadstool is the fleshy, spore-bearing fruiting body of a fungus, typically produced above ground, on soil.

The correct answer is Basil.

Key Points

• Basil herb has anti-inflammatory properties that can help to lower the risk of inflammatory conditions such as arthritis. heart disease, and bowel issues.
• Basil has antibacterial properties. The oils in the herb may help to fight bacteria in people with respiratory, urinary, abdominal, and skin infections.
• Herbs are small plants having a soft and delicate stem.
• Herbs do not have woody stem.
• Herbs have a green and tender stem. We can easily bend the stem of a herb.
• Herbs are short-sized plants. Herbs usually do not grow more than one meter in height. Herbs have a short life-span.

Additional Information

• Most of the plants can be classified into three main groups : herbs, shrubs and trees
• Shrubs are medium-sized plants with a hard woody stem, branching out near the base.
• Stem of a shrub is hard but not very thick.
• Shrubs tend to branch near ground level, so many branches are seen rising just above the ground.
• The shrubs are bigger than herbs but smaller than trees.
• The life span of shrubs is for many years but it is less than that of trees.
• Trees are tall and big plants with hard and thick woody stem.
• The tree have one main stem called ‘trunk’ which usually gives out branches and leaves.
• The trees are very big in size.
• The life-span of trees is very large. Shrubs and trees are both woody plants.

The correct answer is ​Leucoplast.

Key Points

• Plastids are a group of organelles and it is characteristics of plant cells. It is also found in algae. Plastids are divided into four different types:

1. Chloroplast
2. Chromoplast
3. Leucoplast
4. Gerontoplast

• Leucoplast is colourless plastids. They are present in the non-green plant cells that are not exposed to sunlight.
• Photosynthetic pigments are absent in leucoplasts and leucoplasts are mostly specialised for the storage of food.

Additional Information

• The chromoplasts are coloured and occur in the cells of the red, yellow, and orange coloured parts of the plant.
• They have fat-soluble carotenoid pigments like carotene and xanthophylls. which impart colours to plant parts such as fruits, flowers, vegetables, etc.
• Chloroplasts are the green coloured plastids which contain the green pigment chlorophyll in abundance. 
• These organelles serve as the sites for photosynthesis as chlorophyll is capable of absorbing light wavelengths that are required for photosynthesis to occur.
• A gerontoplast is a plastid that develops from a chloroplast during the senescing of plant foliage.

The correct answer is ​Solar energy is converted into chemical energy

Key Points

• Photosynthesis is the process by which plants use sunlight, water, and carbon dioxide to create oxygen and energy in the form of sugar.
• Inside the plant cell are small organelles called chloroplasts, which store the energy of sunlight.
• Within the thylakoid membranes of the chloroplast is a light-absorbing pigment called chlorophyll, which is responsible for giving the plant its green color.
• During photosynthesis, chlorophyll absorbs energy from blue- and red-light waves, and reflects green-light waves, making the plant appear green.

Additional Information

• While there are many steps behind the process of photosynthesis, it can be broken down into two major stages: light-dependent reactions and light-independent reactions.
• The light-dependent reaction takes place within the thylakoid membrane and requires a steady stream of sunlight, hence the name light-dependent reaction.
• The chlorophyll absorbs energy from the light waves, which is converted into chemical energy in the form of the molecules ATP and NADPH.
• The light-independent stage, also known as the Calvin Cycle, takes place in the stroma, the space between the thylakoid membranes and the chloroplast membranes, and does not require light, hence the name light-independent reaction.

The correct answer is ​Its frequency 98.3 million hertz.

Key Points

• In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the carrier signal.Frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave.
• In Frequency modulation, the carrier amplitude remains constant, but its frequency is changed in accordance with the modulating signal.
• FM Radio signals have bandwidth several times that of Amplitude Modulation (AM) signals. Bandwidth six times or larger are common.
• Frequency Modulation index is consistently over 1, requires high bandwidth in the range of 200 kHz, operates in a very high frequency range of 88 to 108 Megahertz.

The correct answer is ​Pituitary gland.

Key Points

• Growth hormone is produced by our brain’s pituitary gland and governs our height, bone length and muscle growth.
• Natural levels of growth hormone fluctuate during the day, seemingly influenced by physical activity. For example, levels rise when we exercise.
• Growth hormone levels increase during childhood and peak during puberty. In this phase of development, growth hormone promotes the growth of bone and cartilage.

Additional Information

• Adrenal glands, also known as suprarenal glands, are small, triangular-shaped glands located on top of both kidneys.
• Adrenal glands produce hormones that help regulate your metabolism, immune system, blood pressure, response to stress and other essential functions.
• The thyroid gland is a vital hormone gland: It plays a major role in the metabolism, growth and development of the human body.
• Pancreas plays a big role in digestion. It is located inside our abdomen, just behind our stomach.
• It's about the size of our hand. During digestion, our pancreas makes pancreatic juices called enzymes. These enzymes break down sugars, fats, and starches.

The correct answer is Algal bloom.

Key Points

• The thick growth of Algae on the water surface is called Algal bloom.
• Algal bloom is the rapid growth or accumulation of algae populations in freshwater or seawater systems.
• It is often identified by discoloration in the water from the pigments of the algae.
• Algal bloom usually refers to the rapid growth of microscopic unicellular algae, not macroscopic algae.
• An example of a macroscopic algal bloom is the kelp forest.

Additional Information

• Silt is a granular material between the size of sand and clay and is composed mostly of broken grains of quartz.
• Silt can occur as clay or as sediment mixed in suspension with water.
• Leaching is the process of separating or extracting a substance from its carrier by means of a solvent.
• An oil spill (sometimes called an oil slick) is the unintentional release of liquid petroleum hydrocarbons into the environment as a result of human activity.

The correct answer is Carbon dioxide.

Key Points

• The atmosphere of Venus is composed of 97% carbon dioxide, 3% nitrogen, and traces of other gases, notably sulfur dioxide.
• There are dense clouds of carbon dioxide and small doses of nitrogen are also present (not in abundance) along with sulfuric acid clouds.
• Such a composition results in a sustained greenhouse effect, making Venus the hottest planet in our Solar System.
• This greenhouse effect is the reason why Venus is the hottest planet.
• These heavy clouds also protect the planet from the bombardment of meteors.
• In increasing order of the distance of the planets from the Sun—Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.

Additional Information

• ​Venus is a small rocky planet, blanketed by a thick layer of yellowish clouds.
• It is similar in size to earth and there are many active volcanoes on Venus.
• Venus spins very slowly, in the opposite direction to most other planets.
• Venus is usually visible to the naked eye.
• It is the brightest star in the evening sky.

The correct answer is Cation.

Key Points

• Cations are positively charged ions.
• They are formed when a metal loses its electrons.
• They lose one or more than one electron and do not lose any protons.
• Therefore, they possess a net positive charge.
• Examples of cations are Calcium (Ca²⁺), Potassium (K⁺), and hydrogen (H⁺).

Additional Information

• ​Ions
• It is formed when the number of protons in an atom does not equal the number of electrons.
• If more protons are present, the ion is positive and is known as a cation; if more electrons are present, the ion is negative and referred to as an anion.
• Ions are highly reactive species.
• It is generally found in a gaseous state and does not occur in abundance on Earth.
• Anions
• It is negatively charged ions.
• It is formed when non-metal gains electrons.
• It gains one or more than one electron and does not lose any protons.
• Therefore, they possess a net negative charge.
• Examples of anions are Iodide (I^–), chlorine (Cl^–), and hydroxide (OH^–).

The correct answer is Tornado.

Key Points

• The tornado takes the shape of a dark funnel when it reaches the ground.
• A tornado is a fast-moving column of air in contact with both the Earth's surface and a cumulonimbus cloud.
• They are often seen as a condensation funnel rising from the base of a cumulonimbus cloud, with a layer of swirling debris and dust beneath it.
• Different forms of tornadoes include tornadoes, waterspouts, and landspouts.
• Tornadoes can be detected using pulse-Doppler radar, by detecting patterns in the velocity and reflectivity data.

Additional Information

• Cyclones are caused by atmospheric disturbances around a low-pressure area, which are characterized by rapid and often disruptive air circulation.
• A tsunami is a series of waves in a water body caused by the displacement of a large volume of water, typically an ocean or a large lake.
• An earthquake is the shaking of the Earth's surface, resulting in a sudden release of energy in the Earth's lithosphere that creates seismic waves.

The correct answer is The kinetic energy of the particles increase.

Key Points

• When a substance becomes hot The kinetic energy of the particles increase.
• When a substance is heated, its particles gain energy and vibrate more intensely.
• The particles collide with nearby particles and make them vibrate more.
• It transfers thermal energy through the material by conduction, from the hot end to the cold end.

