Solution (c)

Explanation: 

Pressure refers to the force applied by an object per unit area. So, pressure is inversely proportional to Area (area increases, pressure decreases and vice versa). Now if the pressure applied by an object is high, it would sink into a porous ground like a sand dune. So, horses, whose hooves are small in size – that is – have a smaller area, apply more pressure than camels, whose hooves are very broad (large area). This is the reason why horses are not even able to walk properly on the desert sand dunes, whereas camels can even run-on sand. Hence option c is correct.

Solution (a)

Explanation:

• It is true that the image of object from the inner side of spoon looks inverted if placed far off. Hence Statement I is correct. 

• The inner side of the spoon acts as a concave mirror. Concave mirrors form both erect and inverted images. When the object is far from the mirror it will form an inverted image of the object. If the object is moved closer to the concave mirror than it forms an erect image. Hence, statement -II is correct and is the correct explanation for statement -I.

Solution (b)

Explanation:

• The phenomenon of Superconductivity refers to a state of matter, wherein the electrical resistance drops to zero, and an electric current is able to flow through the material freely, without any resistance. Thus, leading to zero wastage and dissipation of energy as heat, thus giving 100% efficiency. Hence Statement 1 is correct.
• Generally, it is found only to be possible at very low temperatures, near the Absolute Zero (-273 degrees Celsius/ 0 Kelvin). This is because at this temperature, all activity of subatomic particles of a material nearly ceases. The positive ions form a lattice and do not collide with the electrons carrying the electric current, thus greatly reducing electric resistance. Hence Statement 2 is incorrect.
• The most practical application of Superconductors is to create huge and unusually strong magnetic fields produced through a flowing electric current (in devices called electromagnets). Since Superconductors are able to conduct an unusually large amount of electric current, with almost zero wastage, the resultant magnetic field created is also proportionately stronger than any magnetic field created by current flowing in any normal circumstance in normal materials. This magnetic field can be used in running maglev trains. Hence Statement 3 is correct.

Solution (a)

Explanation:

• Kinetic Energy is the energy possessed by a body by the virtue of being in motion. In accordance with the Law of Conservation of Energy, depending on the situation, the Kinetic energy gets transformed into multiple other forms of energies, when a moving object is suddenly stopped.  In case of the suddenly braked car, it is transformed into heat and sound energy. In case of a ball hit on the wall, it transforms into sound energy, elastic energy, heat energy, etc. In case of a ball thrown upwards, it transforms into potential energy at the top of the motion, etc. Hence option a is correct. 
• The First Law of Thermodynamics (also known as the Law of Conservation of Energy) states that energy can neither be created nor destroyed. It can only be transferred from one object to another or transformed from one form to another. So it is not possible for the Kinetic Energy to simply get destroyed and vanish when the object stops moving. Hence Option b is incorrect.
• As explained in the First Law of Thermodynamics, if an object becomes incapable of holding any energy, the energy simply transfers into another form. The object does not necessarily get destroyed. Also, when the object is stopped, its kinetic energy becomes zero. Hence Option c is incorrect.
•  In some cases, like a ball thrown upwards, the kinetic energy gets transformed into potential energy for the short moment that the ball reaches its maximum height in the air. But kinetic energy doesn’t always get transformed into potential energy only. It may transform into heat energy, or sound energy, etc. For example, when a moving vehicle is stopped suddenly by applying brakes, some of its kinetic energy gets transformed into heat energy due to friction. Hence Option d is incorrect.

Solution (b)

Explanation:

• The movement of a pendulum is an example of Periodic motion. In periodic motion, an object repeats its motion after some time. Hence Pair 1 is incorrectly matched.
• The movement of tip on the hands of a clock is an example of circular motion. If we mark a point anywhere on the hands of a clock, the distance of this point from the centre of the clock, will remain the same as they rotate. Hence Pair 2 is correctly matched.
• Movement of a bus on a straight road is an example of rectilinear motion. In Rectilinear motion, the objects move along a straight line. Hence Pair 3 is incorrectly matched.
• Revolution of earth around sun is an example of circular and periodic motion but not the example of rotational motion. Because in rotational motion, the objects spins on its axis. For example, rotation of earth on its axis. Hence Pair 4 is incorrectly matched.

Solution (a)

Explanation:

• The heating effect of electric current on the wire depends upon its material and also on length and thickness. For different requirements, the wires of different materials and different lengths and thicknesses are used. The wires used for making electric circuits do not normally become hot. On the other hand, the elements of some electric appliances become so hot that they are easily visible like in filament of bulb. Hence Statement 1 is correct.

Fuses make advantage of the property that if a large current passes through a wire, the wire may become so hot that it may even melt and break. These wires are used for making electric fuses. So, when the wire break, it breaks the circuit. Thus, fuses act as a safety device which prevents damages to electrical circuits and possible fires. Hence Statement 2 is incorrect.

Solution (c)

Explanation:

• Electric bells- The coil of wire wound around an iron piece acts as an electromagnet when the current flows through the coil. When the iron strip is in contact with the screw, the current flows through the coil which becomes an electromagnet. It, then, pulls the iron strip. In the process, the hammer at the end of the strip strikes the gong of the bell to produce a sound. Hence option 1 is correct. 
• Security cameras make use of electromagnetic waves not electromagnets. Hence option 2 is incorrect.
• MRI (Magnetic Resonance Imaging)- The Magnetic Resonance Imaging (MRI) scanner uses a powerful electromagnet cooled in liquid helium. The MRI scanner uses the strong magnetic field to create detailed internal images of the body. Hence option 3 is correct.
• Surgery- Surgeons sometimes use electromagnetic tools to remove metal fragments from patients. The magnets attract bits of metal that would otherwise be difficult to find or grasp. Hence option 4 is correct.

Solution (a)

Explanation:

• • Mirage is caused due to total Internal Reflection of light by the various layers of air. It is an optical illusion which is responsible for the appearance of the water layer at short distances in a desert or on the road. Mirage is an example of total internal reflection which occurs due to atmospheric refraction. Hence Pair 1 is correctly matched.
  • The sky is not blue because of refraction, it’s blue because of Rayleigh scattering. Advancement of sunrise and delay of sunset is due to refraction of light. Hence Pair 2 is incorrectly matched.

• A rainbow is formed due to a splitting of white light from the sun into seven colours by water droplets present in the atmosphere of the earth. As light enters the drop, then due to refraction, the colour components of the sunlight are dispersed. It gets bent by different amounts depending upon their wavelengths (we perceive the different wavelengths as different colors) forming the rainbow.  Although it looks like it is formed due to diffraction, but it is not the case. Diffraction, in general, is the bending of waves around a small aperture. It is a process by virtue of which a system of waves spreads out after passing through narrow gaps. Hence Pair 3 is incorrectly matched.

Solution (c)

Explanation:

• When a rocket is launched from the launch pad, it faces a downward pull due to its weight, this is because of the gravitational force of earth. Hence large amount of fuel is required to propel the rocket in the space. In the atmosphere, the constituents of atmosphere cause friction. The surface material of the rockets needs to be resistant to friction. Thus, gravitational force of the earth and frictional force of the atmosphere act on the rocket to oppose its motions immediately when it leaves the launch pad. Hence, only options 3 and 4 are correct. 

Solution (c)

Explanation:

• Frictional force acts on all moving objects, whether rolling or sliding. A ball rolling on the floor comes to halt after some time, it is because of the frictional force acting on the object. The force you need to apply to slide an object is to overcome the force of friction acting on the sliding object. But the force can be reduced by various methods such as aero foil shaping, or use of lubricants on surfaces. Hence Statement 1 is correct.
• Frictional force always acts in the direction opposite to the moving body. This in turn retards the motion. Frictional force in the direction of motion is not feasible. It is a reaction to the motion and takes place because of interlocking of surface profiles of two contact surfaces. Hence smoother the surface lesser the friction. Hence Statement 2 is correct.
• Between two contacting surfaces there will always be a force of friction due to molecular cohesion or adhesion. This can be explained as interlocking of surface irregularities, these irregularities can be minimized but not eliminated. Thus, Friction between two contacting surfaces cannot be reduced to zero. Friction can be reduced to near zero by lubrication and other methods but zero friction cannot be achieved between two contacting surfaces. Hence Statement 3 is incorrect.
• Sliding friction is normally greater than rolling friction. It also depends on the shape of the object, its weight and the nature of surface. Hence Statement 4 is correct.