Additional Information

• There are many effects of heat. It can be chemical as well as physical.
• The important effects of heat on an object are:
• Raises the temperature.
• Increases volume.
• Changes state
• Chemical reaction.
• Changes physical properties.

The correct answer is It is a good conductor of heat.

Key Points

• Mercury is used in thermometers because it remains in liquid form throughout a wide range of temperatures i.e -37.89 degrees Fahrenheit to 674.06 degrees Fahrenheit.
• Mercury has a greater coefficient of thermal expansion than alcohol.
• It is impossible to measure high temperatures because it’s a low boiling point.
• Mercury is the only one in the liquid state at room temperature.
• It's used in thermometers because it has a high coefficient of expansion.
• It is a good conductor of heat.

The correct answer is Tadpole.

Key Points

• In frogs, the hatched eggs develop into Tadpole.
• The frogs hatch anywhere from three to 25 days after the eggs are laid.
• Most hatch not into frogs, but into fish-like tadpoles, complete with gills and a tail.
• Round, neckless creatures, tadpoles feed voraciously during their metamorphosis into frogs.

Additional Information

• An embryo is the initial stage of development of a multicellular organism.
• In organisms that reproduce sexually, embryonic development is part of the life cycle that begins immediately after fertilization of a female egg cell by a male sperm cell.
• Zygote is a eukaryotic cell that is formed by a fertilization event between two gametes.
• The genome of the zygote is the assemblage of DNA in each gamete and contains all the genetic information for a new organism.
• A pupa is a life stage of some insects undergoing transition between immature and mature stages.
• Insects that pass through the pupal stage are holometabolous

The correct answer is Methane.

Key Points

• The major component of bio-gas and Compressed Natural Gas (CNG) is Methane.
• Bio-CNG contains about 92-98 % of methane and only 2-8 % carbon dioxide.
• The high methane content and calorific value combined with the low quantity of moisture, hydrogen sulphide and impurities make Bio-CNG an ideal fuel for automobiles and power generation.
• Compressed natural gas is a fuel that can be used in place of gasoline, diesel fuel and liquefied petroleum gas (LPG).
• CNG is made by compressing natural gas, which is mainly composed of methane (CH4).

Additional Information

The correct answer is 2.

Key Points

• Electric Cell: An electric cell has two terminals, a negative terminal and a positive terminal.
• An electric cell converts internally stored chemical energy into electrical potential energy, allowing current to flow from the positive terminal round to the negative through an external circuit.
• The metal cap is the positive terminal and the metal disc is the negative terminal
• There is a potential difference between the terminals of the cell.

The correct answer is Drip Irrigation.

Key Points

• Drip irrigation is the most efficient method of irrigation. It is preferred in desert regions.
• It is easy to install, easy to design, can be little expensive and can reduce disease problems associated with high levels of moisture on some plants.
• Drip irrigation sometimes called trickle irrigation and works by applying water slowly, directly to the soil drop by drop.

Additional Information

• Furrow irrigation is a method of laying out the water channels in such a way that gravity plays the role of providing just enough water for suitable plants to grow. It is usually made by the planned placement of ridges and furrows.
• Sprinkler irrigation-
• There is no requirement of using many areas of your field for setting up sprinkler irrigation.
• The interference with cultivation for setting up sprinkler irrigation is very less.
• Frequent application of water can be supplied to the plants automatically.

The correct answer is Chlorine.

Key Points

• Chlorine is one of the most common Chemical disinfection for drinking water.
• It is a chemical disinfection method that uses various chlorine or chlorine-containing substances for the oxidation and disinfection of the potable water source.
• The goal of disinfection of public water supplies is to eliminate the pathogens responsible for waterborne diseases.
• The transmission of diseases such as typhoid and paratyphoid fevers, cholera, salmonellosis, and shigellosis can be controlled with treatments that substantially reduce the total number of viable microorganisms in the water.
• Chlorine can be applied for the deactivation of most microorganisms, and it is relatively cheap.

Additional Information

• Halogen is the Six nonmetallic elements that constituted a group of 17 of the periodic table.
• The Halogen elements are fluorine (F), chlorine (Cl), Bromine (Br), Iodine (I), astatine (At), and Tennessine (Tn).

The correct answer is Shock waves created in the atmosphere when clouds of opposite charge meet.

Key Points

• Thunder is caused by the rapid expansion of the air surrounding the path of a lightning bolt.
• Thunder is caused by lightning, which is essentially a stream of electrons flowing between clouds or between clouds or between a cloud and the ground.
• The air surrounding the electron flow can be as hot as 50,000 degrees Fahrenheit, three times hotter than the surface of the Sun.
• Lightning can discharge between areas of a cloud without making contact with the ground.
• When it occurs between two different clouds, it is known as cloud-to-cloud (CC) or inter-cloud lightning.
• When it occurs between regions of different electric potential within a cloud, it is known as intra-cloud (IC) lightning.

Additional Information

• An earthquake is a sudden movement of the earth's crust.
• Earthquakes occur along fault lines, cracks in the Earth's crust where tectonic plates meet.
• They occur where plates are subducting, spreading, sliding or colliding.
• Lightning can occur between opposite charges within a thunderstorm cloud, or between opposite charges in the cloud and on the ground.

The correct answer is Squat low on the ground.

• When you are out in the open and there is a thunderstorm, you should Squat low on the ground.

Key Points

• During a thunderstorm, avoid open vehicles such as convertibles, motorcycles and golf carts.
• Be sure to avoid open structures such as porches, gazebos, baseball dugouts and sports arenas.
• And stay away from open spaces such as golf courses, parks, playgrounds, ponds, lakes, swimming pools and beaches.

Additional Information

• A thunderstorm, also known as a lightning storm or lightning storm, is a storm characterized by the presence of lightning and its acoustic effect on the Earth's atmosphere, known as thunder.
• Relatively weak thunderstorms are sometimes called thunderstorms.

The correct answer is Manometer.

Key Points

• The manometer is a pressure measuring device that is based on the principle of balancing the column of liquid (whose pressure is to be found) by the same or another column of liquid.
• The manometer is an instrument used for measuring pressure.
• The manometer measures pressure using a container with a "U"-shaped tube open at one or both ends.

Additional Information

• A lactometer is an instrument that is used to check the purity of milk by measuring its density.
• It can find out the content of water in the milk or test the richness of the milk. The lactometer works on the principle of gravity of milk.
• Barometer
• It is an instrument that measures atmospheric pressure.
• Hydrometer
• It is an instrument used for carrying out sedimentation analysis based on Stokes's law for particle size less than 75 μ.
• A hydrometer or lactometer is an instrument used for measuring density or relative density of liquids based on the concept of buoyancy. They are typically calibrated and graduated with one or more scales such as specific gravity.

The correct answer is Female Aedes mosquito.

Key Points

• Dengue viruses are spread to people through the bites of infected Aedes species mosquitoes.
• Its symptoms are nausea, vomiting, aches and pains, and rash. While vomiting blood, and bleeding from the nose or gums are symptoms of severe dengue.
• It can be prevented by cleanliness and preventing oneself mosquito bites.
• It can be cured by taking paracetamol and drinking fluids.
• Note: Mosquitoes also cause chikungunya, malaria, Zika virus, West Nile virus, etc.
• Thus, dengue is caused by Aedes mosquito.

Additional Information

• Malaria is transmitted to humans by female mosquitoes of the genus Anopheles.
• Female mosquitoes take blood meals for egg production, and these blood meals are the link between the human and the mosquito hosts in the parasite life cycle.

• 'स्कूल का वार्षिकोत्सव': प्रतिवेदन निम्न में से "संगठनात्मक प्रतिवेदन" अंतर्गत आयेगा।

Key Pointsसंगठनात्मक प्रतिवेदन- संगठनात्मक प्रतिवेदन में किसी सभा, बैठक, संस्था इत्यादि का विवरण दिया जाता है।

यहाँ प्रतिवेदन लिखने वाला अपने बारे में कुछ न बोल कर सारी बातें संगठन या संस्था के संबंध में ही लिखता है।

प्रतिवेदन: स्कूल का वार्षिकोत्सव-

• हमारा स्कूल वर्ष 1980 में स्थापित हुआ था।
• यहाँ शिक्षकों को समय पर वेतन मिलता है।
• सभी बड़ी निष्ठा से काम करते हैं।
• इस वर्ष प्रवेशक परीक्षा में चालीस छात्र प्रथम श्रेणी में ग्यारह द्वितीय श्रेणी में और तीन तृतीय श्रेणी में उत्तीर्ण हुए।

इस विवरण से यह स्पष्ट है कि यह स्कूल हर दिशा में विकास कर रहा है।

Additional Informationविवरणात्मक प्रतिवेदन- विवरणात्मक प्रतिवेदन में किसी यात्रा, मेले, सभा, रैली आदि का विवरण तैयार किया जाता है।

• प्रतिवेदन लिखने वाले को यहाँ बड़ी सच्चाई से विषय का उचित विवरण देना पड़ता है।

व्यक्तिगत प्रतिवेदन- इस प्रतिवेदन में व्यक्ति अपने जीवन से सम्बंधित या फिर विद्यार्थी जीवन पर प्रतिवेदन लिख सकता है।

• व्यक्तिगत प्रतिवेदन कभी-कभी डायरी का रूप भी ले लेता है अर्थात यह प्रतिवेदन का श्रेष्ठतम रूप नहीं है।

दिए गए विकल्पों में से विदेशी शब्द "फकीर"  है।

"फकीर" अरबी भाषा का शब्द है,अतः विदेशी शब्द है।

Key Points

अन्य विकल्प -

• महात्मा- तत्सम शब्द
• लकड़ी - तद्भव शब्द
• लोटा - देशज शब्द

Additional Information

दिए गए विकल्पों में से शुद्ध वाक्य - मैनेजर साहब ने आपको बुलाया है।

Key Points

• मैनेजर साहब आपको बुलाए हैं।- वाक्य में क्रिया अशुद्धि' और परसर्ग  "ने" की अशुद्धि है।
• आपको बुलाया है मैनेजर साहब।- वाक्य में पदक्रम सम्बंधी अशुद्धि' और परसर्ग  "ने "का प्रयोग होगा ।
• बुलाया है मैनेजर साहब ने आपको।- वाक्य में 'पदक्रम सम्बंधी अशुद्धि'।

Additional Information

क्रिया सम्बंधी अशुद्धियाँ- 

वाक्य में क्रिया का प्रयोग कर्ता के लिंग एवं वचन के अनुसार किया जाता है अन्यथा वह वाक्य अशुद्ध समझा जाता है।

उदाहरण -

• अशुद्ध रूप – राम और सीता वन को गई।
• शुद्ध रूप – राम और सीता वन को गए।

पदक्रम सम्बंधी अशुद्धियाँ - हिन्दी मे कर्ता, कर्म और इसके बाद क्रिया का प्रयोग होता है।

• गाय का गर्म दूध लाओ। वाक्य में पहले कर्ता (गाय) फिर कर्म (गर्म दूध) फिर क्रिया (लाओ) का प्रयोग हुआ है।

दिए गए विकल्पों में से "पौवार्त्य" पाश्चात्य का विपरीतार्थक शब्द है।

Key Pointsअन्य विकल्प -

• प्रतीची विलोम शब्द - प्राची
• प्रत्यक्ष का विलोम शब्द - अप्रत्यक्ष, परोक्ष, गुप्त

Additional Informationविपरीतार्थक शब्द -

• जो शब्द किसी दूसरे शब्द का उल्टा अर्थ बताते हैं, उन्हें विलोम शब्द या विपरीतार्थक शब्द या विरुद्धार्थी शब्द कहते है।
• जैसे- हार- जीत, आय- व्यय, आजादी- गुलामी, नवीन- प्राचीन आदि।

दिए गए विकल्पों में से "किं" 'किंकिणी' में उपसर्ग है।

• किं + किणी  ( किं" उपसर्ग व "किणी" शब्द है।)

Key Pointsउपसर्ग-

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।

• अ + सुंदर = असुंदर (मूल शब्द का अर्थ बदल दिया)
• अति + सुंदर = अतिसुंदर (मूल शब्द के अर्थ में विशेषता ला दी)
• आ + हार = आहार (नया शब्द बना दिया)

Additional Informationउपसर्ग  के  प्रकार-

दिए गए विकल्पों में से जाह्नवी, देवनदी और भागीरथी "गंगा" नदी के पर्यायवाची हैं।

गंगा के अन्य पर्यायवाची शब्द - मन्दाकिनी,सुरसरिता, विष्णुपदी, विश्नुपगा, देवपगा, ध्रुवनंदा, सुरसरि, अमरतरंगिनी,  त्रिपथगा।

Key Pointsअन्य विकल्प -

यमुना के पर्यायवाची शब्द -  कालिन्दी, सूर्यसुता, रवितनया, तरणि -तनूजा, तरणिजा, अर्कजा, भानुजा।

• सतलुज नदी - सतलज नदी,शतद्रु
• कावेरी नदी - दक्षिण की गंगा

Additional Information

पर्यायवाची शब्द -

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

कुछ पर्यायवाची शब्द -

• अंबर - आकाश, आसमान, गगन, फलक, नभ।
• आदर्श- प्रतिमान, मानक, प्रतिरूप, नमूना ।
• इज्जत- मान, प्रतिष्ठा, आदर, आबरू।
• उषाकाल- अरुणोदय, प्रातः, प्रभात।
• औषधि- दवा, दवाई, भेषज।
• कपूर- घनसार, हिमवालुका।
• किनारा- तट, कूल, तीर, कगार, पुलिन।
• कनक- कंचन, सुवर्ण, हिरण्य, हेम, हाटक, सोना, स्वर्ण।
• खेल- क्रीड़ा, केलि, तमाशा, करतब।
• गन्ना- ईक्षु, ऊख, ईख, पौंड़ा।
• घड़ा- घट, कलश, कुंभ, घटक, कुट।

निम्न वाक्यों में से संयुक्त वाक्य "उसने गीत गाया और सो गया"  है।

• इस वाक्य में दो सरल वाक्यों को जोड़ने वाला संयोजक ‘और’ है।
• जिसके द्वारा दो सरल वाक्यों को मिलाकर संयुक्त वाक्य बनाया गया।

Key Pointsसंयुक्त वाक्य- जिन वाक्यों में दो या दो से अधिक सरल वाक्य योजकों,

• (और, एवं, तथा, या, अथवा, इसलिए, अतः, फिर भी, तो, नहीं तो, किन्तु, परन्तु, लेकिन, पर आदि)
• से जुड़े हों, उन्हें संयुक्त वाक्य कहते है।

Additional Information

• वह खाना खाकर सो गया -  ये वाक्य एक सरल वाक्य है।

सरल वाक्य -जिन वाक्यों में केवल एक ही उद्देश्य और एक ही विधेय होता है, उन्हें सरल वाक्य कहते हैं।

• रेखा जिस घर में रहती है बहुत गन्दा है - मिश्रित वाक्य है।
• रमा चाहती है कि वह नौकरी करे - मिश्रित वाक्य है।

मिश्रित वाक्य- जिन वाक्यों में एक प्रधान (मुख्य) उपवाक्य हो और अन्य आश्रित (गौण) उपवाक्य हों,

• तथा जो आपस में कि, जो, क्योंकि, जितना, उतना, जैसा, वैसा, जब, तब, जहाँ, वहाँ, जिधर,
• उधर, अगर/यदि, तो, यद्यपि, तथापि, आदि से मिश्रित (मिले-जुले) हों उन्हें मिश्रित वाक्य कहते हैं।

दिए गए विकल्पों में से शुद्ध वाक्य है -मैं खाना खाकर ही सोऊँगा।

Key Points

• मैं खाना खाकर के ही सोऊँगा।-  कारक परसर्ग सम्बन्धी अशुद्धि
• मैं खाना खाकर ही सोएगा। - क्रिया सम्बन्धी अशुद्धि
• मैं खाना खाकर के ही सोएगा। - क्रिया सम्बन्धी अशुद्धि

Additional Informationकारक परसर्ग सम्बन्धी अशुद्धि-

कारकीय परसर्गों की अशुद्धियाँ शुद्ध रचना के लिए कारकीय परसर्गों का समुचित प्रयोग करना आवश्यक है।

सामान्य रूप से ‘ने’, ‘को’, ‘से’, के द्वारा’, ‘में’, ‘पर’, ‘का’, ‘की’, ‘के’, ‘के लिए’ आदि परसर्गों के गलत प्रयोग से अशुद्धियाँ उत्पन्न हो जाती है।

उदाहरण- 

• अशुद्ध-शीला ने पढ़ती है।
• शुद्ध - शीला पढ़ती है।

क्रिया सम्बंधी अशुद्धियाँ- 

वाक्य में क्रिया का प्रयोग कर्ता के लिंग एवं वचन के अनुसार किया जाता है अन्यथा वह वाक्य अशुद्ध समझा जाता है।

उदाहरण -

• अशुद्ध रूप – राम और सीता वन को गई।
• शुद्ध रूप – राम और सीता वन को गए।

सही उत्तर - विश्व+ऐक्य।

 Key Points

• विश्वैक्य' का संधि विच्छेद - "विश्व+ऐक्य"(अ + ऐ = ऐ)।
• विश्वैक्य शब्द में वृद्धि संधि है।