Solution (a)

Explanation:

• Atmosphere is a mass of air and gases. It exerts a pressure on the earth due to its weight called as atmospheric pressure. If we consider atmosphere as a cylinder full of air standing on a unit area then the force exerted by the weight of this column is the atmospheric pressure. As we move upwards, the pressure goes on decreasing as the weight of air column goes on decreasing. The pressure inside our bodies is equal to the atmospheric pressure, otherwise our capillaries would have burst due to pressure difference. One reason why nose bleeds in the higher altitudes is because of higher blood pressure and lower atmospheric pressure at heights. Hence Both statement -I and statement -II are correct and statement -II is the correct explanation for statement -I.

Solution (b)

Explanation:

• The speed of sound in a vacuum is zero meters per second, as sound cannot travel in a vacuum. Sound needs a medium to travel. Sound waves cannot travel in vacuum so we cannot listen to sound in a vacuum. Hence its speed is zero and not the fastest. One of the reasons that we cannot listen to sound of meteors clashing in space is because of vacuum. We can feel the heat of sun but we cannot listen to the sound it creates because of vacuum between sun and the earth. Hence Statement 1 is incorrect.
• Sound travels faster in solids because they are densely packed than liquids, hence sound travels faster in glass than in water. Hence Statement 2 is correct.

The amplitude of a sound wave determines its loudness or volume. A larger amplitude means a louder sound, and a smaller amplitude means a softer sound. Hence Statement 3 is correct.

Solution (b)

Explanation:

• • When a piece of permanent magnet is beaten or is dropped on a hard floor many times, it loses complete or partial magnetism. Actually beating or hitting the magnet a number of times disturbs the alignment random pattern of atoms magnetic property of the substance is partially or completely lost. Hence Statement 1 is correct.
  • When a piece of permanent magnet is heated, alignment of the atoms gets disturbed due to thermal agitation of the atoms, Random pattern of atoms makes partial or complete loss of magnetism. Hence Statement 2 is correct.

• When a magnet is placed inside a coil carrying alternating current (A.C) (not direct current), it loses its magnetic property. The direction of flow of current in A.C. changes rapidly (50 times in a second). Therefore, direction of magnetic field in the coil also changes at same rate and alignment of the atoms of the magnet is lost. Hence Statement 3 is incorrect.

Solution (d)

Explanation:

•  The Kessler Syndrome is a theory proposed by NASA scientist Donald J. Kessler in 1978. It describes a self-sustaining cascading collision of space debris in Low Earth Orbit (LEO). It’s the idea that two colliding objects in space generate more debris that then collides with other objects, creating even more shrapnel and litter until the entirety of LEO is an impassable array of super swift stuff. At that point, any entering satellite would face unprecedented risks of headfirst bombardment. Hence Statement d is correct.

Solution (d)

Explanation:

• The moon’s south pole is especially interesting because the lunar surface area at the south pole of the Moon that remains in shadow is much larger than that of its north pole. The craters on the moon have been untouched by sunlight for billions of years offering an undisturbed record of the solar system’s origins. By studying the chemical composition of rocks and soil these areas could help in obtaining a glimpse of the Earth’s own geological infancy including the emergence of life.  Hence Statement 1 is correct.
•  The lunar south pole is important to get access to low-frequency deep space signals and to probe a launch site for further missions, farther into space, to explore various extra-terrestrial bodies. Hence, its elemental and positional advantages make it a suitable pit stop for future space exploration. Hence Statement 2 is correct.

The lunar south pole is of special interest to scientists because of the occurrence of water ice in permanently shadowed craters. The region is also rich in minerals. Water and minerals are resources for future explorers. Hence Statement 3 is correct.