वृद्धि संधि-

• यदि ‘अ’ या ‘आ’ के बाद ए/ऐ रहे तो ‘ऐ’ और ओ/औ  रहे तो ‘औ’ बन जाता है।
• उदाहरण - मत+एकता-मतैकता, सदा+एव- सदैव, महा+ओज – महौज आदि।

Additional Information

• स्वर संधि पाँच प्रकार की होती है-
• स्वर संधि के प्रकार -
• 1. दीर्घ संधि -  जब एक ही स्वर के ह्रस्व और दीर्घ रूपों को संधि में मिलाया जाता हैं। तो दीर्घ स्वर बन जाता हैं। इस प्रकार की संधि को दीर्घ स्वर संधि कहा जाता हैं।
• उदाहरण - युग + अंतर = युगांतर।
• 2. गुण संधि -  गुण संधि में दो भिन्न स्वरों के मिलने से एक अन्य स्वर बनता हैं। जैसे अ और इ के मिलने से ए बनता हैं।
• उदाहरण - महा + उत्सव = महोत्सव।
• 3. वृद्धि संधि - जब संधि करते समय अ या आ के बाद ए या ऐ आए तो ‘ऐ’, अ या आ के बाद ओ या औ आए तो ‘औ’ हो जाता हैं।
• उदाहरण - पुत्र + एषणा = पुत्रैषणा।
• 4.यण संधि -   कुछ स्वरों को संधि करते समय आपस में मिलाने पर य और र में बदल जाते हैं। ऐसी संधि को यण संधि कहा जाता हैं।
• इस संधि में इ या ई के बाद कोई स्वर आए तो ‘य’ तथा उ या ऊ के बार कोई स्वर आए तो ‘व्’ में परिवर्तित हो जाता हैं।
• उदाहरण - अति + अधिक = अत्यधिक
• 5.अयादि संधि - संधि करते जब ए के बाद अन्य स्वर आए तो ‘अय’, ऐ के बाद कोई अन्य स्वर आए तो ‘आय’,
• ओ के बाद कोई अन्य स्वर आए तो ‘अव’, और औ के बाद कोई अन्य स्वर आए तो ‘आव’ हो जाता हैं। ऐसी संधि को अयादी संधि कहा जाता हैं।
• उदाहरण - श्रो + अन = श्रवण।

'गाल बजाना' मुहावरे का अर्थ है - "बकवास करना"

Key Points

• 'गाल बजाना' मुहावरे का अर्थ है - "बकवास करना", बहुत बढ़-चढ़्कर बातें करना या डींग मारना।

वाक्य प्रयोग - तुम्हारे बस का कुछ नहीं है, बस गाल बजाना जानते हो।

Additional Information

• खबर लेना - सजा देना

वाक्य प्रयोग - चोर को पकने के बाद थानेदार ने कहा की आज इसकी ऐसी खबर लेता हूँ की चोरी करना भूल जायेगा।

• हाथ चलाना - मारपीट करना

वाक्य प्रयोग- मेरी क्लास के दो बच्चों के बीच आज आपस में हाथ चल गये और दोनों को चोट लग गई।

• मन बहलाना  -  मनोरंजन करना

वाक्य प्रयोग- अब कौन सा नाटक दिखाकर इनका मन बहलाया जाए।

'स्वाधीन' शब्द का विलोम होगा "पराधीन"। 

स्वाधीन- स्वयं के अधीन।

पराधीन- दूसरो के अधीन।

Key Points विलोम अर्थ- विपरीत।

• परतंत्र

1. अर्थ- दूसरो के वश में।
2. विलोम-स्वतंत्र।

• अधीन

1. अर्थ- आश्रित।
2. विलोम- अनधीन।

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Additional Information कुछ अन्य महत्वपूर्ण विलोम शब्द-

1. सृष्टि- प्रलय
2. शोषक- पोषक
3. परोक्ष-प्रत्यक्ष
4. कृतज्ञ-कृतघ्न
5. हर्ष- विषाद
6. मानव- दानव

Confusion Points

• स्वाधीन का विपरीत आधीन नहीं होगा।
• क्योकि,स्वाधीन का अर्थ होता है "स्वयं के अधीन"।
• तथा अधीन का स्वयं का अर्थ होता है "आश्रित"।

'स्पृहा' का पर्यायवाची होगा- 'इच्छा'

Key Points

• पर्यायवाची शब्द को ही समानार्थक शब्द कहते है। अर्थात् सामान अर्थ वाले शब्द।
• 'स्पृहा' मतलब "किसी चीज़ की कामना करना"।
• 'स्पृहा'-इच्छा, कामना, अभिलाषा।

Important Points अन्य पर्यायवाची शब्द-

1. पारितोषिक- इनाम,पुरस्कार।
2. इठलाना- इतराना,ऐठना।
3. ईर्ष्या- जलन,कुढ़न।
4. असुर- दानव,दैत्य।
5. बादल- जलद, नीरद।
6. हनुमान- मारुति, पवनसुत।

Mistake Points

• 'स्पृहा' शब्द 'ईर्ष्या' के समान अर्थ देने जैसा प्रतीत होता है,जबकि दोनों के भिन्न अर्थ है।
• स्पृहा का अर्थ किसी वस्तु या किसी की कामना करना है।
• तथा, ईर्ष्या का अर्थ जलन,भावना करने जैसे भाव है।

मुहावरे का अर्थ होगा- "गुदडी का लाल"

अर्थात् "गरीब के घर में गुणवान व्यक्ति"

वाक्य प्रयोग- झोपड़ पट्टी में रहने वाले शिवम ने कक्षा 12 में अच्छे नंबर से पास होकर सिद्ध कर दिया की वह "गुदड़ी का लाल" है।

Key Pointsमुहावरा एक अरबी भाषा का शब्द है।

हिन्दी में इसे 'वाग्धारा' कहते है।

• "चींटी के पर लगना" मुहावरे का अर्थ- अपने संकट के नज़दीक होना।

          वाक्य प्रयोग- विभीषण ने रावण से प्रश्न किया कि, हे रावण तेरे "चींटी के सामान पर निकल आये" थे जो तूने सीता माता का हरण किया?

• "एक आँख से देखना"- सबको एक ही नज़र से देखना।

          वाक्य प्रयोग- एक अच्छा शासक वह हो���ा है जो अपने साम्राज्य में सभी को "एक आँख से देखता" है।

• "नाम कमाना"- शोहरत हासिल करना।

           वाक्य प्रयोग- कार्तिका ने कठिन परिश्रम करके मेडिकल की पढ़ाई पूरी की और डॉक्टर बनकर अपना "नाम कमाया"। 

Additional Information कुछ महत्वपूर्ण मुहावरे-

• 'अगर-मगर करना'- बहाने बनाना।
• वाक्य प्रयोग- छोटी को काम का बोलते ही वो "अगर-मगर" करने लगती है।
• 'रीढ़ टूट जाना'- निराश हो जाना।
• वाक्य प्रयोग- मोहन के रिजल्ट को देख कर उसके पापा की "रीढ़ टूट गयी"।

Confusion Points मुहावरा और लोकोक्ति- दोनों का प्रयोग सामान्य बातचीत के दौरान किया जाता है।

• मुहावरा- किसी सामान्य-सी बात को विशेष वाक्य के साथ कहने पर वह मुहावरा कहलाता है।
• उदाहरण- "कान काटना"।
• लोकोक्ति- लोक में प्रचलित उक्ति। किसी बात को कहावत के माध्यम से कहना लोकोक्ति कहलाती है।
• उदाहरण- "मन चंगा तो कठौती में गंगा"।

रेखांकित शब्द "सार्वनामिक विशेषण" है।

अतः यह पुस्तक अभी छपी है में रेखांकित शब्द -"यह" एक सार्वनामिक विशेषण है।

Key Points

• संज्ञा- "किसी वस्तु, नाम इत्यादि को हम संज्ञा कहते है"।

           जैसे- कविता, चाबी आदि। 

• सर्वनाम- "जो शब्द संज्ञा के जगह पर प्रयोग किये जाते है सर्वनाम कहलाते है"।

              जैसे- मैं, तुम, यह, वह आदि।

• विशेषण- "जो शब्द संज्ञा या सर्वनाम की विशेषता बताते है उन्हें विशेषण कहते है"।

                जैसे- मोती किताब, पतला लड़का आदि।

• सार्वनामिक विशेषण- "ऐसे सर्वनाम जो विशेषण के रूप में प्रयोग किये जाते है सार्वनामिक विशेषण कहलाते है"।
  

      जैसे- यह घर मेरा है।

Additional Information

1. विशेषण- "जो शब्द संज्ञा या सर्वनाम की विशेषता बताते है उन्हें विशेषण कहते है"।
2. विशेष्य- "जिसकी विशेषता बताई जाये उसे विशेष्य कहते है"।

• उदाहरण- पतली लड़की गिर गयी।
• यहाँ 'पतली' विशेषण है तथा 'लड़की' विशेष्य है।

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विशेषण- 4 प्रकार के होते है-

1. सार्वनामिक विशेषण।
2. गुणवाचक विशेषण।
3. संख्यावाचक विशेषण।
4. परिमाणबोधक विशेषण।​​

​

Mistake Points

• "यह पुस्तक अभी छपी है" इसमें 'यह' एक सर्वनाम है, परन्तु यहाँ पर 'सार्वनामिक विशेषण' होगा।
• क्योंकि, जब 'यह', 'वह', 'जो', 'सो' अकेले आते है तब 'सर्वनाम' होते है, और जब किसी संज्ञा के साथ आते है तो 'सार्वनामिक विशेषण' हो जाते है।
• उदाहरण- यह**(सर्वनाम)** पुस्तक**(संज्ञा)** अभी छपी है।

'तख्तनशीन' में प्रत्यय-"नशीन"।

1. तख्त+नशीन = तख्तनशीन।
2. वंद+न = वंदन।
3. कुल+ईन = कुलीन।

Key Pointsप्रत्यय= प्रति+अय 

अर्थात् शब्द के पीछे लगने वाले शब्दांश को प्रत्यय कहते है।

प्रत्यय का अपना अकेले कोई अर्थ नहीं होता,.न ही इनका स्वतंत्र तरीके से प्रयोग किया जाता है। 

प्रत्यय दो प्रकार के होते है-

       1. कृत प्रत्यय- धातु में लगते।

           उदाहरण- लेखक (अक प्रत्यय,लेख् धातु)

       2. तद्धित प्रत्यय- धातु को छोड़कर संज्ञा, सर्वनाम, विशेषण आदि में लगते।

           उदाहरण- सेठानी (आनी प्रत्यय)

Additional Information

• उपसर्ग- शब्द के प्रारम्भ में लगते।
• संख्या- 13

कुछ अन्य महत्वपूर्ण  उपसर्ग-

1. प्रख्यात- प्र
2. दुधारू- दु
3. निगोड़ा- नि
4. अनमोल- अन
5. परलोक- पर

कुछ अन्य महत्वपूर्ण प्रत्यय- 

1. ग्रामीण- ईन
2. भवदीय- ईय
3. खटोला- ओला
4. झटका- का
5. सुनहरा- हरा

Mistake Points

• हिन्दी में उपसर्ग-13
• संस्��ृत में उपसर्ग-22
• तख्तनशीन में "शीन" प्रत्यय नहीं होगा।

सही उत्तर: जलज, क्योंकि यह आकाश का पर्यायवाची नहीं है।

 Key Points

• गगन, नभ, अंतरिक्ष ; आकाश के पर्यायवाची हैं।
• जबकि जलज, कमल का पर्यायवाची है।

 Additional Information

• व्योम, आसमान, अम्बर, शून्य आदि आकाश के पर्यायवाची शब्द हैं।

 Mistake Points

• ऐसे शब्द जिनमें अज प्रत्यय लगा हो, उनका अर्थ होता है जन्मा।
• जैसे- जलज का अर्थ है जल में जन्मा, अर्थात कमल

सही उत्तर: सा

'मरासा' का संधि विच्छेद: मरा+सा= मरासा

 Additional Information

मूल शब्द के पीछे जुड़ने वाले शब्द प्रत्यय कहलाते है।

 Mistake Pointsयहां मूल शब्द 'मरा' और प्रत्यय 'सा' है।

सही उत्तर: वर्ण है ।

• भाषा की लघुत्तम इकाई जिसे और अधिक टुकड़ों में न बांटा जा सके वर्ण कहलाती है।
• जैसे- क्,ख्,ग् आदि।

 Key Points

• शब्द- दो या दो से अधिक वर्णों के अर्थपूर्ण मेल को शब्द कहते हैं।
• जैसे- आकाश, राम, सत्य आदि।
• वाक्य- दो या दो से अधिक शब्दों के सार्थक समूह को वाक्य कहते हैं।
• जैसे- राम विद्यालय जाता है।
• पद- जब जब कोई शब्द किसी वाक्य में प्रयोग होता है तो वह एक पद का निर्माण करता है। इसके 5 प्रकार हैं -
• संज्ञा, सर्वनाम, विशेषण, क्रिया, अव्यय

Mistake Points वाक्य में प्रयुक्त एक शब्द को पद कहा जाता है ओर उसके समूह को पूर्ण वाक्य।

सही उत्तर: स्पर्धा, जिसका अर्थ है किसी काम में दूसरों से बढ़ने की इच्छा।

Key Points

 

Additional Information वाक्यांश के लिए एक शब्द, व्याकरणिक दृष्टि से प्रयत्न लाघव का उदाहरण है।

 Mistake Pointsस्पर्धा के लिए आमतौर पर प्रतिस्पर्धा शब्द प्रयोग में लाया जाता है।

सही उत्तर: स्वर का उच्चारण स्वतंत्र रूप से किया जा सकता है।

बिना किसी वर्ण की सहायता के उच्चारित होने वाली ध्वनि, स्वर कहलाते हैं।

स्वर तीन प्रकार के होते हैं- ह्रस्व, दीर्घ, संयुक्त

 Key Pointsव्यंजन- वे वर्ण जिनका उच्चारण बिना स्वर की सहायता से नहीं किया जा सकता तथा प्रत्येक व्यंजन के अंत में 'अ' की ध्वनि छिपी रहती है, व्यंजन कहलाते हैं।

• जैसे- क‌=क्+अ

                   ख=ख्+अ

अयोगवाह- वे वर्ण जो न तो स्वर होते हैं और न व्यंजन किंतु स्वरों की सहायता से उपयोग में लाए जाते हैं, अयोगवाह कहलाते हैं। विसर्ग और अनुनासिक अयोगवाह हैं।

• जैसे- अंगद, दुःख।

Mistake Points अ,आ,इ,ई,उ,ऊ,ऋ,ए,ऐ,ओ,औ- स्वर हैं।

शब्‍द "पौराणिक" में 'पुराण' मूल शब्‍द और 'इक' प्रत्‍यय है। 

Key Points

• शब्‍द 'पौराणिक' इक प्रत्‍यय से मिलकर बना है।
• पौराणिक = पुराण + इक
• पौराणिक का अर्थ- पुराण संबंधी
• पुराण का अर्थ- पुराना, प्राचीन ​

Additional Information

'जो कठिनाई से मिले' - "दुर्लभ"

Key Points

• जो कठिनाई से मिलता हो वाक्‍यांश के लिए एक शब्‍द- 'दुर्लभ'
• दुर्लभ का विलोम शब्‍द- 'सुलभ'

अन्‍य विकल्‍प 

Additional Information 

'कितनी सुंदर तस्‍वीर है' यह वाक्‍य विस्‍मयवाचक वाक्‍य है। 

Key Points

• कितनी सुंदर तस्‍वीर है, इस वाक्‍य में तस्‍वीर की सुन्‍दरता का वर्णन किया गया है।
• कितनी विस्‍मयवाचक शब्‍द है।

अन्‍य विकल्‍प 

Additional Information

वाक्‍य- शब्‍दों के सार्थक व व्‍यवस्थित समूह को वाक्‍य कहते हैं। वाक्‍य किसी भी भाषा की मूलभूत इकाई है। 

अर्थ के आधार पर वाक्‍य के आठ भेद हैं- 

1. विधानवाचक वाक्‍य (विधि वाक्‍य)
2. निषेधवाचक वाक्‍य
3. प्रश्‍नवाचक वाक्‍य
4. इच्‍छार्थक वाक्‍य
5. सन्‍देह (सम्‍भावनार्थक वाक्‍य)
6. आज्ञार्थक वाक्‍य
7. शर्तसूचक वाक्‍य
8. विस्‍मयादिबोधक वाक्‍य

शुद्ध वाक्य- 'वह मेरी बात को हँसी में टाल गया'।

Key Points

• 'वह मेरी बात को हँसी में टाल गया' सही वाक्‍य है। अन्‍य वाक्‍य अशुद्ध हैं।

अन्‍य विकल्‍प 

Additional Information

वाक्‍य में अशुध्दियॉं:- 

• ​वाक्‍य सम्‍प्रेषण की सबसे महत्‍वपूर्ण और सार्थक इकाई है अत: वाक्‍यगत अशुद्धियों को शुद्ध रूप में लिखना वाक्‍य को अधिक सरल बनाता है।
• वाक्‍य में पदक्रम, पुनरावृत्ति, वर्तनी, शब्‍द-अर्थ, संज्ञा, सर्वनाम, लिंग, वचन, क्रिया, विशेषण, क्रिया-विशेषण आदि अशुद्धियॉं हो सकती हैं।