Solution (a)

Explanation:

• • Geosynchronous Satellite Launch Vehicle (GSLV) is an expendable space launch vehicle designed, developed, and operated by the Indian Space Research Organisation (ISRO) to launch satellites and other space objects into Geosynchronous Transfer Orbits.  Polar Satellite Launch Vehicle (PSLV) is the third generation launch vehicle of India. It is the first Indian launch vehicle to be equipped with liquid stages.

• GSLV has the capability to put a heavier payload in the orbit than the Polar Satellite Launch Vehicle (PSLV). PSLV can carry satellites up to a total weight of 2000 kg into space and reach up to an altitude of 600-900 km. GSLV can carry weight up to 5,000 kg and reach up to 36,000 km. Hence Statement 1 is incorrect.

• PSLV is designed mainly to deliver earth observation or remote sensing satellites. Whereas, GSLV has been designed for launching communication satellites. GSLV delivers satellites into a higher elliptical orbit, Geosynchronous Transfer Orbit (GTO) and Geosynchronous Earth Orbit (GEO). Hence Statement 2 is correct.

PSLV is the third-generation launch vehicle of India with 4 stages while GSLV is a three-stage launcher with strap-on motors. Hence Statement 3 is incorrect.

Solution (c)

Explanation:

• Asteroids are referred to as rocky or metallic bodies and are primarily found in the asteroid belt, a region between Mars and Jupiter. On the other hand, comets are composed of ice, frozen gases, dust, and organic compounds, and they typically originate from the outer reaches of the solar system, such as the Kuiper Belt and the Oort Cloud. Hence Statements 1 and 3 are correct.

• Both asteroids and comets revolve around the Sun. The motion of celestial bodies in our solar system is governed by gravitational forces, causing them to orbit the Sun. Therefore, asteroids and comets share this fundamental characteristic of orbiting the Sun. Hence Statement 2 is incorrect.

Solution (c)

Explanation:

• Ultrasounds are high frequency waves. Ultrasounds are able to travel along well defined paths even in the presence of obstacles. Ultrasonic welding uses ultrasonic energy at high frequencies (20–40 kHz) to produce low amplitude (1–25 μm) mechanical vibrations. These vibrations generate heat at the joint interface of the parts being welded which resulted in melting of the thermoplastic materials and weld formation after cooling. Hence Statement 1 is correct.
• Ultrasonic waves are allowed to pass through the metal block and detectors are used to detect the transmitted waves. If there is even a small defect, the ultrasound gets reflected back indicating the presence of the flaw or defect.  Hence Statement 2 is correct.
• The process in which sound waves and echoes are used to determine objects in space is called echolocation. Bats emit sound waves that lie in the ultrasound frequency range from their mouth and nose. These sound waves hit the objects around them and reflect, producing echoes. The bats then detect these echoes; it helps them judge the object’s size, shape, and distance. These days ultrasonic echolocation is being widely used in traffic management applications and for sorting and counting objects in an assembly line.  Hence Statement 3 is correct.  

Calculations of change of radio waves from rotating satellites are used in the navigation systems of marine and can also be used in radar surveillance to determine the speed of automobiles. Hence Statement 4 is incorrect.

Solution (b)

Explanation:

• Defence Research and Development Organisation (DRDO) has recently carried out successful maiden flight test of Long Range Glide Bomb (LRGB) GAURAV from Su-30 MK-I platform of the Indian Air Force (IAF). 
• GAURAV is an air launched 1,000 kg class glide bomb capable of hitting targets at long distance. After being launched, the glide bomb steer towards the target using highly accurate hybrid navigation scheme with a combination of INS and GPS data. 

It is an Air to Surface LRGB with conventional warheads to destroy enemy air strips, bunkers, hard installations, buildings etc. It is designed to integrate with fighter aircrafts. It consists of an Inertial Navigation based guidance system with Digital Control. Hence option b is correct.

Solution (b)

Explanation:

• A Supersonic Combustion Ramjet (Scramjet) engine is an advanced air-breathing jet engine designed to operate at extremely high speeds. Scramjets do not have rotating compressors, instead they rely on the forward motion of the aircraft to compress incoming air.