रचना के आधार पर दिए गए वाक्‍य का सरल रूप- 'गांधी जी का नाम सबने सुना है।' 

Key Points

• गांधी जी का नाम सबने सुना है यह एक साधारण या सरल वाक्‍य है।
• गांधी जी का नाम किसने नहीं सुना है। यह प्रश्‍नवाचक वाक्‍य है।

अन्‍य विकल्‍प 

 Additional Information

• वाक्‍य- शब्‍दों के सार्थक व व्‍यवस्थित समूह को वाक्‍य कहते हैं। वाक्‍य किसी भी भाषा की मूलभूत इकाई है।
• वाक्‍य के दो अंग हैं- उद्देश्य और विधेय

 वाक्‍य के पॉंच भेद है- 

1. अर्थ के आधार पर
2. रचना के आधार पर
3. शैली के आधार पर
4. क्रिया के आधार पर
5. आकृति के आधार पर

Given :

The radius of the right circular cylinder = 6 cm

Formula used :

Volume of cylinder(V) = πr²h

Calculation :

So, Increased radius(R) = $\frac{100+50}{100}\times r$ = $\frac{3}{2}\times r$

Increased Volume(V₁)= $π\times(\dfrac{3}{2} r)^2\times h$

Now, taking ratio of V₁ : V = $\frac{π\times(\dfrac{3}{2} r)^2\times h}{{π\times r^2\times h}}$ = 9 : 4

Percentage increase in volume = $\frac{9-4}{4}\times 100$

⇒ $\frac{5}{4}\times 100$ = 125%

∴ The answer is 125% .

Given:

the quadratic polynomial x2 + 2x - 3

Formula used:

a³ + b³ = (a + b)(a² - ab + b²)

or a3 + b3 = (a + b)³ - 3ab(a + b)

Calculation:

f(x) = x2 + 2x - 3

α and β are zeroes of f(x)

$α+β$ = $-\frac{b}{a}$ = $-\frac{2}{1}$ = - 2

$αβ$ = $\frac{c}{a}$ = $-\frac{3}{1}$ = - 3

Now, $\frac{α^2}{β}+\frac{β^2}{α}=$ $\frac{(α^3 +β^3)}{αβ}$ 

⇒ $\frac{(α+β)^3 - 3αβ(α+β)}{αβ}$

⇒ $\frac{(-2)^3 - 3(-3)(-2)}{(-3)}$

⇒ $\frac{-8-18}{-3}$

⇒ $\frac{26}{3}$

∴ $\frac{α^2}{β}+\frac{β^2}{α}=$ $\frac{26}{3}$.

Given:

The mean of 16 numbers is 12.

Calculation:

Total of 16 numbers = 16 × 12 = 192

If each number is multiplied by 3

New total is = 192 × 3

∴ New Mean = $\frac{192\times 3}{16}$ = 36.

∴ The new mean is 36.

Given:

In trapezium PQRS, PQ || SR and SR ⊥ SP.

∠RQT = 70° and ∠PRQ = 25°

Calculation:

SR ⊥ SP,

∠RSP = 90°

Alternate angles,

∠RQT = 70° and ∠SRQ = 70°.

Given ∠PRQ = 25° hence, ∠SRP = 45°

We know that sum of angle of triangle $\triangle$SPR= 180°

⇒ ∠SRP + ∠RSP + ∠SPR = 180°

⇒ 45° + 90° + ∠SPR = 180°

⇒ ∠SPR = 180° - 45° - 90°

∴ ∠SPR = 45° 

Hence, the correct answer is option 1.

Given:

ST || QR and ST : QR = 3 : 8.

Formula Used:

Ratio of area of similar triangle = Ratio of square of corresponding sides

Calculation:

We know that,

$\frac{Area\ of\ \triangle PST}{Area\ of \ \triangle PQR} = \frac{(ST)^2}{(QR)^2}$

$\frac{Area\ of\ \triangle PST}{Area\ of\ \triangle PQR} = \frac{(3)^2}{(8)^2}$

$\frac{Area\ of\ \triangle PST}{Area\ of\ \triangle PQR} = \frac{9}{64}$

∴ $Area\ of\ \triangle PST$ = 9

Area of trapezium QRTS = $Area\ of\ \triangle PQR$ - $Area\ of\ \triangle PST$

Area of trapezium QRTS = 64 - 9 = 55.

∴ The ratio of the area of Δ PST and trapezium QRTS is 9:55.

Given:

∠1 = 100 + x and ∠2 = 3x.

Concept Used:

When two lines are intersected by a transversal, then the corresponding angles are equal

∴ ∠1 = ∠2 

Calculation:

We know that,

⇒ ∠1 = ∠2 

⇒ 100 + x = 3x

⇒ 2x = 100

⇒ x = 50.

Given:

Lower limit = 1399.5

The difference of the lower limit and the upper limit is 100

Formula Used:

Class mark = $\frac{1}{2}$ (lower limit + upper limit)

Calculation:

The difference of the lower limit and the upper limit is 100

⇒ Upper limit - lower limit = 100

⇒ Upper limit = 1399.5 + 100

⇒ Upper limit = 1499.5

We know that,

⇒ Class mark = $\frac{1}{2}$(lower limit + upper limit)

⇒ Class mark = $\frac{1}{2}$(1499.5 + 1399.5)

⇒ Class mark = $\frac{1}{2}$(2899)

∴ Class mark = 1449.5.

Given:

numbers 51, 59, 67, 75, .......

Formula Used:

n^th term of a arithmetic progression is 

t_n = a + (n-1)d

t_n = n^th term 

a = first number in the series

d = common difference 

Calculation:

numbers 51, 59, 67, 75, .......

here, a = 51, d = 59 - 51 = 8

∴ t_n = a + (n-1)d

tn = 51 + (n-1) 8

tn = 51 + 8n - 8

tn = 43 + 8n.

Hence 43 + 8n is the correct option.

Given:

(x + y) = 4 and xy = 6

Formulas Used:

x²-y² = (x-y)(x+y)

x³-y³ = (x-y)(x²+xy+y²)

Calculation:

⇒ $\frac{x^2-y^2}{x^3-y^3}$ = $\frac{ (x-y)(x+y)}{(x-y)(x^2+xy+y^2)}$

⇒ $\frac{x^2-y^2}{x^3-y^3}$ = $\frac{(x+y)}{x^2+xy+y^2}$

⇒ $\frac{x^2-y^2}{x^3-y^3}$ = $\frac{(x+y)}{(x+y)^2 - xy}$

⇒ $\frac{x^2-y^2}{x^3-y^3}$ = $\frac{4}{(4)^2-6}$

∴  $\frac{x^2-y^2}{x^3-y^3}$= $\frac{2}{5}$

Hence, the correct answer is option 1.

Shortcut Trick

A system of linear equations has a unique solution if the ratio of the coefficients of x is not equal to the ratio of the coefficients of y.

Comparing 4ax + 3by = c and 3cx + 2dy = a, we check the ratio: 4a/3c ≠ 3b/2d.

Cross-multiplying gives: 4a × 2d ≠ 3c × 3b ⇒ 8ad ≠ 9bc.

∴ The correct answer is 8ad ≠ 9bc.

Alternate Method

Given:

First Equation: 4ax + 3by = c

Second Equation: 3cx + 2dy = a

Formula Used:

For two equations a₁x + b₁y = c₁ and a₂x + b₂y = c₂, the condition for a unique solution is:

a₁/a₂ ≠ b₁/b₂

Calculations:

⇒ Comparing the given equations with standard form:

⇒ a₁ = 4a, b₁ = 3b

⇒ a₂ = 3c, b₂ = 2d

⇒ Applying the condition: (4a) / (3c) ≠ (3b) / (2d)

⇒ 4a × 2d ≠ 3b × 3c

⇒ 8ad ≠ 9bc

∴ The correct answer is 8ad ≠ 9bc.

Additional Information

Infinite Solutions Condition

A system has infinitely many solutions if the ratios of all coefficients are equal: a₁/a₂ = b₁/b₂ = c₁/c₂.

No Solution Condition

A system has no solution (inconsistent) if a₁/a₂ = b₁/b₂ ≠ c₁/c₂, representing parallel lines.

Consistency

A system is called consistent if it has at least one solution (either unique or infinite) and inconsistent if it has no solution.

Given:

Polynomial is x2 - 5

Calculation:

Let the zeros be α and β

x2 - 5 = 0

⇒ x2 = 5

⇒ x = $\pm \sqrt{5}$

 $α = \sqrt{5}$ and $β = -\sqrt{5}$

∴ Sum of zeroes $α+β = \sqrt{5}-\sqrt{5}$ = 0

Concept used:

Mixed recurring decimal means the decimal fractional values have some of the digits which are repeating and some of the digits are not repeating.

Calculation:

As per the options:

$0.\overline{123}$ = 0.123123123.... → Pure recurring decimal

$0.\overline{16}$ = 0.161616..... → Pure recurring decimal

$0.3\overline{8}$ = 0.388888..... → Mixed recurring decimal

$0.\overline{1}$ = 0.1111111..... → Pure recurring decimal

∴ $0.3\overline{8}$ has some of the digits are not repeating so this is considered as mixed recurring decimal.

Given :

To find probability of getting an award

Calculation :

Let the total number of chances be '4' 

Favourable chances of getting a car = 1

Favourable chances of getting an award = 3 x 1 = 3

Probability = $\dfrac{Number\ of\ favourable\ outcomes }{Total\ number\ of\ outcomes}$ = $\dfrac{3}{4}$ 

∴ The answer is $\frac{3}{4}$ .

Given:

$\frac{\sqrt {2}+1}{\sqrt {2}-1}=a+b\sqrt 2$

Calculation:

⇒ $\frac{\sqrt {2}+1}{\sqrt {2}-1}=a+b\sqrt 2$

⇒ $\frac{\sqrt{2}+1}{\sqrt{2}-1} \times \frac{\sqrt{2}+1}{\sqrt{2}+1}$ = $a + b\sqrt{2}$

⇒ $\frac{(\sqrt{2}+1)^2}{2-1}$ = $a + b\sqrt{2}$

⇒ $2+1+2\sqrt{2}$ = $a + b\sqrt{2}$

⇒ $3+2\sqrt{2}$ = $a + b\sqrt{2}$

∴ a = 3 and b= 2.

Hence, the correct answer is option 3.

Given:

total coins = 30 and worth Rs. 10

Calculation:

Let the number of 50 paise coins be 2x

Then the number of 25 paise coins = 4x

According to the question,

0.25 × 4x + 0.5 × 2x = Rs. 10

⇒ x + x = 10

⇒ 2x = 10 

⇒ x = 10/2 = 5

∴ The number of 25 paise coins = 4x = 4 × 5 = 20

Calculation:

When 4 dice are thrown simultaneously, then the total number of possible outcomes is 6 × 6 × 6 × 6.

The chances that all the dice show the same number

(1,1,1,1), (2,2,2,2), (3,3,3,3), (4,4,4,4), (5,5,5,5), (6,6,6,6)

The chances that all the dice show the same number = 6

∴ The probability is = $\frac{6}{6\times6\times6\times6}$ = $\frac{1}{216}$.

Given:

Mother is 15 years older than her son.

The product of their ages 4 years hence is 450.

Calculation:

Mother is 15 years older than her son m = 15 + s

The product of their ages 4 years hence is 450.

mother age m = 19 + s

son age = s + 4

According to the question,

⇒ (19  + s)(s + 4) = 450

⇒ (19s + 76 + s² + 4s) = 450

⇒ s² + 23s - 374 = 0

⇒ s² + 34s - 11s - 374

⇒ (s + 34)(s - 11) = 0

⇒ s = 11

∴ Mother is 15 years older than her son, m = 15 + s

⇒ 15 + 11 = 26 years.

Shortcut TrickBy hit and trial method

By considering option(2), we have

Let the present age of mother = 26 years.

Then son's age = 26 - 15 = 11 years

After 4 year hence,

Mother's age = 26 + 4 = 30 years

Son's age = 11 + 4 = 15 years

Their product = 30 × 15 = 450 years satisfied

Given :

The marks obtained by 100 students in a test.

Formula used:

Probability = $\dfrac{Number\ of\ favourable\ outcomes }{Total\ number\ of\ outcomes}$

Calculation:

Total number of students = 100

Probability = $\dfrac{Number\ of\ favourable\ outcomes }{Total\ number\ of\ outcomes}$ 

⇒ $\dfrac{30}{100} = \dfrac{3}{10}$ 

∴ The answer is $\frac{3}{10}$ .

Given :

In triangle ABC, AB ⊥ AC and in triangle DEF, DE ⊥ EF and also AB || EF and BD = CF

Solution :

In, triangle ABC, AB ⊥ AC, means ∠ A = 90º

Similarly, in case of triangle DEF, ∠ E = 90º

Now, BD = CF, 

Adding DC on both the side 

BD + DC = CF + DC 

BC  =  DF 

Now, for ∠ A = ∠ E and BC = DF

We can conclude that Triangle ABC is congruent to Triangle DEF

So, Ratio of AB : EF = 1 : 1

∴ The answer is 1 : 1 .

Formula Used:

(x+y)(x-y) = (x² - y²)

Calculation:

⇒ (2 + x)(2 - x)(4 + x2)(16 + x4) + (x8 - 256) 

⇒ [(2)² - (x)²](4 + x2)(16 + x4) + (x8 - 256) 

⇒ (4 - x²)(4 + x2)(16 + x4) + (x8 - 256) 

⇒ (16 - x4)(16 + x4) + (x8 - 256) 

⇒ (256 - x⁸) + (x8 - 256)  = 0

Given :

$\cot \theta = \frac{x}{y}$

Calculation:

$\dfrac{x \sin \theta + y \cos \theta}{x \cos \theta + y \sin \theta}$

⇒ $\dfrac{sin\theta (x + y \cot \theta)}{sin\theta (x \cot \theta + y)}$

⇒ $\dfrac{(x + y \cot \theta)}{(x \cot \theta + y)}$ 

⇒ $\dfrac{(x + y \times{\dfrac{x}{y}})}{(x \times{\dfrac{x}{y}} + y)}$ 

⇒ $\dfrac{2x}{({\dfrac{x^2+y^2}{y}})}$ = $\dfrac{2xy}{x^2+y^2}$

∴ $\dfrac{x \sin \theta + y \cos \theta}{x \cos \theta + y \sin \theta}$ = $\dfrac{2xy}{x^2+y^2}$

Given:

h = height of cone 

r = radius of cone

Height of the cone is thrice the radius of the cone

h = 3r

Formula Used:

Slant height of cone l = $\sqrt{r^2+h^2}$

Calculation:

l = $\sqrt{r^2+h^2}$

l = $\sqrt{r^2+(3r)^2}$

l = $\sqrt{r^2+9r^2}$

l = $\sqrt{10}r$.

Given :

ABCD is a parallelogram, E is the midpoint of DC and F is the midpoint of BC, and AC = 12 cm

Calculation :

As E and F are points of side DC and BC respectively

So, CG = $\dfrac{1}{4}\times AC = \dfrac{1}{4}\times 12 = 3\ cm$

∴ The answer is 3 cm.

Given:

side of cube = 4 cm

Need to build a cube of side 12 cm using cube of 4cm. 

Calculation:

Volume occupied by one cube of side 4 cm = 4×4×4 = 64 cm³

Volume of cube side 12cm = = 12×12×12 = 1728 cm³

∴ No. of cubes of side 4cm which would fit in a cube of 12 cm= 1728/64 = 27 cubes.

Given :

Height of frustum part of cone = 6 cm

Larger radii(R) = 16 cm 

Smaller radii(r) = 4 cm 

Concept used :

Similarity of triangles, i.e Thales theorem.

Calculation :

Let the total height of cone be 'h' cm .

According to question,

$\dfrac{r}{R} =\dfrac{h-6}{h}$ or $\dfrac{4}{16} =\dfrac{h-6}{h}$ or h = 8 cm

∴ The answer is 8 cm .

Here, the erroneous part is 'in high pressure.'

Key Points 

• The error lies in the part "in high pressure" of the sentence.
• The meaning of the phrase "work under high pressure" is being made to feel forced to do something (as by arguments, threats, etc.).
• Example: The mayor has to work under high pressure.
• ​So, we have to replace "in" with "under" to make the sentence grammatically correct.
• Therefore, the correct answer is Option 2.
  

Correct sentence*: We had to work under high pressure to meet the deadline.*

Hinglish

• त्रुटि वाक्य के "in high pressure" भाग में है।
• वाक्यांश "work under high pressure" का अर्थ कुछ करने के लिए मजबूर महसूस करने के लिए किया जा रहा है (तर्क, धमकी, आदि के रूप में)
• Example: The mayor has to work under high pressure.
• इसलिए, हमें वाक्य को व्याकरणिक रूप से सही बनाने के लिए "in" को "under" से बदलना होगा।
• इसलिए, सही उत्तर विकल्प 2 है।

The correct answer is 'though.'