• Scramjet engines use oxygen from the atmosphere for combustion of hydrogen fuel, which means they rely on atmospheric oxygen as the oxidizer. This distinguishes them from traditional rocket engines, which do not use oxygen from the atmosphere for combustion of fuels. Hence Statement 1 is incorrect.
• Compared to traditional rocket engines, Scramjets offer higher fuel efficiency due to their higher specific impulse (thrust per unit of propellant) at hypersonic speeds. Hence Statement 2 is correct.
• The Scramjet represents an advancement over the ramjet engine, demonstrating efficient performance at hypersonic speed and facilitating supersonic combustion. Hence Statement 3 is correct.

Solution (b)

Explanation:

Context: Union Home Minister and Minister of Cooperation, Shri Amit Shah, attended the 20th Raising Day ceremony of the National Disaster Response Force (NDRF) as the Chief Guest in Vijayawada, Andhra Pradesh. 

• The National Disaster Response Force is aimed at specialized response to natural and man-made disasters. Hence statement 1 is correct.
• It was established under section 44 of the Disaster Management Act of 2005.
• It is a multi-skilled and highly specialist force capable of dealing with all types of natural and man-made disasters like floods, cyclones, earthquakes, landslides, building collapse, trains and road accidents, etc.
• It responds to natural disasters under multi-lateral and bilateral agreements at the international level. Hence statement 2 is correct.
• The NDRF teams responded during a triple disaster (Earthquake, Tsunami, and Radiation Leakage) in Fukushima, Japan in 2011 and during Earthquake in Nepal in 2015.
• It functions under the purview of the Ministry of Home Affairs (MHA). Hence statement 3 is incorrect.
• It is headed by a Director General.

Source: https://pib.gov.in/PressReleseDetailm.aspx?PRID=2094319&reg=3&lang=1

Solution (b)

Explanation:

Context: A wolf has given birth to eight pups at the Bankapur Wolf Sanctuary in Koppal district recently.

• Indian Grey Wolf is a nocturnal animal. Hence statement 1 is correct.
• It is a subspecies of grey wolf that ranges from Southwest Asia to the Indian Subcontinent.
• It travels in smaller packs and is less vocal than other variants.
• It is protected under Schedule I of the Wildlife Protection Act of 1972. Hence statement 2 is correct.
• It inhabits areas dominated by scrub, grasslands, and semi-arid pastoral agroecosystems. 
• It has a wide distribution range that extends from the Indian subcontinent to Israel.
• Bankapur Wolf Sanctuary and Mahuadanr Wolf Sanctuary are the protected areas in India dedicated to it. Hence statement 3 is incorrect.

Source: https://www.thehindu.com/news/national/karnataka/endangered-indian-grey-wolf-gives-birth-to-eight-pups-in-karnatakas-first-wolf-sanctuary/article69115610.ece

Solution (c)

Explanation:

Context: On January 30, 1948, at exactly 5.17 pm, Nathuram Godse fired three shots at Mahatma Gandhi from his Beretta M1934. The Mahatma died on the spot.

Narayan Apte, Vishnu Karkare, and Madanlal Pahwa were all involved in the assassination attempt on Mahatma Gandhi. During the trial of Godse, he tried to take sole responsibility for the crime. But his arguments were rejected. A Bench of the Punjab High Court in Shimla in 1949 upheld the convictions and sentences of five people for the larger conspiracy: Godse, his younger brother Gopal, Narayan Apte, Vishnu Karkare, and Madanlal Pahwa. Hence option c is correct.

Source: https://indianexpress.com/article/explained/explained-history/godse-mahatma-gandhi-assassination-convict-apte-9808210/

Solution (c)

Explanation:

Context: India celebrated its 76th Republic Day on Sunday with a grand display of its military might that included elite marching contingents, missiles and indigenous weapon systems. 