Key Points   

• Let us see the meanings of the given options:
• "Besides" can be used as a preposition meaning “except” or “in addition to.”
• It can also be used as an adverb meaning “as well” or “moreover.”
• Example: I’ve never loved anyone besides you!
• Indeed: "Indeed" means really or certainly, often used to emphasize something.
• Example: Indeed, it could be the worst environmental disaster in Europe this century.
• Though: "Though" means but.
• It is usually used at the end of a sentence and indicates a partial negation.
• Example: They're coming next week, I don't know which day though .
• But: “But” indicates a complete negation and is usually used after a comma, in the middle of a sentence.
• Example: I like him but I can't meet him.
• The given blank can have "but" or "though", but "though" is more accurate as it can be used at the end of a sentence, indicating a partial negation.
• So, the correct answer is Option 3.
  

Correct sentence: The colleagues don’t appear nice. I like the office, though.

The correct answer is 'have been.'

Key Points 

• In the given sentence, we can see that the subjects "my friend" and "I" are connected with the help of the conjunction "and."
• When the subject of the sentence is composed of two or more nouns or pronouns connected by "and", we use a plural verb.
• Example: The doctoral student and the committee members write every day.
• ​Out of all the options, the plural form of the verb is "have been."
• Therefore, the correct answer is Option 3.
  

Correct sentence: My friend and I have been invited to the party.

Here, the erroneous part is 'thousands of dollar​.'

Key Points 

• The error lies in the part "thousands of dollar" of the sentence.
• It should be written either "thousand dollar" or "thousands of dollars" in the given sentence.
• "Thousands" means many thousands not just one thousand.
• Example: Thousands of people attended the function.
• "Thousand" stands for one thousand.
• "Of" does not follow thousand.
• Example: Thousand people attended the function. (It means one thousand people attended the function)
• In the given sentence, we are talking about "dollar" which means "one dollar".
• So either we must use "thousand dollar" or "thousands of dollars" in the given sentence.
• Hence, the correct answer is Option 2.

Therefore, the correct sentence is either "The accountant stole thousand dollar by juggling the company's books." OR "The accountant stole thousands of dollars by juggling the company's books."

The correct answer is "to, in, at."

Key Points 

• Let us see the meanings of the given prepositions​:
• At: We use "at" when we refer to an address.
• Example: Education starts at home.
• Into: We use "into" to talk about the movement of something, usually with a verb that expresses movement (e.g. go, come, straight).
• It shows where something is or was going.
• Example: Helen came into the room.
• "On" is used to show that something is in a position above something else and touching it, or that something is moving into such a position.
• Example: Look at all the books on your desk!
• In: We use "in" when something is located inside of a defined space. ​
• Example: I’m in the building now.
• Through: When we talk about movement from one side to another but ‘in something’, such as long grass or a forest, we use "through" instead of across.
• Example: I love walking through the forest.
• Of: We use "of" when we want to show that people or things relate to other things or people.​
• Example: Tiffany stared at the floor of her room.
• For: We use "for" to talk about a purpose or a reason for something.
• Example: I bought that for you.
• ​​We also use the to-infinitive to express purpose.
• The word "combat" is a verb so we must use "to" in the first blank.
• The second blank talks about a closed, defined space, so the correct answer is "in" for it.
• The third blank refers to a position, so the correct answer is "at" for it.
• ​Therefore, the correct answer is Option 2.
  

​

Correct sentence: A good way to combat the annual floods in Bihar is to build houses at an elevation.

The correct answer is 'It was William James who said, “Might is right.'

Key Points  

• The given sentence is in the direct speech
• Punctuation is used in direct speech to separate spoken words, or dialogue, from the rest of a story.
• The words spoken by a character sit inside inverted comma ( ' ) or double inverted comma( " ).
• We must remember to open - and close - the speech marks at the start - and end - of the direct speech.
• The sentence "Might is right" is a direct speech, so it must be under the double inverted comma ( ").
• So, option 4 can be opted out.
• Words "William James" is a proper noun, so it must be in the capitals.
• So, option 3 can be opted out.
• We have to add a comma ( , ) after the reporting clause "It was William James who said."
• ​Therefore, the correct answer is Option 2.
  

​

Correct sentence: It was William James who said, “Might is right.”

The correct answer is 'tele.'

<br>

Key Points  

• According to the sentence, we are talking about "the idiot box" which is a television.
• The meaning of the prefix "tele" is distant : at a distance : over a distance.
• Example: Telegram, telegraph, telepathy
• ​The word television comes from Ancient Greek 'tele' which means 'far', and Latin 'vision' which means 'sight'.
• ​Thus, the correct answer is Option 1.
  

Correct sentence: ‘Because of the passive nature of the viewer, the televison is rightly called ‘the idiot box'.

The correct answer is 'haven't taken.'

<br>

Key Points   

• We use "for" when we measure the duration – when we say how long something lasts.
• Structure: For + a period of time
• To measure a period of time up to the present, we use the present perfect tense and not the present tense.
• Structure of present perfect tense: Subject + has/have + V3 + for + a period of time
• Example: I have lived here for ten years.
• ​The pronoun "I" always take plural verbs, so we must "have" in the given sentence.
• Also, the V3 form of the verb "take" is "taken."
• ​Thus, the correct answer is Option 2.
  

Correct sentence: I haven't taken an exam for two years.

The correct answer is 'I asked if the children could get tasty meals at school.'

Key Points 

• The given interrogative sentence is in the direct speech.
• The rules of Direct and Indirect speech for interrogative sentence conversions.
• Inverted commas are removed in indirect speech.
• The reporting verb said/said to is changed to "asked, demanded, ordered, enquired" as per the nature of the sentence.
• Imperative sentences do not normally have an expressed subject.
• This is because the subject ‘you’ is usually understood.
• Therefore, we need to add a subject "I" in the indirect speech in this context.
• The first person in the reported speech changes according to the subject of reporting speech.
• In Reported Speech change of the second person depends on the object of reporting speech.
• The third person remains unchanged.
• To make the indirect speech for questions that can be answered in YES/NO, the word "if" or "whether" is used before the reported speech within the sentence.
• "Can" changes to "could."
• Structure: 
• (Can + Subject+ V1 + Object?) (Direct Speech)
• (If + Subject + could + V1 + Object ) (Indirect Speech)
• Example:  
• He said to me "Can you help me?"
• He asked me if I could help him.
• ​Therefore, the correct answer is Option 4.
  

Correct sentence: I asked if the children could get tasty meals at school.

The correct answer is 'The police officer asked what country I came from.'

Key Points 

• The rules for changing Direct Speech to Indirect Speech:
• The given sentence is in Simple Present Tense.
• Simple Present Tense 'come' changes to Simple Past Tense 'came'.
• Remove the commas and inverted commas.
• The reporting verb said/said to is changed in asked, demanded, ordered, enquired as per the nature of the sentence.
• Remove the question mark in the sentence of Indirect speech.
• The question is changed to assertive form and is simply placed after the reporting verb.
• Example: 
• John said to me, "What do you want?" (Direct speech)
• John asked me what I wanted. (Indirect speech)
• Therefore, the correct answer is Option 2.
  

​

Correct sentence: The police officer asked what country I came from.

The correct answer is 'Finally, the files were found under the filing cabinet by the clerk.​'

Key Points 

• The given sentence is in Active Voice.
• As per the given question we have to change it into Passive Voice.
• The structure of the given sentence is as follows:
• Subject + V2 + Object. (Active Voice)
• Subject (objective case)+ was/were + V3 + Object (subjective case). (Passive Voice)
• Example:
• Their cousin showed them some rare photographs. (Active Voice)
• They were shown some rare photographs by their cousin. (Passive Voice)
• The subject of the given sentence is 'The clerk'.​​
• The object of the given sentence is 'the files'.
• The subject will be put in place of the object and the object will be put in place of the subject.
• And 'found' will be changed into 'were found'.
• "The files" is a plural noun so we must "were" with it.
• Therefore, as per the points mentioned above, we find that the correct answer is Option 2.
  

​

Correct sentence: Finally, the files were found under the filing cabinet by the clerk.

The correct answer is 'Could you please telephone me about this next month?'

<br>

Key Points 

• Whenever we transform any sentence, we should not change its tense and meaning.
• The given interrogative sentence has interrogative sense in the part "you could", so we must frame question with the help of that part only.
• The option 1 is a question tag, so it is incorrect.
• The option 2 is a declarative statement, so it is also incorrect.
• The option 3 is showing the use of the modal verb "will" which is absent in the given sentence.
• So, it is also incorrect.
• ​Therefore, the correct answer is Option 4.
  

​​Correct sentence: Could you please telephone me about this next month?