• The parade’s theme of Republic Day 2025 was “Swarnim Bharat: Virasat aur Vikas.” Hence statement 1 is correct.
• A total of 31 tableaus, themed ‘Swarnim Bharat: Virasat aur Vikas’, rolled down the ceremonial boulevard on Kartavya Path. Among them, 16 were from states and Union Territories and another 15 were from Central ministries, departments, and organizations — all highlighting various government schemes and cultural heritage.
• For the first time, a Tri-services tableau was displayed with the theme ‘Shashakt aur Surakshit Bharat’ (strong and secure India). It showed a Joint Operations Room facilitating networking and communication among the Army, the Navy, and the Air Force. Hence statement 2 is correct.

Source: https://indianexpress.com/article/india/republic-day-2025-india-cultural-heritage-military-might-pm-modi-9800576/ 

 Solution (b)

Explanation:

Context: In its 100th launch, the Indian Space Research Organisation (ISRO) is geared to send off a 2,250-kg navigation satellite on board GSLV-F15 from Sriharikota on January 29 at 06.23 am, the space agency said.

The NVS-02 is the second of the five second-generation satellites developed by the space agency to replace the existing satellites in the country’s navigation constellation Indian Regional Navigation Satellite System. With the first launch of 2025, the Indian Space Research Organisation achieved the significant milestone of having carried out 100 launches. NVS-02 Mission is one of the five replacement satellites for the Indian Regional Navigation Satellite System, also referred to as NavIC (Navigation with Indian Constellation). It is one of the five replacement satellites for the Indian Regional Navigation Satellite System, also referred to as NavIC (Navigation with Indian Constellation). It has been enabled with a third frequency L1, which is mostly utilized by the US Global Positioning System (GPS). Hence option b is correct.

Source: https://indianexpress.com/article/india/100th-launch-isro-nvs-satellite-longer-lifespan-indigenous-atomic-clocks-9797713/

 Solution (c)

Explanation:

Context: The global economy is slowing down, making it harder for labour markets to recover fully since the outbreak of the COVID-19 pandemic, according to the International Labour Organization’s (ILO) report, World Employment, and Social Outlook: Trends 2025, released in Geneva.

Reports published by the International Labour Organization:

• World Employment and Social Outlook
• World Social Protection Report
• World of Work Report
• Global Wage Report

Hence option c is correct.

Note:

Ease of Living Index is published by the World Bank.

Source: https://www.thehindu.com/news/national/global-labour-market-recovery-slow-india-an-exception-ilo-report/article69105663.ece#:~:text

Solution (b)

Explanation:

Context: The Telangana government has welcomed the order of the Krishna Water Disputes Tribunal-II (KWDT-II), chaired by Justice Brijesh Kumar, to adjudicate the matter of water allocation between Telangana and Andhra Pradesh based on the new terms of reference (TOR) provided under Section 3 of the Interstate River Water Disputes Act (ISRWD), 1956.

• Krishna River rises in western Maharashtra in the Western Ghats range near Mahabaleshwar. Hence statement 1 is incorrect.
• Its basin extends over an area of about 258,948 sq. km, which is nearly 8 percent of the total geographical area of the country. 
• It passes through Maharashtra, Karnataka, Telangana, and Andhra Pradesh. Hence statement 2 is correct.
• It is bounded by the Balaghat range on the north, by the Eastern Ghats on the south and the east, and by the Western Ghats on the west.
• Its principal tributaries are the Ghatprabha, the Malprabha, the Tungabhadra, the Bhima, the Musi, and the Munneru. Hence statement 3 is correct.

Source: https://www.thehindu.com/news/national/telangana/telangana-welcomes-kwdt-ii-order-to-base-on-krishna-water-allocation-on-new-terms-of-reference/article69105850.ece

 Solution (d)

Explanation:

Context: Recently, a group of fishermen were said to be stranded on Kenya’s popular Lake Naivasha for a long and blamed the water hyacinth that has taken over large

parts of it.

Lake Naivasha is a shallow freshwater lake located in Kenya. It is fed by the perennial Malewa and Gilgil Rivers, which drain the Aberdare Mountains of central Kenya. It is designated as the Ramsar site. Hence option d is correct.

Source: https://www.thehindu.com/sci-tech/science/invasive-water-hyacinth-threatens-fishers-livelihoods-on-popular-kenyan-lake/article69115884.ece

Solution (d)

Explanation:

Context: Kerala’s martial art form Kalaripayattu has become a bone of contention ahead of the 38th edition of the National Games which is scheduled to commence from January 28 in Uttarakhand.

Hence option d is correct.

Source: https://indianexpress.com/article/india/38th-national-games-tussle-over-kalaripayattus-removal-from-competition-list-9786314/

Solution (c)

Explanation:

Context: Recently, the US President signed an executive order renaming Denali to Mount McKinley.

Mount McKinley is the highest peak in North America. It is located near the centre of the Alaska Range, with two summits rising above the Denali Fault, in south-central Alaska, U.S. Hence option c is correct.

Source: https://indianexpress.com/article/explained/explained-global/denali-mckinley-trump-renaming-9791597/ 

Solution (d) 

Explanation:

Assumption 1 is correct. The passage mentions, “Government investment must match up with the challenge of educating the future.” This implies the government needs to increase funding in the education sector to match with the challenges of the education sector. So, this assumption is correct. 

Assumption 2 is incorrect. The passage mentions „to dealing with more students‟ implies there is an increase in enrollment and that leads to more students. But the passage nowhere mentions the reason behind it. So, this assumption is incorrect. 

Assumption 3 is correct. The passage mentions, “From designing bridge courses that can help restore children‟s skills and confidence”. This implies a need for bridge courses to improve children‟s learning. 

Assumption 4 is correct. The passage mentions, “Educationists fear that the learning loss caused by the pandemic might be inter-generational, with grave consequences for the economy and society.” This implies that damage in the education sector can impact both society and the economy in future. So, the socio-economic development of the nation will be impacted with an impact on the education sector today. So, this assumption is correct. 

Solution (b) 

Explanation:

Option (a) is incorrect. The passage nowhere mentions family. It mentions that home is where we find peace and a connection between mind and soul. So, this is an incorrect option. 

Option (b) is correct. The passage mentions, “So, many of us are so lost in the material that we are unaware of the needs of our own mind and soul. We are so lost in the bodily and physical, that we could be living lavishly, eating opulently, travelling like kings, and dressing like fashionistas and yet have vacant, homeless eyes, broken hearts and restless minds.” This implies that we are running behind bodily and physical needs, and not focusing on what our mind and soul needs for our inner peace. So, this option best reflects the critical message of the passage. 

Option (c) is close but incorrect. The passage nowhere mentions how many of us are able to establish this connection. Also, the statement does not reflect the other main ideas of the passage, which option (b) does. So, this option is incorrect. 

Option (d) is incorrect. The first part of the statement is correct as the passage mentions that life is not all about physical and bodily materials. The second part of the statement is incorrect as the passage mentions, “We are so lost in the bodily and physical”. This implies that instead of taking care of bodily needs we must focus on our inner peace, i.e. connection of mind and soul. So, this option is incorrect.

Solution (a)

Explanation

In 52 cards, there are 26 black cards and 26 red cards.

Probability of drawing red card in first draw = 26/52 = 1/2

Second card is drawn without replacement. So, the total number of red cards will be 25 and total cards will be 51.

Probability of drawing red card in second draw = 25/51

Thus, the probability that both the cards are red = (1/2) × (25/51) = 25/102

Solution (c)

Explanation

Let average of 19 innings be X

Total of 19 innings = 19X

Total of 20 innings = 19X + 205

As given, (19X + 205)/20 = X + 7.5

or 19X + 205 = 20X + 150

or X = 55

Solution (b)

Explanation

Radius of ground = Side of equilateral triangle

Area of equilateral triangle = 100√3 m 2

Area of equilateral triangle = √3/4 × (Side) 2

⇒ 100√3 = √3/4 × (Side) 2

⇒ 400 = (Side) 2

⇒ Side = √(400)

⇒ Side = 20 m

So, the radius of the circular ground = 20 m

Area of the circular ground = π×20×20 = 400π sq. metre